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Forecasting &
Predictive Analytics
TM
with ForecastX
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Forecasting &
Predictive Analytics
with ForecastXTM
Seventh Edition
Barry Keating
J. Holton Wilson
University of Notre Dame
Central Michigan University
John Galt Solutions, Inc.
Chicago
Boston Burr Ridge, IL Dubuque, IA New York San Francisco St. Louis Bangkok
Bogotá Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan
Montreal New Delhi Santiago Seoul Singapore Sydney Taipei Toronto
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To: Maryann, John, Ingrid, Vincent,
Katy, Alice, Mike, and Casey Keating
To: Zhihong Ren
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Preface
The seventh edition of Forecasting and Predictive Analytics with ForecastX™
builds on the success of the first six editions. While a number of significant
changes have been made in this seventh edition, it remains a book about prediction methods for managers, forecasting practitioners, data scientists, and students
who will one day become business professionals and have a need to understand
practical issues related to prediction in all its forms. Our emphasis is on authentic
learning of the forecasting and analytics methods that practitioners have found
most useful. Forecasting and Predictive Analytics with ForecastX™ is written for
students and others who want to know how forecasting is really done.
Content Updates
Major overall updates for this edition include:
•
•
•
•
Four new chapters on predictive analytics
The addition of Learning Objectives to all chapters
Updated data throughout the book
Updated and clarified ForecastX™ software sections
Today, most business planning routinely begins with a sales forecast. Whether you
are an accountant, a marketer, a human resources manager, a data scientist, or a
financial analyst, you will have to predict something sooner or later. This book is designed to lead you through the most helpful techniques to use in any prediction effort.
The analytics materials included in the sixth edition have been expanded to
include four full chapters in the seventh edition; this is a recognition of the importance of these tools in today’s prediction efforts. The examples we offer are, for
the most part, based on actual historical data, much like that you may encounter
in your own forecasts. The techniques themselves are explained as procedures that
you may replicate with your own data.
Specific chapter updates include:
Chapter 1. Introduction to Business Forecasting and Predictive Analytics
• Added Stages in the development of business forecasting are added.
• Steps to obtain better forecasts are added.
• A discussion of survey results is added showing what functional areas in an
organization contribute to a forecast and which area owns the forecast.
Chapter 2. The Forecast Process, Data Considerations, and Model Selection
• New exercises and updated data in others are added.
• Discussion of trend, seasonal, and cyclical components of a time series, including new data, is added.
vi
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Preface vii
Chapter 3. Extrapolation 1. Moving Averages and Exponential Smoothing
• Sections on Simple, Holt’s and Winters’ exponential smoothing models are
completely rewritten to clarify how they work and how to interpret the results.
• The use of all methods for dealing with seasonal data is discussed, including
the deseasonalizing of data, making the forecast, then putting the seasonality
back into the forecast.
• “Event Modeling” section is expanded to include a complete example.
• New exercises and updated data in others are added.
Chapter 4. Extrapolation 2. Introduction to Forecasting with Regression
Trend Models
• A comparison of the look of regression results from Excel and from ForecastX™ is added to show that they are equivalent, even if the formatting is
different.
• An explanation of seasonal indices and how to get seasonal indices using
ForecastX™ is added.
• A complete explanation of calculating the mean absolute percent error (MAPE)
is added, including a table with an example.
• An example of cross sectional forecasting is added.
• The steps to use when evaluating a regression model are clarified.
Chapter 5. Explanatory Models 1. Forecasting with Multiple Regression
Causal Models
• The discussion of steps to use when evaluating regression models is expanded
and clarified.
• An example of accounting for a recession in a multiple regression model with
an introduction to business cycle information from FRED is added.
• Discussion of how missing variables may affect serial correlation is clarified,
with an example.
• Discussion of the use of a seasonal Durbin-Watson statistic DW4 versus DW1
is added.
• An appendix concerning forecast combinations (ensembles) with a full discussion of detecting bias is added.
Chapter 6. Explanatory Models 2. Time-Series Decomposition
• Discussion of ways to estimate cycle turning points using actual private housing starts data with detailed graphics is added.
Chapter 7. Explanatory Models 3. ARIMA (Box-Jenkins)−Type Forecasting
Models
• The ARIMA philosophy of modelling is introduced.
• An intuitive approach to explaining ARIMA is used to reduce complexity.
• The individual components of ARIMA (autoregressive models and moving
average models) are explained.
• Stationarity is explained and the handling of nonstationarity is demonstrated.
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viii Preface
•
•
•
Numerous examples are included.
The application of ARIMA to time-series data is detailed.
“Overfitting” is explained along with detection and correction.
Chapter 8. Predictive Analytics: Helping to Make Sense of Big Data
• Entirely new chapter.
• The field of predictive analytics as an extension of forecasting is introduced.
• The three primary tools of analytics are defined.
• The new vocabulary and terminology used in analytics are listed.
• The importance of correlation is stressed.
• The “steps” in any data mining/analytics process are described.
• The data used in analytics is differentiated from the data commonly used in
forecasting.
• The new diagnostic statistics used by data scientists are described.
Chapter 9. Classification Models: The Most Used Models in Analytics
•
•
•
•
•
•
•
Entirely new chapter.
The most used technique in analytics, classification algorithms, is introduced.
The use of the kNN algorithm is taught.
CART models (a second type of classification algorithm) is demonstrated.
A third classification algorithm is introduced: the Naive Bayes algorithm.
The final classification technique, Logit, is detailed.
Actual examples of each technique are covered in detail.
Chapter 10. Ensemble Models and Clustering
• Entirely new chapter.
• Ensemble models are introduced with the rationale for their use in analytics.
• Two important ensemble techniques are discussed and demonstrated: bagging
and boosting.
• A third, newer ensemble is detailed: random forests.
• Clustering is introduced as a completely different class of analytics technique.
• Each of the techniques in the chapter is demonstrated step-by-step with actual
examples.
Chapter 11. Text Mining
• Entirely new chapter.
• Text mining (and all its variants) is introduced first in a general manner.
• The concept of data reduction is demonstrated, and its importance is demonstrated in the context of text mining.
• The “bag of words” approach to text mining is used with examples and software.
• “Bag of words” analysis is detailed in an extended example involving newsgroups.
• The newer approach to text mining involves “natural language processing;”
this is shown with an extended example.
• Text mining and the more traditional data mining are combined through
example to demonstrate the power of using both together.
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Preface ix
Chapter 12. Forecast/Analytics Implementation
•
Graphics related to the forecasting process are added.
McGraw-Hill Connect® Learn Without Limits!
Connect® is a teaching and learning platform that is proven to deliver better results for students and instructors. Connect® empowers students by continually
adapting to deliver precisely what they need, when they need it, and how they
need it, so your class time is more engaging and effective.
New to the seventh edition, Connect® includes SmartBook®, instructor resources, and student resources. For access, visit connect.mheducation.com or
contact your McGraw-Hill sales representative.
Auto-Graded End-of-Chapter Questions
Connect® includes selected questions from the end of chapter in an auto-graded
format that instructors can assign as homework and practice for students. Filtering
and reporting capabilities for learning objective, topic, and level of difficulty are
also available.
SmartBook®
Proven to help students improve grades and study more efficiently, SmartBook®
contains the same content within the print book but actively tailors that content to
the needs of the individual. SmartBook®’s adaptive technology provides precise,
personalized instruction on what the student should do next, guiding the student
to master and remember key concepts, targeting gaps in knowledge and offering
customized feedback, and driving the student toward comprehension and retention of the subject matter. Available on desktops and tablets, SmartBook® puts
learning at the student’s fingertips—anywhere, anytime.
Instructor Resources
The Instructor’s Edition within Connect® is password-protected and a convenient place for instructors to access course supplements that include the complete
solutions to all problems and cases, PowerPoint slides that include both lecture
materials for nearly every chapter and nearly all the figures (including all the
spreadsheets) in the book, and the Test Bank, which now includes filters for topic,
learning objective, and level of difficulty for choosing questions and reporting on
them, and is available in three ways:
• As Word files, with both question-only and answer files.
• In TestGen, a desktop test generator and editing application for instructors to provide
printed tests that can incorporate both McGraw-Hill’s and instructors’ questions.
• As a Connect® assignment for online testing and automatic grading; can be
used for actual exams or assigned as quizzes or practice.
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x
Preface
Student Resources
As described above, SmartBook® provides a powerful tool to students for personalized instruction. Connect® also provides access to other course supplements
of interest to students. For the convenience of students, we also are providing the
website www.mhhe.com/Keating7e that will contain all of the Excel files used to
generate the data and the images in the chapters. This page will also include access information to the software referred to in this text.
Software Partnerships
ForecastXTM
As with the sixth edition, we again use the ForecastX™ software as the tool to implement the methods described in the text. This software is made available through an
agreement with John Galt Solutions, Inc. Every forecasting method discussed in the
text can be implemented with this software (the predictive analytics techniques, however, require separate software). Based on our own experiences and those of other
faculty members who have used the sixth edition, we know that students find the
ForecastX™ software easy to use, even without a manual or other written instructions. However, we have provided a brief introduction to the use of ForecastX™ at
the end of each relevant chapter. There is also an extensive User’s Guide within the
software itself for those who may want more extensive coverage, including information on advanced issues not covered in the text but included in the software.
John Galt Solutions provides us with the ForecastX™ software that does contain
proprietary algorithms, which in some situations do not match exactly with the results
one would get if the calculations were done by hand. Their proprietary methods, however, have proven successful in the marketplace as well as in forecast competitions.
We are confident that faculty and students will enjoy using this widely adopted, commercially successful software. However, the text also can be used without reliance on this particular package. All data files are provided in Excel format
so that they can be easily used with almost any forecasting or statistical software.
As with previous editions, nearly all data in the text is real, such as jewelry sales,
book store sales, and total houses sold. In addition, we have continued the use of
an ongoing case involving forecasting sales of The Gap, Inc., at the end of most
chapters to provide a consistent link. Additionally, a number of excellent sources
of data are referenced in the text. These are especially useful for student projects
and for additional exercises that instructors may wish to develop.
Analytic Solver® for Education
Analytic Solver® for Education (hereafter referred to as Analytic Solver) can be used
with Microsoft Excel for Windows (as an add-in), or “in the cloud” at AnalyticSolver.
com using any device (PC, Mac, tablet) with a web browser. It offers comprehensive
features for prescriptive analytics (optimization, simulation, decision analysis) and
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Preface xi
predictive analytics (forecasting, data mining, text mining); its optimization features
are upward compatible from the standard Solver in Excel. Analytic Solver includes:
• A more interactive user interface, with optimization, simulation, and data mining elements always visible alongside the main spreadsheet.
• A model analysis tool that reveals the characteristics of an optimization model
(e.g., whether it is linear or nonlinear, smooth or nonsmooth).
• Faster/more powerful ‘solver engines’ for optimization, plus the ability to
solve problems with uncertainty using simulation optimization, robust optimization, and stochastic programming methods.
• The ability to build and run sophisticated Monte Carlo simulation models for
risk analysis.
• An interactive simulation mode that allows simulation results to be shown
instantly whenever a change is made to a simulation model.
• Parameterized optimization, simulation, and ‘what-if’ analysis reports see the
effect of varying data in a model in a systematic way.
• Tools to build and solve decision trees within a spreadsheet.
• A full range of time series forecasting, data mining, and text mining algorithms, from logistic regression to neural networks.
• The ability to draw summarized results and statistically representative samples
from SQL databases and Apache Spark ‘Big Data’ clusters.
• Basic data visualization features, plus direct links to advanced data visualization tools such as Tableau and Power BI.
If interested in having students get individual licenses for class use, instructors
should send an email to support@solver.com to get their course code and receive
student pricing and access information. Note that this software is no longer free
with the purchase of this text, but low-cost student licenses are available.
Prevedere
Prevedere is an industry insights and predictive analytics company, helping business leaders make better decisions by providing a real-time view of their company’s future. Our external real-time insights engine constantly monitors the
world’s data, identifying future threats or opportunities to business performance.
Along with a team of industry experts, data scientist, and economists, Prevedere
helps business leaders make the right decisions in an ever-changing world. Instructors interested in getting complimentary access to Prevedere for themselves
and their students should go to www.prevedere.com or call 1-888-686-7746 and
ask for University Relations.
Acknowledgements
The authors would like to thank the students at the University of Notre Dame
and Central Michigan University for their help in working with materials included in this book during its development. Their comments were invaluable in preparing clear expositions and meaningful examples for this seventh
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xii
Preface
edition. Comments from students at other universities in the United States and
elsewhere have also been appreciated. It has been particularly gratifying to
hear from students who have found what they learned from a course using this
text to be useful in their professional careers. We are accessible; drop us an
email if you have a comment.
The final product owes a great debt to the inspiration and comments of our
colleagues, especially Professors Thomas Bundt of Hillsdale College and Tunga
Kiyak at Michigan State University. In addition, we would like to thank the staff
at John Galt Solutions for facilitating our use of the ForecastX™ software. We
also thank Professor Eamonn Keogh at the University of California, Riverside, for
sharing with you his illuminating examples of data mining techniques.
Adopters of the first six editions who have criticized, challenged, encouraged, and
complimented our efforts deserve our thanks. The authors are particularly grateful to
the following faculty and professionals who used earlier editions of the text and/or
have provided comments that have helped to improve this seventh edition.
Paul Altieri
Central Connecticut State University
Peter Bruce
Statistics.com
Margaret M. Capen
East Carolina University
Thomas P. Chen
St. John’s University
Ronald L. Coccari
Cleveland State University
Lewis Coopersmith
Rider University
Ali Dogramaci
Rutgers, the State University
of New Jersey
Farzad Farsio
Montana State University
Robert Fetter
Yale University
Benito Flores
Texas A & M University
Dan Fylstra
Frontline Systems
Kenneth Gaver
Montana State University
Rakesh Gupta
Adelphi University
Joseph Kelley
California State University,
Sacramento
Thomas Kelly
BMW of Canada
Eamonn Keogh
University of California, Riverside
Krishna Kool
University of Rio Grande
Paul Mackie
John Galt Solutions
John Mathews
University of Wisconsin−Madison
Joseph McCarthy
Bryant College
Elam McElroy
Marquette University
Rob Roy McGregor
University of North Carolina, Charlotte
Jared Myers
Prevedere
John C. Nash
University of Ottawa
Thomas Needham
US Bancorp
Anne Omrod
John Galt Solutions
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Preface xiii
Nitin Patel
Massachusetts Institute of Technology
Gerald Platt
San Francisco State University
Melissa Ramenofsky
University of Southern Alabama
Helmut Schneider
Louisiana State University
Stanley Schultz
Cleveland State University
Nancy Serafino
United Telephone
Galit Shmueli
University of Maryland
Donald N. Stengel
California State University, Fresno
Kwei Tang
Louisiana State University
Rich Wagner
Prevedere
Dick Withycomb
University of Montana
We are especially grateful to have worked with the following publishing professionals on our McGraw-Hill book team: Noelle Bathurst, Tobi Philips, Michele
Janicek, Erika Jordan, Daryl Horrocks, and Harper Christopher.
We hope that all of the above, as well as all new faculty, students, and business
professionals who use the text, will be pleased with the seventh edition.
Barry Keating
Barry.P.Keating.1@nd.edu
J. Holton Wilson
Holt.Wilson@cmich.edu
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Brief Contents
1
Introduction to Business Forecasting
and Predictive Analytics 1
7
Explanatory Models 3. ARIMA
(Box-Jenkins) Forecasting Models
2
The Forecast Process, Data
Considerations, and Model
Selection 47
8
Predictive Analytics: Helping to
Make Sense of Big Data 394
3
Extrapolation 1. Moving Averages
and Exponential Smoothing 92
9
Classification Models: The Most
Used Models in Analytics 430
10
Ensemble Models and
Clustering 477
11
Text Mining
12
Forecast/Analytics
Implementation 533
4
Extrapolation 2. Introduction to
Forecasting with Regression Trend
Models 159
5
Explanatory Models 1. Forecasting
with Multiple Regression Causal
Models 220
6
Explanatory Models 2. Time-Series
Decomposition 302
xiv
INDEX 557
506
336
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Contents
Chapter 1
Introduction to Business Forecasting
and Predictive Analytics 1
Introduction 1
Forecasting Is Essential for Success in
Business 2
Stages in the Development of Business
Forecasting 2
The Structure of This Text
3
Section 1: Time Series Models 4
Section 2: Demand Planning 5
Section 3: Analytics 5
Quantitative Forecasting Has Become Widely
Accepted 6
Forecasting in Business Today 7
Comments from the Field: Post Foods 9
Comments from the Field: Petsafe 9
Comments from the Field: Global Forecasting
Issues, Ocean Spray Cranberries 10
Forecasting in the Public and Not-for-Profit
Sectors 10
A Police Department 10
The Texas Legislative Board 11
The California Legislative Analysis Office 11
Forecasting and Supply Chain Management 12
Collaborative Forecasting 14
Computer Use and Quantitative Forecasting 15
Qualitative or Subjective Forecasting
Methods 16
Sales Force Composites 16
Surveys of Customers and the General Population 16
Jury of Executive Opinion 17
The Delphi Method 17
Some Advantages and Disadvantages
of Subjective Methods 18
New-Product Forecasting
18
Using Marketing Research to Aid New-Product
Forecasting 19
The Product Life Cycle Concept
Aids in New-Product Forecasting 20
Analog Forecasts 21
Test Marketing 21
Product Clinics 22
Type of Product Affects New-Product
Forecasting 22
The Bass Model for New-Product
Forecasting 22
Forecasting Sales for New Products
That Have Short Product Life Cycles 24
A Simple Naive Forecasting Model 27
Evaluating Forecasts 29
Using Multiple Forecasts 32
Sources of Data 32
Forecasting Total New Houses Sold 33
Steps to Better Time Series Forecasts 34
Integrative Case: Forecasting Sales of
the Gap 35
Background of the Gap and Gap Sales
An Introduction to ForecastX™
35
39
Forecasting with the ForecastX Wizard™
39
Using the Five Main Tabs on the Opening
ForecastX™ Screen 39
Suggested Readings and Web Sites 44
Exercises 44
Chapter 2
The Forecast Process, Data
Considerations, and Model Selection 47
Introduction 47
The Forecast Process 48
Trend, Seasonal, and Cyclical Data Patterns
Data Patterns and Model Selection 54
A Statistical Review 56
51
Descriptive Statistics 56
The Normal Distribution 60
The Student’s t-Distribution 65
From Sample to Population: Statistical
Inference 67
Hypothesis Testing 68
Correlation 73
xv
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xvi
Contents
Correlograms: Another Method of Data
Exploration 76
Total New Houses Sold: Exploratory Data
Analysis and Model Selection 79
Business Forecasting: A Process, Not an
Application 80
Integrative Case: The Gap
81
Comments from the Field: Anchorage Economic
Development Center Secures Time-Saving
Forecasting Accuracy 83
Using ForecastXTM to Find Autocorrelation
Functions 84
Suggested Readings 86
Exercises 87
Chapter 3
Extrapolation 1. Moving Averages and
Exponential Smoothing 92
Moving Averages 93
Simple Exponential Smoothing 100
Holt’s Exponential Smoothing 105
Winters’ Exponential Smoothing 111
The Seasonal Indices 114
Adaptive–Response-Rate Single Exponential
Smoothing 115
Using Single, Holt’s, or ADRES Smoothing
to Forecast a Seasonal Data Series 118
New-Product Forecasting (Growth Curve
Fitting) 121
Gompertz Curve 125
Logistics Curve 128
Bass Model 131
The Bass Model in Action 132
Event Modeling 135
Forecasting Jewelry Sales with Exponential
Smoothing 140
Summary 142
Integrative Case: The Gap 143
Using ForecastXTM to Make Exponential
Smoothing Forecasts 145
Suggested Readings 150
Exercises 150
Chapter 4
Extrapolation 2. Introduction to
Forecasting with Regression Trend
Models 159
The Bivariate Regression Model 160
Visualization of Data: An Important
Step in Regression Analysis 161
A Process for Regression Forecasting 163
Forecasting with a Simple Linear Trend 164
Using a Causal Regression Model to Forecast 169
A Jewelry Sales Forecast Based on Disposable
Personal Income 171
Statistical Evaluation of Regression Models 178
Basic Diagnostic Checks for Evaluating Regression
Results 178
Using the Standard Error of the Estimate
Serial Correlation 185
Heteroscedasticity 190
Cross-Sectional Forecasting 191
Forecasting Total Houses Sold with
Two Bivariate Regression Models 193
183
Comments from the Field 198
Integrative Case: The Gap 199
Using ForecastXTM to Make Regression
Forecasts 201
Further Comments on Using ForecastXTM
to Develop Regression Models 204
Suggested Readings 208
Exercises 208
Chapter 5
Explanatory Models 1. Forecasting with
Multiple Regression Causal Models 220
The Multiple-Regression Model 221
Initial Considerations When Selecting
Independent Variables 222
Developing Multiple-Regression
Models 223
A Three-Dimensional Scattergram
Statistical Evaluation of
Multiple-Regression Models
225
227
The First Four Quick Checks in Evaluating
Multiple-Regression Models 228
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Contents xvii
Finding the Long-Term Trend 311
Measuring the Cyclical Component 312
Multicollinearity 234
Serial Correlation: An Extended Look 236
Serial Correlation and the Omitted-Variable
Problem 237
Alternative-Variable Selection Criteria
240
Accounting for Seasonality in a MultipleRegression Model 242
The Time-Series Decomposition Forecast
Using a Dummy Variable to Account
for a Recession 248
Extensions of the Multiple-Regression
Model 251
Advice on Using Multiple Regression
in Forecasting 256
Independent Variable Selection 257
The Gap Example (With Leading
Indicators) 259
Integrative Case: The Gap 265
Using ForecastXTM to Make Multiple-Regression
Forecasts 269
Suggested Readings 272
Exercises 273
Appendix: Combining Forecasts
(Ensemble Models) 278
Introduction 278
Bias 279
What Kinds of Forecasts Can be Combined? 281
Considerations in Choosing the Weights for
Combined Forecasts 282
One Technique for Selecting Weights When
Combining Forecasts 283
An Application of the Regression Method for
Combining Forecasts 284
Summarizing the Steps for Combining Forecasts 287
Integrative Case: The Gap 289
Using ForecastXTM to Combine Forecasts
Suggested Readings 298
Exercises 300
Overview of Business Cycles 313
Business Cycle Indicators 314
The Cycle Factor for Private Housing
Starts 315
291
Chapter 6
Explanatory Models 2. Time-Series
Decomposition 302
The Basic Time-Series Decomposition Model 303
Deseasonalizing the Data and Finding
Seasonal Indices 306
318
Forecasting Winter Daily Natural Gas Demand
at Vermont Gas Systems 321
Integrative Case: The Gap 321
Using ForecastXTM to Make Time-Series
Decomposition Forecasts 326
Suggested Readings 329
Exercises 330
Chapter 7
Explanatory Models 3. ARIMA (BoxJenkins) Forecasting Models 336
Introduction 336
The Philosophy of Box-Jenkins 337
Moving-Average Models 339
Autoregressive Models 346
Mixed Autoregressive and Moving-Average
Models 348
Stationarity 351
The Box-Jenkins Identification
Process 355
ARIMA: A Set of Numerical Examples 360
Example 1
Example 2
Example 3
Example 4
360
360
363
366
Forecasting Seasonal Time Series
Total Houses Sold 372
372
ARIMA in Actual Use: Intelligent
Transportation Systems 375
Integrative Case: Forecasting Sales of
the Gap 376
Overfitting 379
Using ForecastXTM to Make ARIMA
(Box-Jenkins) Forecasts 380
Suggested Readings 382
Exercises 383
Appendix: Critical Values of Chi-Square
392
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xviii
Contents
Chapter 8
Predictive Analytics: Helping to Make
Sense of Big Data 394
Applying Analytics in Financial Institutions’
Fight Against Fraud 395
Introduction 399
Big Data 400
Analytics 401
Big Data and Its Characteristics 402
“Datafication” 405
Data Mining
406
Database Management 407
Data Mining Versus Database Management 407
Patterns in Data Mining 409
The Tools of Analytics 409
Statistical Forecasting and Data Mining 411
Terminology in Data Mining: Speak Like a Data
Miner 411
Correlation 412
Early Uses of Analytics 413
The “Steps” in a Data Mining Process
The Data Itself 416
415
Overfitting 417
Accuracy and Fit (Again) 418
Some Other Data Considerations 418
Sampling/Partitioning 420
Diagnostics (Evaluating Predictive Performance) 421
The Confusion Matrix and Misclassification Rate 421
The Lift Chart 423
The Receiver Operating Curve (ROC) and Area
Under the Curve (AUC) 426
What Is to Follow 427
Suggested Readings 427
Exercises 428
Chapter 9
Classification Models: The Most Used
Models in Analytics 430
Introduction 430
A Data Mining Classification Example:
k-Nearest-Neighbor (kNN) 434
A Business Data Mining Classification Example:
k-Nearest-Neighbor (kNN) 438
Classification Trees: A Second
Classification Technique 445
A Business Data Mining Example: Classification
Trees 449
A Business Data Mining Example: Regression
Trees 452
Naive Bayes: A Third Classification
Technique 454
Logit: A Fourth Classification Technique
Bank Distress 467
Summary 472
Suggested Readings 472
Exercises 473
Chapter 10
Ensemble Models and Clustering
463
477
Introduction 477
Ensembles 478
Error Due to Bias 478
Error Due to Variance 479
The Case for Boosting and Bagging 480
Bagging 481
Boosting 486
Random Forest® 487
A Bagging Example 487
A Boosting Example 490
A Random Forest (i.e., Tree) Example 491
Clustering 493
Usefulness of Clustering 495
How Clustering Works 496
A Clustering Example (k-Means Clustering) 497
A Hierarchical Clustering Example
(Agglomerative Bottom-Up Clustering) 500
Suggested Readings and Web Sites 503
Exercises 504
Chapter 11
Text Mining
506
Introduction 506
Why Turn Text into Numbers? 507
Where to Start—The “Bag of Words”
Analysis 507
Newsgroups 510
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Contents xix
In Pictures 514
Understanding SVD 515
Back to the Usenet Example 516
A Logistics Regression Classification
of the Usenet Postings 520
Natural Language Processing 521
Data Mining and Text Mining
Combined 524
Target Leakage 529
Conclusion 529
Suggested Readings 530
Exercises 531
Chapter 12
Forecast/Analytics Implementation
Forecasting Involves a Definite Flow
The Forecast Process 535
534
A Nine-Step Forecasting Process 537
Step 1. Specify Objectives 537
Step 2. Determine What to Forecast 538
Step 3. Identify Time Dimensions 538
Step 4. Data Considerations 538
Step 5. Model Selection 539
Step 6. Model Evaluation 539
Step 7. Forecast Preparation 540
Step 8. Forecast Presentation 540
Step 9. Tracking Results 541
Choosing a Forecasting Technique
Sales Force Composite (SFC) 543
542
533
Customer Surveys (CS) 543
Jury of Executive Opinion (JEO) 545
Delphi Method 545
Naive 545
Moving Averages 545
Simple Exponential Smoothing (SES) 545
Adaptive–Response-Rate Single Exponential
Smoothing (ADRES) 546
Holt’s Exponential Smoothing (HES) 546
Winters’ Exponential Smoothing (WES) 546
Regression-Based Trend Models 546
Regression-Based Trend Models with
Seasonality 546
Regression Models with Causality 547
Time-Series Decomposition (TSD) 547
ARIMA 547
Data Mining 548
Text Mining 548
Special Forecasting Considerations
548
Event Modeling 549
Combining Forecasts (Ensembles) 549
New-Product Forecasting (NPF) 550
Data Mining 550
Text Mining 551
Using ProcastTM in ForecastXTM to
Make Forecasts 552
Suggested Readings 555
Exercises 556
Index
557
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Chapter One
Introduction to Business
Forecasting and
Predictive Analytics
INTRODUCTION
If you can get the forecast right, you have the
potential to get everything else in the supply
chain right.
©VLADGRIN/Getty Images
I believe that forecasting or demand management may have the
potential to add more value to a business than any single activity
within the supply chain. I say this because if you can get the forecast
right, you have the potential to get everything else in the supply chain
right. But if you can’t get the forecast right, then everything else you
do essentially will be reactive, as opposed to proactive planning.
Al Enns, Director of Supply Chain Strategies, Motts North America, Stamford,
Connecticut1
LEARNING OBJECTIVES
After studying this chapter, you should be able to:
1.
2.
3.
4.
5.
6.
7.
8.
Explain the three stages of prediction evolution.
Explain how the organization of this text relates to the stages of prediction.
Distinguish between qualitative and quantitative forecasting.
Discuss four types of qualitative forecast methods.
Explain how forecasting relates to supply chain efficiency.
Discuss forecasting for new products.
Describe the naive forecasting method.
Explain what the MAPE is and how it is used in forecasting.
1
Sidney Hill, Jr., “A Whole New Outlook,” Manufacturing Systems 16, no. 9 (September 1998),
pp. 70–80.
1
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2
Chapter One
FORECASTING IS ESSENTIAL FOR SUCCESS IN BUSINESS
If you are reading this text as part of the course requirements for a college degree,
consider yourself fortunate. Many college graduates, even those with degrees in
business or economics, do not ever study forecasting, except as a sidelight in a
course that has other primary objectives. And yet, we know that forecasting is an
essential element of most business decisions.
The need for personnel with forecasting expertise is growing. For example, Levi Strauss only started its forecast department in 1995 and within four
years had a full-time forecasting staff of 30. Many people filling these positions have had little formal training in forecasting and are paying thousands
of dollars to attend educational programs. In annual surveys conducted by the
Institute of Business Forecasting, it has been found that there are substantial
increases in the staffing of forecasters in full-time positions within American
companies.
Stages in the Development of Business Forecasting
We might think of business forecasting as having developed in three stages. One
way of looking at this development is illustrated in Figure 1.1. Almost anything
FIGURE 1.1
Stages of light bulb
and forecasting
evolution.
The Three Stages of Light Bulb Evolution
40 Watts
Short Life
Hot
12 Watts
Longer Life
Hot
4 Watts
“Forever” Life
Cool
The Three Stages of Prediction Evolution
Stage I
Time Series
Models
Stage II
Demand Planning
Models
Stage III
Predictive Analytics
Models
Naïve Model
Moving Average Model
Simple Ex. Smoothing
Holt’s Ex. Smoothing
Holt Winter’s Model
Decomposition Model
ARIMA
Simple Regression
Multiple Regression
Nonlinear Regression
Event Model
Classification
Clustering/Segmentation
Association Rule Mining
Text Mining
Entity Analytics
Sentiment Analysis
Willingness to Purchase
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Introduction to Business Forecasting and Predictive Analytics 3
you think about has gone through some evolution. In lighting, we went from
primitive torches to kerosene to the first light bulbs developed by Edison in the
late 1870s. Incandescent light bulbs like the one at the left in the top panel of
Figure 1.1 became a worldwide standard for many years. Such light bulbs had a
relatively short life, were hot, and were not energy efficient. In the late 20th century, new, more energy-efficient, longer lasting, but still hot bulbs became common. Then, in the early 21st century, LED bulbs that were cool, energy efficient,
and long-lasting became the new norm.
Forecasting has gone through an evolution as well. Very early forecasting was
judgmental (or subjective). In your reading, you will see that judgmental forecasting has only brief coverage. A variety of quantitative tools have been shown to
outperform judgmental forecasting in most situations. However, judgments will
always be important in forecasting in selecting the right forecast tools, cleaning
data files, and adjusting final forecasts when human judgments are needed to adjust forecasts to account for factors not included in the data history. We will come
back to this later in the chapter.
Quantitative methods have allowed organizations to forecast more accurately.
The first stage of the development of quantitative forecasting relied on various
time series models. Time series methods that extrapolate historical data patterns
to make predictions about the future are widely used. The most common of these
are included in this text. Examples are shown in the left side of the lower panel
in Figure 1.1.
As research moved forward, forecasters began using causal models. These
models help an organization “shape” the future rather that accept an extrapolation
of historical patterns. By modelling causality, one can mold the future and better
plan for the demand that lies ahead. For example, one can develop causal regression models that include independent variable that can be adjusted to meet an
organizations needs. For example, promotions may be incorporated into a forecast
model. Forecast methods that allow for causality are included in the text, as shown
in the middle panel at the bottom of Figure 1.1.
The emergence of “Big Data” has brought with it an increased need for other
analytical tools. Today every organization is confronted with a deluge of data.
Organizations have more data than can easily be converted into actionable information using traditional statistical methods. New predictive analytical tools such
as data or text mining have emerged and are being used by organizations globally.
This has moved us into “Stage III” in the evolution of forecasting and predictive
analytics.
THE STRUCTURE OF THIS TEXT
We have divided the coverage of business forecasting and predictive analytics into
three major sections. These are designed to help you progress in your ability to
understand and use tools/methods in a logical way that will help you master the
material.
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4
Chapter One
Section 1: Time Series Models
We begin with this current chapter (“Introduction to Business Forecasting and
Predictive Analytics”) in which you will get acclimated to some forecasting terminology, see examples of forecasting success, understand the difference between
qualitative (subjective) and quantitative (objective) forecasts, understand judgmental, extrapolation and explanatory approaches to forecasting, as well as learn
some ways to deal with new product forecasting for which we have little or no
historical data. Throughout the remainder of the text, our primary focus will be
on quantitative forecast applications that have come to dominate business forecasting. You will also get your first introduction to the ForecastXTM software.
This software is quite sophisticated. It is software widely used in the business
world both in the United States and abroad. For predictive analytics, we will use
XLMiner; this software will allow you to estimate and experience the algorithms
used in analytics (including text mining).
In Chapter 2, “The Forecast and Prediction Process: Data Considerations, and
Model Selection,” you will learn about the three major components of time series
data, review some basic statistical concepts, start to think about when different
methods would be most likely to lead to good forecasts, continue with the Gap,
Inc. example that will be seen often through the text, and see some introductory
forecast examples. In addition, your ability to work with the ForecastXTM software will be expanded.
In Chapter 3, “Extrapolation 1: Moving Averages and Exponential Smoothing,” you really get into the meat of forecasting. This chapter focusses on some
of the forecasting methods that analyze historical data, then replicate the patterns observed in the past to make predictions (forecasts) for the future. You
will learn when moving averages can be used to forecast, how to use and interpret a variety of exponential smoothing models (including why they are called
exponential smoothing models), what is meant by an “Event” model and when/
how such a model can be used, look deeper into new product forecasting, and
see application of the material in Chapter 3 to the Gap example. Your ability to
use the ForecastXTM software will be extended to the appropriate methods from
the chapter.
In Chapter 4, “Extrapolation 2: Introduction to Forecasting with Regression
Trend Models,” takes the concepts from Chapter 3 in a slightly different direction.
In this chapter, you will learn how to apply regression analysis to make predictions about the future. Most students taking this class will have had some prior
exposure to regression analysis. However, we have structured the discussion so
that even with no prior background, one can learn the material. You will learn
to apply simple trends for prediction and to use a causal regression model. You
will also learn how you can modify a simple trend to take into account seasonal
variations in data. An important element of your learning in this chapter will be
how to evaluate whether a regression model is truly useful. Again you will see an
application to the Gap data and will learn how to implement regression forecasts
using ForecastXTM.
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Introduction to Business Forecasting and Predictive Analytics 5
Section 2: Demand Planning
Chapter 5, “Explanatory Models 1: Forecasting with Multiple Regression Causal
Models,” builds on the information you learned in Chapter 4 to explicitly take into
account causality. You will see that the evaluation of a causal regression model
necessitates one additional step to be sure causal variables do not have too much
overlap in the degree of their causality. Examples will help you master the concepts. One of the examples will be an extension of your ability to forecast the data
in the ongoing Gap example. At the end of the chapter, you will learn how to use
ForecastXTM to make a causal regression forecast in different ways. This depends
on whether you want to specify values of the causal variables in the forecast horizon, whether you want ForecastXTM to predict those for you, or whether you
prefer a mix of these approaches. There is an appendix to Chapter 4 that explains
how you can use regression to combine forecasts from different methods. You will
learn that often one can obtain forecast improvement by doing so.
In Chapter 6, “Explanatory Models 2: Times-Series Decomposition,” you will
learn about a classical approach to forecasting. This method explicitly breaks a
time series of data into individual components, with the most important in forecasting being trend, seasonality and cycle. The method forecasts each component
separately and then puts them together to form a forecast of the original series.
Time series decomposition (TSD) is an appealing method in part because the math
involved is quite simple. In fact, in days gone by, it was actually done by hand. One
very useful result from TSD is that it generates an explicit measure of the degree
of seasonality. Once more, TSD will be applied to forecasting the Gap data series.
Chapter 7, “Explanatory Models 3: ARIMA (Box-Jenkins) Forecasting Models” introduces you to a method of forecasting that often out performs others. However, performance comes with a price. That price in the case of ARIMA is overfitting. You will learn to use the power of ARIMA along with details of how to avoid
its most serious shortcoming. ARIMA forecasts are often used as baseline forecasts
allowing you to compare how other models perform compared to ARIMA.
Section 3: Analytics
In Chapter 8, “Predictive Analytics: Helping to Make Sense of Big Data Results,”
you will learn the language of predictive analytics along with the new diagnostic
measures that are commonly used by data scientists. This chapter is a departure
from previous ones since it introduces a new and different form of prediction. The
new algorithms will seem strange at first, but their predictive power is becoming
more evident each year.
In Chapter 9, “Classification Models: The Most Used Models in Analytics,”
you will learn that all predictive analytics algorithms can be divided into a few
categories; classification models are by far the most often used of these categories. As with all prediction, there is no one model that qualifies as the “best one.”
You will learn that each classification model has limitations as well as advantages
in actual practice. These supervised learning techniques are used in a wide variety
of business situations.
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6
Chapter One
Chapter 10, “Ensemble Models and Clustering,” continues the discussion in
Chapter 9 by adding new classification models to your toolkit. In that process,
you will improve your understanding of both the new diagnostic statistics and
some common methods for enhancing most of the classification algorithms. You
will also learn about two other classes of predictive analytics models: association
rules and cluster analysis. This will be your first look at “unsupervised learning.”
Chapter 11, “Text Mining: The Use of Unstructured Data,” may seem to you
to be the strangest of all the techniques you have learned. However, it is also the
one that allows you to analyze the largest trove of unstructured data available: text.
E-mails, blogs, social media, reviews, warranty claims, and internet documents
are mainly text. Up to this point in your study of prediction, that text has remained
outside of your ability to analyze and go from data to information. In this chapter,
textual data of all types becomes available as an input to many of the algorithms
you have already learned. Text mining is not so much a new algorithm as it is a
method for introducing text as an input to the models we already have.
In Chapter 12, “Forecast/Analytics Implementation,” you will learn some of
the practical aspects of applying the knowledge learned in the first 11 chapters. In
this chapter, you will learn a nine-step procedure that can be helpful in establishing a forecasting process that works in a wide variety of organizations.
QUANTITATIVE FORECASTING HAS BECOME WIDELY ACCEPTED
We think of forecasting as a set of tools that helps decision makers make the
best possible predictions about future events. In today’s rapidly changing business
world, such predictions can mean the difference between success and failure. It is
not reasonable to rely solely on intuition, or one’s “feel for the situation,” in projecting future sales, inventory needs, personnel requirements, and other important
economic or business variables.
Quantitative methods have been shown to be helpful in making better predictions
about the future course of events than judgments alone.2 Sophisticated computer
software packages make quantitative methods readily accessible to nearly everyone.
In a survey done a decade ago, it was found that about 80 percent of forecasting
was done with quantitative methods.3 The trend toward more and deeper analytics
makes this even more true today. Sophisticated software such as ForecastXTM make
it relatively easy to implement quantitative methods in a forecasting process. There
is a danger, however, in using forecasting software unless you are familiar with the
concepts upon which the programs are based. Thus, in this text, you will learn about
a variety of methods as well as how to implement them.
This text and its accompanying computer software (ForecastXTM) have been
carefully designed to provide you with an understanding of the conceptual basis
2
J. Holton Wilson and Deborah Allison-Koerber, “Combining Subjective and Objective
Forecasts Improves Results,” Journal of Business Forecasting 11, no. 3 (Fall 1992), pp. 12–16.
3
Chaman Jain, “Benchmarking Forecasting Models,” Journal of Business Forecasting 26, no. 4
(Winter 2007–08), p. 17.
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Introduction to Business Forecasting and Predictive Analytics 7
Personal judgments
based on practical experience and/or thorough
research should always
play an important role
in the preparation of any
forecast.
for many modern quantitative forecasting models, along with programs that have
been written specifically for the purpose of allowing you to put these methods to
use. You will find both the text and the software to be extremely user-friendly.
After studying the text and using the software to replicate the examples we present, you will be able to forecast economic and business variables with greater
accuracy than you might now expect. But a word of warning is appropriate. Do
not become so enamored with quantitative methods and computer results that you
fail to think carefully about the series you wish to forecast. In the evolution of
forecasting over the last several decades, there have been many changes, but the
move to more quantitative forecasting has been the most dramatic. This has been
due primarily to the availability and quality of data and to the increased accessibility of user-friendly forecasting software.4 Personal judgments based on practical
experience and/or thorough research should always play an important role in the
preparation of any forecast.
FORECASTING IN BUSINESS TODAY
Forecasting in today’s business world is becoming increasingly important as firms
focus on increasing customer satisfaction while reducing the cost of providing products and services. Six Sigma initiatives and lean thinking are representative of moves
in this direction. The term lean has come to represent an approach to removing waste
from business systems while providing the same, or higher, levels of quality and
output to customers (business customers as well as end users). Major business costs
involve inventory, raw materials, various supplies, and final products. Through better
forecasting, inventory costs can be reduced and wasteful inventory eliminated.
Two professional forecasting organizations offer programs specifically aimed at
increasing the skills and abilities of business professionals who find forecasting an
important part of their job responsibilities. The International Institute of Forecasters
(IIF) offers many events at which professional forecasters share ideas with others
and can participate in various tutorials and workshops designed to enhance their
skills (https://forecasters.org/ ). With the leadership of Len Tashman, in 2005 the IIF
started a practitioner-oriented journal, Foresight: The International Journal of Applied Forecasting, aimed at forecast analysts, managers, and students of forecasting.
The Institute of Business Forecasting (IBF) offers a variety of programs for
business professionals where they can network with others and attend seminars and
workshops to help enhance their forecasting skills (see www.ibf.org). Examples
include the “Demand Planning and Forecasting Best Practices Conference,”
“Supply Chain Forecasting Conference,” and “Business Forecasting Tutorials.”
The IBF also publishes a journal that focuses on applied forecasting issues (The
Journal of Business Forecasting).
Both IIF and IBF offer forecast certification programs. IIF offers three levels of certification as a Certified Professional Demand Forecaster (CPDF); see
4
Barry Keating et al., “Evolution in Forecasting: Experts Share Their Journey,” Journal of
Business Forecasting 25, no. 1 (Spring 2006), p. 15.
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8
Chapter One
www.cpdftraining.org. IBF offers two levels of certification as a Certified Professional Forecaster (CPF); see www.ibf.org/certjbf.cfm. Both organizations present
a variety of workshops and training sessions to prepare business professionals for
certification. After completing this course, you will have a good knowledge base
to get started toward certification from these organizations.
Business decisions almost always depend on some forecast about the course
of events. Virtually every functional area of business makes use of some type of
forecast. For example:
1. Accountants rely on forecasts of costs and revenues in tax planning.
2. The personnel department depends on forecasts as it plans recruitment of new
employees and other changes in the workforce.
3. Financial experts must forecast cash flows to maintain solvency.
4. Production managers rely on forecasts to determine raw-material needs and the
desired inventory of finished products.
5. Marketing managers use a sales forecast to establish promotional budgets.
Because forecasting is useful in so many functional areas of an organization it is
not surprising that this activity is found in many different areas. Consider the following survey results concerning forecasting responsibility within their organizations:5
Functional Area
Sales
Marketing
Finance
Planning
Production
Logistics
Purchasing
The sales forecast is
often the root forecast
from which others, such
as employment requirements, are derived.
Percent Contributing
Information to the
Forecast
Percent That “Own”
the Forecast
84%
81%
48%
43%
38%
24%
12%
43%
31%
18%
21%
4%
7%
4%
The sales forecast is often the root forecast from which others, such as employment
requirements, are derived. As early as the mid-1980s, a study of large Americanoperated firms showed that roughly 94 percent made use of a sales forecast.6 The
ways in which forecasts are prepared and the manner in which results are used vary
considerably among firms.
As a way of illustrating the application of forecasting in the corporate world,
we will look at two examples of successes with business forecasting. In these examples, you may see some terms with which you are not fully familiar at this time.
However, you probably have a general understanding of them, and when you have
completed the text, you will understand them all quite well.
5
Adapted from T. M. McCarthy, D. F. Davis, S. L. Golicic, and J. T. Mentzer, “The Evolution of
Sales Forecasting Management,” Journal of Forecasting, 25, (2006): 303-324, p. 309.
6
Wilson and Allison-Koerber, pp. 12–16.
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Comments from the Field
Due to a manual and high-level forecasting process,
Post Foods struggled to plan production timely and
accurately. Forecasts were produced mainly by input
from the sales team, which focused on recent events,
driving short-term volatility of the forecast. Forecasts
were produced at the national and monthly level, making it difficult to plan by location or incorporate the
promotional demand that drives Post’s business. To
maintain customer service levels, Post was forced to
drive up inventory to compensate.
Post selected John Galt Solutions to drive a new
statistical forecasting and planning process. This allowed Post to drive their forecasts by item and location, giving the production team the detail they needed
to produce an accurate plan.
1.1
In the first few months of implementation, Post was
able to reduce finished goods inventory 12 percent
while maintaining customer service. With the superior
forecast accuracy, Post could plan their material requirements far into the future, enabling them to use
sophisticated hedging strategies to improve their
procurement costs and meet strategic objectives. Post
has also been able to reduce the number of changes
to the production schedule, making it easier for them
to sustain their plan over time and reducing cost
further. In addition, by managing the planning process,
Post eliminated the delays in forecast entry, gaining further efficiency and making effective decisionmaking possible.
Comments from the Field
Since 1991, Radio Systems and their Petsafe and Invisible Fence brands have led the industry in pet training,
containment, safety, and lifestyle product solutions.
Radio Systems released the world’s first do-it-yourself
electronic pet fence in 1991 and followed up in 1998
with the world’s first wireless electronic pet fence. With
Radio Systems products, pet owners can rest secure in
the knowledge that their pets are protected humanely.
During a period of rapid growth, Radio Systems recognized the importance of a one-number consensus
forecast. With 12 sales managers dispersed throughout
the United States and three in Europe, reconciling the
forecast posed a major technical challenge. Forecast
accuracy and inventory management were also crucial, due to the international sourcing of many of Petsafe’s components.
In order to improve supply chain performance,
Radio Systems sought to produce a forecast that was
both grounded in solid statistics and reflected the numerous opinions of the sales managers. The solution
Post Foods
Petsafe
1.2
that they chose had to be able to centralize those
numerous plans from worldwide sources, be easy for
the sales managers to understand and use, and not
require major installation at the overseas locations.
Petsafe determined that the Planning Portal from
John Galt was uniquely able to meet their global collaboration needs. The Planning Portal’s Web-based architecture enables far-flung collaborators to contribute
to a one-number plan without implementing a bulky
software package on the client side. In addition, they
obtained the world’s most advanced statistical baseline to build the consensus.
The sales team was able to pick up on the software
in only a few hours, allowing Radio Systems to quickly
work on producing their consensus.
Radio Systems’ planners were able to not only
build a one-number consensus forecast but also to
construct a formal supply and operations planning
(S&OP) process that includes project managers and
SKU directors.
9
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Comments from the Field
1.3
3
Global Forecasting Issues, Ocean Spray Cranberries
Ocean Spray is one example of a company that faces
many global challenges that affect forecasting.
Sean Reese, a demand planner at Ocean Spray
Cranberries, Inc., summarized some issues that are
particularly important for anyone involved in forecasting in a global environment. First, units of measurement
differ between the United States and most other countries. Where the United States uses such measures as
ounces, pounds, quarts, and gallons, most other countries use grams, kilograms, milliliters, and liters. Making
appropriate conversions and having everyone involved
understand the relationships can be a challenge.7
Second, seasonal patterns reverse between the
Northern and Southern Hemispheres, so it makes a
difference whether one is forecasting for a Northern
or Southern Hemisphere market. Third, such cultural
differences as preference for degree of sweetness,
shopping habits, and perception of colors can impact
sales. The necessary lead time for product and ingredient shipments can vary a great deal depending on
the geographic regions involved. Further, since labels
are different, one must forecast specifically for each
country rather than the system as a whole. Consider,
for example, two markets that may at first appear similar: the United States and Canada. These two markets
use different units of measurement, and in Canada labels must have all information equally in both French
and English. Thus, products destined to be sold in one
market cannot be sold in the other market, so each
forecast must be done separately.
FORECASTING IN THE PUBLIC AND NOT-FOR-PROFIT SECTORS
The need to make decisions based on judgments about the future course of events
extends beyond the profit-oriented sector of the economy. Hospitals, libraries,
blood banks, police and fire departments, urban transit authorities, credit unions,
and a myriad of federal, state, and local governmental units rely on forecasts of
one kind or another. Social service agencies such as the Red Cross and the Easter
Seal Society must also base their yearly plans on forecasts of needed services and
expected revenues. The following three examples will help you see that the importance of forecasting goes well beyond for profit businesses.
A Police Department
Brooke Saladin, working with the research and planning division of the police
department in a city of about 650,000 people, was effective in forecasting the
demand for police patrol services.8 This demand is measured by using a callfor-service workload level in units of hours per 24-hour period. After a thorough
statistical analysis, five factors were identified as influential determinants of the
call-for-service work load (W):
7
Sean Reese, “Reflections of an International Forecaster,” Journal of Business Forecasting
22, no. 4 (Winter 2003–04), pp. 23, 28.
8
Brooke A. Saladin, “A Police Story with Business Implications and Applications,” Journal of
Business Forecasting 1, no. 6 (Winter 1982–83), pp. 3–5.
10
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Introduction to Business Forecasting and Predictive Analytics 11
POP
ARR
AFF
VAC
DEN
a population factor
an arrest factor
an affluence factor
a vacancy factor
a density factor
You will learn how to develop, evaluate, and apply multiple regression models in
Chapter 5. The following multiple regression model was developed on the basis
of a sample of 40 cruiser districts in the city:
W = 5.66 + 1.84POP + 1.70ARR − 0.93AFF + 0.61VAC + 0.13DEN
Using the remaining 23 cruiser districts to test this model, Saladin found that “the
absolute error in forecasting workload ranged from 0.07827 to 1.49764, with an
average of 0.74618.”9 This type of model is useful in planning the needs for both
personnel and equipment.
The Texas Legislative Board
In Texas, the Legislative Budget Board is required to forecast the growth rate for Texas
personal income, which then governs the limit for state appropriations. The state
comptroller’s office also needs forecasts of such variables as the annual growth rates
of electricity sales, total nonagricultural employment, and total tax revenues. Richard
Ashley and John Guerard have used techniques like those to be discussed in this text
to forecast these variables and have found that the application of time-series analysis
yields better one-year-ahead forecasts than naive constant-growth-rate models.10
The California Legislative Analysis Office
Dr. Jon David Vasche, senior economist for the California Legislative Analysis
Office (LAO), needed to prepare economic and financial forecasting for the state.
He has noted that these forecasts are essential, since the state’s budget must be
prepared long before actual economic conditions are known.11 The key features of
the LAO’s forecasting approach are:
1. Forecasts of national economic variables. The Wharton econometric model is
used with the adaptations that reflect the LAO’s own assumptions about such
policy variables as monetary growth and national fiscal policies.
2. California economic submodel. This model forecasts variables such as trends
in state population, personal income, employment, and housing activity.
9
Ibid., p. 5.
Richard Ashley and John Guerard, “Applications of Time-Series Analysis to Texas Financial
Forecasting,” Interfaces 13, no. 4 (August 1983), pp. 46–55.
11
Jon David Vasche, “Forecasting Process as Used by California Legislative Analyst’s Office,”
Journal of Business Forecasting 6, no. 2 (Summer 1987), pp. 9–13; and “State Demographic
Forecasting for Business and Policy Applications,” Journal of Business Forecasting, Summer
2000, pp. 23–30.
10
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12
Chapter One
3. State revenue submodels. These models are used to forecast the variables that
affect the state’s revenue. These include such items as taxable personal income,
taxable sales, corporate profits, vehicle registrations, and cash available for
investment.
4. Cash-flow models. These models are used to forecast the flow of revenues over
time.
In developing and using forecasting models, “the LAO has attempted to strike
a balance between comprehensiveness and sophistication on the one hand, and
flexibility and usability on the other.”12 LAO’s success is determined by how accurately it forecasts the state’s revenues. In the three most recent years reported,
the “average absolute value of the actual error was only about 1.6 percent.”13
FORECASTING AND SUPPLY CHAIN MANAGEMENT
In recent years, there has been increased attention to supply chain management
issues. In a competitive environment, businesses are forced to operate with maximum efficiency and with a vigilant eye toward maintaining firm cost controls,
while continuing to meet consumer expectations in a profitable manner. To be
successful, businesses must manage relationships along the supply chain more
fully than ever before. This can be aided by effectively using the company’s own
sales organization and making forecasting an integral part of the sales and operations planning (S&OP) process.
We can think of the supply chain as encompassing all of the various flows
between suppliers, producers, distributors (wholesalers, retailers, etc.), and consumers. Throughout this chain, each participant, prior to the final consumer, must
manage supplies, inventories, production, and shipping in one form or another.
For example, a manufacturer that makes cellular phones needs a number of different components to assemble the final product and ultimately ship it to a local
supplier of cellular phone services or some other retailer. One such component
might be a leather carrying case. The manufacturer of the carrying case may have
suppliers of leather, clear plastic for portions of the case, fasteners, dyes, and possibly other components. Each one of these suppliers has its own suppliers back
one more step in the supply chain. With all of these businesses trying to reduce
inventory costs (for raw materials, goods in process, and finished products), reliability and cooperation across the supply chain becomes essential.
Forecasting has come to play an important role in managing supply chain relationships. If the supplier of leather phone cases is to be a good supply chain partner, it must have a reasonably accurate forecast of the needs of the cellular phone
company. The cellular phone company, in turn, needs a good forecast of sales to
be able to provide the leather case company with good information. It is probably
obvious that if the cellular phone company is aware of a significant change in
12
13
Vasche, “Forecasting Process,” pp. 9, 12.
Ibid., p. 12.
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Introduction to Business Forecasting and Predictive Analytics 13
To help make the entire
supply chain function
more smoothly, many
companies have started
to use collaborative
forecasting systems in
which information about
the forecast is shared
throughout the relevant
portions of the supply
chain.
sales for a future period, that information needs to be communicated to the leather
case company in a timely manner.
To help make the entire supply chain function more smoothly, many companies have started to use collaborative forecasting systems in which information
about the forecast is shared throughout the relevant portions of the supply chain.
Often, in fact, suppliers have at least some input into the forecast of a business further along the supply chain in such collaborative forecasting systems.14
Having good forecasts at every stage is essential for efficient functioning of the
supply chain.
At the beginning of the text, at the very start of page 1, you read the following
quote from Al Enns, director of supply chain strategies, at Motts North America:
I believe that forecasting or demand management may have the potential to add
more value to a business than any single activity within the supply chain. I say this
because if you can get the forecast right, you have the potential to get everything
else in the supply chain right. But if you can’t get the forecast right, then everything else you do essentially will be reactive, as opposed to proactive planning.15
Daphney Barr, a planning coordinator for Velux-America, a leading manufacturer
of roof windows and skylights, has similarly observed that:
Demand planning is the key driver of the supply chain. Without knowledge of
demand, manufacturing has very little on which to develop production and inventory plans while logistics in turn has limited information and resources to develop
distribution plans for products among different warehouses and customers. Simply
stated, demand forecasting is the wheel that propels the supply chain forward and
the demand planner is the driver of the forecasting process.16
These are two examples of the importance business professionals give to the role
of forecasting.
There is another issue that is partially related to where a business operates along
the supply chain that is important to think about when it comes to forecasting. As
one gets closer to the consumer end of the supply chain, the number of items to
forecast tends to increase. For example, consider a manufacturer that produces a
single product that is ultimately sold through discount stores. Along the way, it
may pass through several intermediaries. That manufacturer only needs to forecast
sales of that one product (and, of course, the potentially many components that go
into the product). But consider Wal-Mart, which sells the product to consumers
throughout the United States. Just think of the tens of thousands of stockkeeping
units (SKUs) that Wal-Mart sells and must forecast. Clearly the methods that the
14
Many forecasting software packages facilitate collaborative forecasting by making the
process Web-based so that multiple participants can potentially have access to, and in some
cases input into, the forecast process.
15
Sidney Hill, Jr., “A Whole New Outlook,” Manufacturing Systems 16, no. 9 (September 1998),
pp. 70–80. (Emphasis added.)
16
Daphney P. Barr, “Challenges Facing a Demand Planner: How to Identify and Handle Them,”
Journal of Business Forecasting 21, no. 2 (Summer 2002), pp. 28–29. (Emphasis added.)
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14
Chapter One
manufacturer considers in preparing a forecast can be much more labor intensive
than the methods that Wal-Mart can consider. An organization like Wal-Mart will
be limited to applying forecasting methods that can be easily automated and can
be quickly applied. This is something you will want to think about as you study
the various forecast methods discussed in this text.
COLLABORATIVE FORECASTING
The recognition that improving functions throughout the supply chain can be
aided by appropriate use of forecasting tools has led to increased cooperation
among supply chain partners. In the simplest form, the process is as follows: A
manufacturer that produces a consumer good computes its forecast. That forecast
is then shared with the retailers that sell that product to end-use consumers. Those
retailers respond with any specific knowledge that they have regarding their future
intentions related to purchases based on known promotions, programs, shutdowns,
or other proprietary information about which the manufacturer may not have had
any prior knowledge. The manufacturer then updates the forecast including the
shared information. In this way, the forecast becomes a shared collaborative effort
between the parties.
All participants in the supply chain stand to benefit. With so much to gain, it’s
no wonder that there are many companies that have successfully implemented
collaborative forecasting partnerships. Companies that have adopted collaborative
forecasting programs have generally seen very positive results.
The value of information sharing has been documented in many studies. Consider one such study of a small to midsized retailer with about $1 billion in
annual sales. This retailer operates at more than 20 locations each with multiple retail outlets including department stores, mass merchandisers, and convenience stores. As a result of sharing information in the supply chain, the retailer
achieved supply chain savings at the two biggest locations of about 15 percent
and 33 percent.17
To effectively use collaborative planning, forecasting, and replenishment
(CPFR), a company must be prepared to share information using electronic data
transfer via the Internet. A number of software developers offer programs that
are designed to create that data link between parties. It is this link to electronic
data and the use of the Internet that is the first hurdle companies must overcome
when considering CPFR. A company needs to be committed to an electronic data
platform including available hardware, software, and support staff. Depending
on the size of the company and the complexity of the integration, the amount of
resources can vary greatly.
One of the most interesting problems to consider when establishing a collaborative relationship is how to deal with a nonparticipant. That is, if a manufacturer
17
Tonya Boone and Ram Ganeshan, “The Value of Information Sharing in the Retail Supply
Chain: Two Case Studies,” Foresight, 9 (Spring 2008), pp. 12–17.
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Introduction to Business Forecasting and Predictive Analytics 15
sells to two customers—one that enters the collaborative relationship and one
that doesn’t—are they both entitled to the benefits that result? At the center of
the issue is the preferential delivery of goods to the customer with the collaborative relationship. If that customer is guaranteed first delivery of goods over
the nonparticipating customer, then the nonparticipant bears nearly all the risk of
stock-outs.
Information surrounding collaboration, such as new product launches and
special promotions, is very sensitive and could be at risk. Securing this information and ensuring that it doesn’t become public knowledge add to the
importance of the job of the software administrator. At the very least, the issue
of confidentiality must be addressed between the parties, and proper measures
should be put in place to ensure all parties are satisfied that their interests are
protected.
COMPUTER USE AND QUANTITATIVE FORECASTING
In today’s business environment, computers are at the heart of business analytics,
including forecasting. The widespread availability of computers has contributed
to the use of quantitative forecasting techniques, many of which would not be
practical to carry out by hand. Most of the methods described in this text fall into
the realm of quantitative forecasting techniques that are reasonable to use only
when appropriate computer software is available. A number of software packages,
at costs that range from about $100 to many thousands of dollars, are currently
marketed for use in developing forecasts. You will find that the software that accompanies this text will enable you to apply the most commonly used quantitative
forecasting techniques to data of your choosing.
The use of personal computers in forecasting has been made possible by rapid
technological changes that have made desktop and laptop computers very fast and
capable of storing and processing large amounts of data. User-friendly software
makes it easy for people to become proficient in using forecasting and other analytic programs in a short period of time. The dominance of PC forecasting software is clear at the annual meetings of the major forecasting associations. At these
meetings various vendors of PC-based forecasting software packages display and
demonstrate their products.
The importance of quantitative methods in forecasting has been stressed by
Charles W. Chase, Jr., who was formerly director of forecasting at Johnson &
Johnson Consumer Products, Inc., and now is at the SAS Institute, Inc. He says,
“Forecasting is a blend of science and art. Like most things in business, the rule
of 80/20 applies to forecasting. By and large, forecasts are driven 80 percent mathematically and 20 percent judgmentally.”18
18
Charles W. Chase, Jr., “Forecasting Consumer Products,” Journal of Business Forecasting 10,
no. 1 (Spring 1991), p. 2.
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16 Chapter One
QUALITATIVE OR SUBJECTIVE FORECASTING METHODS
Quantitative techniques using the power of the computer have come to dominate
the forecasting landscape. However, there is a rich history of forecasting based
on subjective and judgmental methods, some of which remain useful even today.
These methods are probably most appropriately used when the forecaster is faced
with a severe shortage of historical data and/or when quantitative expertise is not
available. In some situations, a judgmental method may even be preferred to a
quantitative one. Very long range forecasting is an example of such a situation.
The computer-based models that are the focal point of this text have less applicability to such things as forecasting the type of home entertainment that will be
available 40 years from now than do those methods based on expert judgments. In
this section, several subjective or judgmental forecasting methods are reviewed.
Sales Force Composites
The sales force can be a rich source of information about future trends and changes
in buyer behavior. These people have daily contact with buyers and are the closest
contact most firms have with their customers. If the information available from
the sales force is organized and collected in an objective manner, considerable
insight into future sales volumes can be obtained.
Members of the sales force are asked to estimate sales for each product they
handle. These estimates are usually based on each individual’s subjective “feel”
for the level of sales that would be reasonable in the forecast period. Often a range
of forecasts will be requested, including a most optimistic, a most pessimistic, and
a most likely forecast. Typically, these individual projections are aggregated by
the sales manager for a given product line and/or geographic area. Ultimately, the
person responsible for the firm’s total sales forecast combines the product-line
and/or geographic forecasts to arrive at projections that become the basis for a
given planning horizon.
While this process takes advantage of information from sources very close to
actual buyers, a major problem with the resulting forecast may arise if members
of the sales force tend to underestimate sales for their product lines and/or territories. This behavior is particularly likely when the salespeople are assigned quotas
on the basis of their forecasts and when bonuses are based on performance relative
to those quotas. Such a downward bias can be very harmful to the firm. Scheduled
production runs are shorter than they should be, raw-material inventories are too
small, labor requirements are underestimated, and in the end, customer ill will
is generated by product shortages. The sales manager with ultimate forecasting
responsibility can offset this downward bias, but only by making judgments that
could, in turn, incorporate other bias into the forecast.
Surveys of Customers and the General Population
In some situations, it may be practical to survey customers for advanced information about their buying intentions. This practice presumes that buyers plan their
purchases and follow through with their plans. Such an assumption is probably
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Introduction to Business Forecasting and Predictive Analytics 17
more realistic for industrial sales than for sales to households and individuals. It
is also more realistic for big-ticket items such as cars than for convenience goods
such as toothpaste or tennis balls.
Survey data concerning how people feel about the economy are sometimes
used by forecasters to help predict certain buying behaviors. One of the commonly
used measures of how people feel about the economy comes from a monthly survey conducted by the University of Michigan Survey Research Center (SRC). The
SRC produces an Index of Consumer Sentiment (UMICS) based on a survey of
individuals, 40 percent of whom are respondents who participated in the survey
six months earlier and the remaining 60 percent new respondents selected on a
random basis. This index has its base period in 1966, when the index was 100.
High values of the UMICS indicate more positive feelings about the economy
than do lower values. Thus, if the UMICS goes up, one might expect that people
are more likely to make certain types of purchases.
Jury of Executive Opinion
The judgments of experts in any area are a valuable resource. Based on years of
experience, such judgments can be useful in the forecasting process. Using the
method known as the jury of executive opinion, a forecast is developed by combining the subjective opinions of the managers and executives who are most likely to
have the best insights about the firm’s business. To provide a breadth of opinions,
it is useful to select these people from different functional areas. For example,
personnel from finance, marketing, and production might be included.
The person responsible for making the forecast may collect opinions in individual interviews or in a meeting where the participants have an opportunity
to discuss various points of view. The latter has some obvious advantages such
as stimulating deeper insights, but it has some important disadvantages as well.
For example, if one or more strong personalities dominate the group, their
opinions will become disproportionately important in the final consensus that
is reached.
The Delphi Method
The Delphi method is similar to the jury of executive opinion in taking advantage
of the wisdom and insight of people who have considerable expertise about the
area to be forecast. It has the additional advantage, however, of anonymity among
the participants. The experts, perhaps five to seven in number, never meet to discuss their views; none of them even knows who else is on the panel.
The Delphi method can be summarized by the following six steps:
1. Participating panel members are selected.
2. Questionnaires asking for opinions about the variables to be forecast are distributed to panel members.
3. Results from panel members are collected, tabulated, and summarized.
4. Summary results are distributed to the panel members for their review and
consideration.
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18
Chapter One
5. Panel members revise their individual estimates, taking account of the information received from the other, unknown panel members.
6. Steps 3 through 5 are repeated until no significant changes result.
Through this process, there is usually movement toward centrality, but there is
no pressure on panel members to alter their original projections. Members who
have strong reason to believe that their original response is correct, no matter how
widely it differs from others, may freely stay with it. Thus, in the end, there may
not be a consensus.
The Delphi method may be superior to the jury of executive opinion, since
strong personalities or peer pressures have no influence on the outcome. The processes of sending out questionnaires, getting them back, tabulating, and summarizing has been made much more efficient by using Internet-based processes.
Some Advantages and Disadvantages
of Subjective Methods
Subjective (i.e., qualitative or judgmental) forecasting methods are sometimes
considered desirable because they do not require any particular mathematical
background of the individuals involved. As future business professionals, like
yourself, become better trained in quantitative forms of analysis, this advantage
will become less important. Historically, another advantage of subjective methods
has been their wide acceptance by users. However, our experience suggests that
users are increasingly concerned with how the forecast was developed, and with
most subjective methods, it is difficult to be specific in this regard. The underlying
models are, by definition, subjective.
This subjectivity is nonetheless the most important advantage of this class of
methods. There are often forces at work that cannot be captured by quantitative
methods. They can, however, be sensed by experienced business professionals and
can make an important contribution to improved forecasts. Wilson and AllisonKoerber have shown this dramatically in the context of forecasting sales for a large
item of food-service equipment produced by the Delfield Company.19 Quantitative
methods reduced errors to about 60 percent of those that resulted from the subjective
method that had been in use. When the less accurate subjective method was combined with the quantitative methods, errors were further reduced to about 40 percent
of the level when the subjective method was used alone. It is clear from this result,
and others, that there is often important information content in subjective methods.
NEW-PRODUCT FORECASTING
Quantitative forecasting methods, which are the primary focus of this text, are not
usually well suited for predicting sales of new products, because they rely on a historical data series for products upon which to establish model parameters. Often
judgmental methods are better suited to forecasting new-product sales because
19
Wilson and Allison-Koerber, “Combining Subjective and Objective Forecasts,” p. 15.
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Introduction to Business Forecasting and Predictive Analytics 19
there are many uncertainties and few known relationships. However, there are
ways to make reasonable forecasts for new products. These typically include both
qualitative judgments and quantitative tools of one type or another. One way to
deal with the lack of known information in the forecasting of new products is to
incorporate a modified version of the Delphi method.
Using Marketing Research to Aid
New-Product Forecasting
Various market research activities can be helpful in new-product forecasting. Surveys of potential customers can provide useful preliminary information about the
propensity of buyers to adopt a new product. Test-market results and results from
the distribution of free samples can also provide estimates of initial sales. On the
basis of predictions about the number of initial innovators who will buy a product,
an S-shaped market-penetration curve can be used to forecast diffusion of the new
product throughout the market.
Whitlark, Geurts, and Swenson have used customer purchase intention surveys
as a tool to help prepare forecasts of new products.20 They describe a three-step
process that starts with the identification of a demographic profile of the target
market, then the probability of purchase is estimated from survey data, and finally
a forecast is developed by combining this probability with information on the size
of the target market. A sample of consumers from the target market is asked to
respond to an intent-to-purchase scale such as: definitely will buy; probably will
buy; might or might not buy; probably will not buy; and definitely will not buy.
Probabilities are then assigned to each of the intention-to-buy categories, using
empirical evidence from a longitudinal study of members of the target market
covering a length of time comparable to the length of time for the proposed forecast horizon. An example of these probabilities for a three- and a six-month time
horizon is shown in Table 1.1. Note that the probabilities of purchase increase as
the time horizon increases.
TABLE 1.1
Probabilities
Assigned to
Purchase-Intention
Categories
Intention-toPurchase Category
Three-Month
Time Horizon
Six-Month
Time Horizon
Definitely will buy
64%
75%
Probably will buy
23
53
Might or might not buy
5
21
Probably will not buy
2
9
Definitely will not buy
1
4
Source: Whitlark, David B., Geurts, Michael D., and Swenson, Michael J. “New Product Forecasting with a Purchase
Intention Survey,” Journal of Business Forecasting 10, no. 3 (Fall 1993), pp. 18–21.
20
David B. Whitlark, Michael D. Geurts, and Michael J. Swenson, “New Product Forecasting with
a Purchase Intention Survey,” Journal of Business Forecasting 10, no. 3 (Fall 1993), pp. 18–21.
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20
Chapter One
Applying this method to two products produced good results. For the first
product, the three-month forecast purchase rate was 2.9 percent compared with
an actual purchase rate of 2.4 percent. In the six-month time horizon, the forecast
and actual rates were 15.6 percent and 11.1 percent, respectively. Similar results
were found for a second product. In the three-month horizon, the forecast and actual percents were 2.5 percent versus 1.9 percent, while in the six-month forecast
horizon, the forecast was 16.7 percent and the actual was 16.3 percent.
The Product Life Cycle Concept
Aids in New-Product Forecasting
The concept of a product life cycle (PLC), such as is shown in Figure 1.2, can
be a useful framework for thinking about new-product forecasting. During the
introductory stage of the product life cycle, only consumers who are classified
as “innovators” are likely to buy the product. Sales start low and increase slowly
at first; then, near the end of this stage, sales start to increase at an increasing
rate. Typically, products in this introductory stage are associated with negative
profit margins as high front-end costs and substantial promotional expenses are
incurred.
As the product enters the growth stage of the life cycle, sales are still increasing
at an increasing rate as “early adopters” enter the market. Eventually, in this stage
the rate of growth in sales starts to decline and profits typically become positive.
Near the end of the growth stage, sales growth starts to level off substantially as
the product enters the maturity stage. Here profits normally reach the maximum
level. Businesses often employ marketing strategies to extend this stage as long as
possible. However, all products eventually reach the stage of decline in sales and
are, at some point, removed from the market (such as Oldsmobile cars, which had
been in the automobile market for a century).
This notion of a product life cycle can be applied to a product class (such as
personal passenger vehicles), to a product form (such as sport utility vehicles),
or to a brand (such as the GMC Yukon). Product life cycles are not uniform in
shape or duration and vary from industry to industry. For high-tech electronic
The Product Life Cycle
FIGURE 1.2
A product life cycle
curve.
Growth
Sales
Maturity
Decline
Introduction
Time
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Introduction to Business Forecasting and Predictive Analytics 21
products, life cycles may be as short as six to nine months. An example would be
a cell phone.
The forecasting approach that is best will vary depending on where a product
or product class is in the life cycle. Once the mid-to-late growth stage is reached,
there is probably sufficient historical data to consider a wide array of quantitative
methods. The real forecasting problems occur in the introductory stage (or in the
preintroductory product development stage). Here the forecaster finds traditional
quantitative methods of limited usefulness and must often turn to marketing research techniques and/or qualitative forecasting techniques.
Analog Forecasts
The basic idea behind the analog method is that the forecast of the new product
is related to information that you have about the introduction of other similar
products in the past. Suppose that you work for a toy company that sells toys to
children in the 4-to-14 age group. Two years ago for the Christmas season, you
introduced a toy that was based on a popular animated Christmas movie. The percentage of total market households that purchased that product was 1.3 percent,
60 percent of potential toy stores stocked the product, and your company spent
$750,000 on promotions. Now you have a new toy to bring to market this Christmas season, and you need some estimate of sales. Suppose that this new product
appeals to a narrower age range such that the likely percentage of households that
would purchase the product is 1.1 percent and that you can expect comparable
promotional support as well as comparable acceptance by retailers in stocking the
product. Assuming that the only change is the percentage of households likely to
purchase the product, the relation of sales of the new product to the old one would
be 1.1 ÷ 1.3 (which equals 0.84615). If the previous product sold 100,000 units in
the first quarter of introduction and 120,000 in the second quarter of introduction,
you might forecast sales for your new product as 84,615 in the first quarter and
101,538 in the second quarter. If the size of the relevant population, the percentage of stores stocking the product, or the promotional effort changes, you would
adjust the forecast accordingly.
Test Marketing
Test marketing involves introducing a product to a small part of the total market
before doing a full product roll-out. The test market should have characteristics
that are similar to those of the total market along relevant dimensions. For example, usually we would look for a test market that has a distribution similar to the
national market in terms of age, ethnicity, and income, as well as any other characteristics that would be relevant for the product in question. The test market should
be relatively isolated in terms of the product being tested to prevent product and/
or information flow to or from other areas. For example, Kansas City, Missouri,
would not usually be a good test market because there would be a good deal of
crossover between Kansas City, Missouri, and Kansas City, Kansas. Indianapolis,
Indiana, on the other hand, might be a better choice of a test market for many
types of products because it has a demographic mix that is similar to the entire
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22
Chapter One
country and is relatively isolated in the context discussed here. Suppose we do a
test market in one or more test cities and sell an average of 1.7 units per 10,000
households. If, in the total market, there are 100 million households, we might
project sales to be 17,000 units ([1.7 ÷ 10,000] × 100,000,000 = 17,000). The
cost of doing a local roll-out is far less than a national roll-out and can provide
significant new information.
Product Clinics
The use of product clinics is a marketing research technique in which potential customers are invited to a specific location and are shown a product mock-up or prototype, which in some situations is essentially the final product. These people are
asked to “experience the product,” which may mean tasting a breakfast cereal, using
a software product, or driving a test vehicle. Afterward, they are asked to evaluate
the product during an in-depth personal interview and/or by filling out a product
evaluation survey. Part of this evaluation would normally include some measure of
likelihood to purchase the product. From these results, a statistical probability of
purchase for the population can be estimated and used to predict product sales. The
use of in-home product evaluations is a similar process. A panel of consumers is
asked to try the product at home for an appropriate period of time and then is asked
to evaluate the product, including an estimate of likelihood to purchase.
Type of Product Affects New-Product Forecasting
All products have life cycles and the cycles have similar patterns, but there may
be substantial differences from one product to another. Think, for example, about
products that are fashion items or fads in comparison with products that have
real staying power in the marketplace. Fashion items and products that would be
considered fads typically have a steep introductory stage followed by short growth
and maturity stages and a decline that is also very steep.
The Bass Model for New-Product Forecasting
The Bass model for sales of new products, first published in 1969, is probably the
most notable model for new-product forecasting. Its importance is highlighted by
the fact that it was republished in Management Science in December 2004.21 This
model gives rise to product diffusion curves that look like those illustrated in Figure 1.3. The Bass model was originally developed for application only to durable
goods. However, it has been adapted for use in forecasting a wide variety of products with short product life cycles and new products with limited historical data.
The model developed by Bass is:
​St​  ​​ = pm + ​(q − p)​​  *​ ​Yt​  ​​ − ​(q∕m)​​  *​ ​Yt​  2​  ​
21
Frank M. Bass, “A New Product Growth Model for Consumer Durables,” Management
Science 50, no. 12S (December 2004), pp. 1825–32. See also Gary Lilien, Arvind Rangaswamy,
and Christophe Van den Bulte, “Diffusion Models: Managerial Applications and Software,”
ISBM Report 7-1999, Institute for the Study of Business Markets, Pennsylvania State University.
Available at http://www.ebusiness.xerox.com/isbm/dscgi/ds.py/Get/File-89/7-1999.pdf.
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Introduction to Business Forecasting and Predictive Analytics 23
100
100
80
80
80
60
40
20
0
1990 1995 2000 2005 2010 2015 2020
% of final users
100
% of final users
% of final users
FIGURE 1.3 Examples of new-product diffusion curves.
60
40
20
0
Year
Product A
1990 1995 2000 2005 2010 2015 2020
Year
60
40
20
0
1990 1995 2000 2005 2010 2015 2020
Product B
Year
Product C
Where:
St = Sales at time period t.
p = Probability of initial purchase at time t = 0. This reflects the importance
of innovators and is called the coefficient of innovation.
m = Number of initial purchases of product over the life cycle (excludes
replacement purchases).
q = Coefficient of imitation representing the propensity to purchase based on
the number of people who have already purchased the product.
Yt = Number of previous buyers at time t.
The values for p, q, and m can be estimated using a statistical tool called regression analysis, which is covered in Chapters 4 and 5 of this text. The algebraic form
for the regression model is:
​St​  ​​ = a + b ​Y​ t−1​​ + c ​Y​ t−1​​ ​​​​ 2​
From the regression estimates for a, b, and c the values of p, q, and m can be
derived. Note that:
a = pm
b​ ​  =​  q −​ p​​
c = −q/m
Bass shows that:
p = a / m q = − mc and m = (− b ± ​[ ​b​​  2​− 4ac ]​​  0.5​) / 2c
Getting the estimates of the three parameters in the Bass model is the difficult
part. If the product is entirely new and in a prelaunch stage, we might gather data
for an analogous product for which a sales history is known, such as a previous
model of a cell phone. Once the product has been launched, knowing even four or
five values of sales we can get preliminary estimates of the parameters. As a sales
history develops, these estimates can be refined.
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Chapter One
1600
1400
Baseline PLC sales
Decline in Sales During
Maturity Stage
1200
1000
800
600
400
Accelerated Decline to EOL
Introductory
Surge Followed
by a Steep Drop
200
Ju
n
Ju
l
A
ug
Se
p
O
ct
N
ov
D
ec
Ja
n
Fe
b
0
Fe
b
M
ar
A
pr
M
ay
A Typical PLC for a
short-lived product.
An initial product
launch is followed by
a sharp decline, then
a more modest drop
in sales, and finally a
steeper drop to the end
of the PLC. (Data are
in the c1t2&f3,4 file.)
n
Ju
l
A
ug
Se
p
O
ct
N
ov
D
ec
Ja
n
FIGURE 1.4
Ju
24
Forecasting Sales for New Products
That Have Short Product Life Cycles
In an age of rapid change there are many products that have short product life cycles.
This is especially true of high-tech products for which technological change and/or
marketing strategies make products obsolete relatively quickly. Cell phones would
be a good example. New cell phones with a variety of enhancements seem to appear
almost weekly. Such products may have a life cycle of perhaps 12 to 24 months,
which means that there is little time to gather historical data upon which to base a
forecast. It also means that the initial forecasts are exceptionally important because
there is less time to recover from either over- or underprojecting sales.
The life cycle for this type of situation may look something like that shown in
Figure 1.4. Upon introduction, sales are typically high then drop quickly, level out
to a slower rate of decline for some period, followed by a more rapid drop to the end
of the product’s life cycle (EOL). We illustrate this in Figure 1.4 for a product with a
20-month PLC. The data shown in such a graph can frequently be developed by looking at the historic PLC for similar products, such as past generations of cell phones.22
Suppose that we know that there has been a seasonal pattern for similar products in
the past. Based on this knowledge, a natural bump to sales can be expected during the
back-to-school period in August and September, followed by increased buying during
the holiday season and another bump when people get tax returns in March. Based on
knowledge from past product introductions, the seasonal indices are estimated to be:
August, 1.15
September, 1.10
November, 1.10
December, 1.30
March, 1.05
You will see how such seasonal indices are computed later in the text. A complete list of the seasonal indices (SI) for this product is shown in Table 1.2.
22
The work of Burress and Kuettner at Hewlett-Packard provides a foundation for this example.
See Jim Burress and Dorothea Kuettner, “Forecasting for Short-Lived Products: HewlettPackard’s Journey,” Journal of Business Forecasting 21, no. 4 (Winter 2002–03), pp. 9–14.
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TABLE 1.2 Modifying a Baseline Forecast for a Product with a Short PLC
(c1t2)
The baseline forecast for each month is multiplied by the seasonal index for that month (SI) as well as by factors that represent the percentage
change in sales expected from other factors such as price cut (P) or various promotional strategies (H and S). The influence of factors such as SI, P,
H, and S could be additive if they are expressed in number of units rather than as a percent adjustment. (c1t2&f4,5)
School
Promotion
(S)
After SI Adj
0.80
1.00
1.00
1.00
0.00
0.00
0.00
0.00
Jul
1,500
0.80
1.00
1.00
1.00
1,200.00
1,200.00
1,200.00
1,200.00
Aug
1,200
1.15
1.00
1.00
1.05
1,380.00
1,380.00
1,380.00
1,449.00
Sep
1,170
1.10
1.00
1.00
1.05
1,287.00
1,287.00
1,287.00
1,351.35
Oct
1,140
0.90
1.15
1.00
1.00
1,026.00
1,179.90
1,179.90
1,179.90
Nov
1,110
1.10
1.10
1.10
1.00
1,221.00
1,343.10
1,477.41
1,477.41
Dec
1,080
1.30
1.05
1.10
1.00
1,404.00
1,474.20
1,621.62
1,621.62
Jan
1,050
0.65
1.00
1.00
1.00
682.50
682.50
682.50
682.50
Feb
1,020
0.70
1.00
1.00
1.00
714.00
714.00
714.00
714.00
Mar
990
1.05
1.00
1.00
1.00
1,039.50
1,039.50
1,039.50
1,039.50
Apr
960
0.85
1.00
1.00
1.00
816.00
816.00
816.00
816.00
May
930
0.80
1.00
1.00
1.00
744.00
744.00
744.00
744.00
Jun
900
0.80
1.00
1.00
1.00
720.00
720.00
720.00
720.00
Jul
795
0.80
1.10
1.00
1.00
636.00
699.60
699.60
699.60
Aug
690
1.15
1.05
1.00
1.04
793.50
833.18
833.18
866.50
Sep
585
1.10
1.00
1.00
1.04
643.50
643.50
643.50
669.24
Oct
480
0.90
1.00
1.00
1.00
432.00
432.00
432.00
432.00
Nov
375
1.10
1.00
1.05
1.00
412.50
412.50
433.13
433.13
Dec
270
1.30
1.00
1.05
1.00
351.00
351.00
368.55
368.55
Jan
165
0.65
1.00
1.00
1.00
107.25
107.25
107.25
107.25
Feb
0
0.70
1.00
1.00
1.00
0
0
0
0
SI
After SI,
P, & H Adj
After SI,
P, H, & S
Adj
0
Month
Price
Cut (P)
Holiday
Promotion
(H)
After SI &
P Adj
Jun
Baseline
PLC Sales
25
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26
Chapter One
We can also incorporate the marketing plans for the product into the PLC
forecast. Suppose that the marketing mix for the product calls for a skimming
introductory price followed by a price cut three months after the product launch.
This price cut is expected to increase sales by 15 percent the first month of the
cut (October, in our example), followed by 10 and 5 percent increases in the
following two months (November and December), after which time the market
has fully adjusted to the price drop. A similar price cut is planned for the following July to help prop up sales as the life cycle moves into a more rapid rate
of decline. Typically, a price cut this late in the PLC has less effect, as can be
seen in Table 1.2.
In addition, two promotional campaigns are planned for the product: one designed to promote the product as a holiday gift, and the other to communicate the
benefits to students of having the product as the school year gets under way. The
holiday promotion is expected to have a 10 percent lift in both the first November
and December and a 5 percent lift the next holiday season. The back-to-school
promotion is expected to add 5 percent to sales the first August and September
and 4 percent at the beginning of the following school year.
These seasonal and marketing mix constructs are used to adjust the baseline
new-product life cycle, as illustrated in Table 1.2. The baseline forecast is first
FIGURE 1.5
Adjusted baseline
forecasts. The
upper graph shows
the new-product life
cycle baseline forecast
adjusted only for
seasonality (S). The
bottom graph shows
the baseline forecast
and the forecast
after adjustment
for seasonality,
and marketing mix
strategies including
pricing (P), a holiday
promotion (H), and
a back-to-school
promotion (S).
(c1t2&f3,4)
1600
Baseline PLC sales
After SI adj
1400
1200
1000
800
600
400
200
0
n
Ju
t
r
c n
b r
p
l g
y n
v
Ju Au Se Oc No De Ja Fe Ma Ap Ma Ju
1800
t
b
p
l g
v c n
Ju Au Se Oc No De Ja Fe
Baseline PLC sales
After SI, P, H, & S adj
1600
1400
1200
1000
800
600
400
200
0
n
Ju
t
r
c n
b r
p
l g
y n
v
Ju Au Se Oc No De Ja Fe Ma Ap Ma Ju
t
b
p
l g
v c n
Ju Au Se Oc No De Ja Fe
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Introduction to Business Forecasting and Predictive Analytics 27
multiplied by the seasonal indices, then by the factors representing the expected
effect of each part of the marketing mix. Additional marketing mix relationships,
such as distribution and awareness strategies, could be included in a similar
manner.
The sales forecast based on the seasonal adjustment (the column headed “After
SI Adj”) is found by multiplying the baseline forecast by the seasonal indices (SI).
The baseline forecast and the seasonally adjusted forecast are shown in the top of
Figure 1.5. Each subsequent adjustment for marketing mix elements is done in a
similar manner until the final adjusted forecast is developed. This final forecast
is shown in the right-hand column of Table 1.2. The baseline and final adjusted
forecast are shown in the bottom graph of Figure 1.5.
A SIMPLE NAIVE FORECASTING MODEL
The simplest of all forecasting methods is to assume that the next period will be
identical to the present. You may have used this method often in deciding what
clothes to wear. If you had not heard a professional weather forecast, your decision about today’s weather might be based on the weather you observed yesterday.
If yesterday was clear and the temperature was 70°F, you might assume today to
be the same. If yesterday was snowy and cold, you might expect a similar wintry
day today. In fact, without evidence to suggest otherwise, such a weather forecast
is quite reasonable. Forecasts based solely on the most recent observation of the
variable of interest are often referred to as “naive forecasts.”
In this section, we will use the naive method to forecast the monthly value
of the University of Michigan Index of Consumer Sentiment (UMICS). For this
example, we use data from January 2016 through December 2016. These data
are given and shown graphically in Figure 1.6. In both forms of presentation, you
can see that the UMICS varied considerably throughout this period, from a low
FIGURE 1.6 University of Michigan Index of Consumer Sentiment (UMICS). (c1f6 c1f 7 c1t3)
UMICS
6
6
01
-2
01
D
ec
-2
6
01
-2
N
ov
6
-2
01
O
ct
01
Se
p
-2
ug
01
6
6
Date
A
l-2
16
Ju
20
6
nJu
-2
01
6
ay
-2
01
M
pr
A
-2
01
6
6
01
M
ar
-2
Fe
b
Ja
n-
20
16
100
98
96
94
92
90
88
86
84
82
80
Jan-2016
Feb-2016
Mar-2016
Apr-2016
May-2016
Jun-2016
Jul-2016
Aug-2016
Sep-2016
Oct-2016
Nov-2016
Dec-2016
Jan-2007
UMICS
92.0
91.7
91.0
89.0
94.7
93.5
90.0
89.9
91.2
87.2
93.8
98.2
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28
Chapter One
of 87.2 in October 2016 to a high of 98.2 in December 2016. The fluctuations in
most economic and business series (variables) are usually best seen after converting the data into graphic form, as you see in Figure 1.6. You should develop the
habit of observing data in graphic form when forecasting.
The simplest naive forecasting model, in which the forecast value is equal to
the previous observed value, can be described in algebraic form as follows:
Ft = At−1
where Ft represents the forecast value for time period t and At−1 represents the
observed value one period earlier (t − 1). In terms of the UMICS data we wish to
forecast, the model may be written as:
UMICSFt = UMICSt−1
where UMICSFt is the University of Michigan Index of Consumer Sentiment naive
forecast at time period t and UMICSt−1 is the observed University of Michigan
Index of Consumer Sentiment one period earlier (t −1). This naive forecast was
done using Excel. The results are shown in Table 1.3 .
Note that each forecast value simply replicates the actual value for the preceding month. The results are presented in graphic form in Figure 1.7 , which clearly
shows the one-period shift between the two series. The forecast for every month
is exactly the same as the actual value for the month before.
TABLE 1.3
The Actual UMICS
and a Naive Forecast
of the UMICS.
(c1f6 c1f 7 c1t3)
Table 1.3 (c1f6 c1f7 c1t3)
Date
UMICS
Naive Forecast
Jan-2016
92
Feb-2016
91.7
92
Mar-2016
91
91.7
Apr-2016
89
91
May-2016
94.7
89
Jun-2016
93.5
94.7
Jul-2016
90
93.5
Aug-2016
89.8
90
Sep-2016
91.2
89.8
Oct-2016
87.2
91.2
Nov-2016
93.8
87.2
Dec-2016
98.2
93.8
Jan-2017
98.2
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Introduction to Business Forecasting and Predictive Analytics 29
100
98
96
94
92
90
88
86
84
82
80
17
20
6
n-
6
01
Ja
-2
01
D
ec
6
01
N
ov
-2
16
O
ct
-2
6
p-
20
01
Se
6
A
ug
-2
01
16
l-2
Ju
20
6
n-
01
Ju
M
ay
-2
01
6
6
-2
01
-2
A
pr
16
20
b-
Fe
Ja
n-
20
16
UMICS
Naive Forecast
M
ar
FIGURE 1.7
The University
Index of Consumer
Sentiment (UMICS)
and a naive forecast.
Note how the naive
forecast (dotted line)
lags the actual
values (solid line).
(c1f6 c1f 7 c1t3)
EVALUATING FORECASTS
It is rare to find one
model that is always
best for any given set of
business or economic
data.
You have now looked at a forecasts of the University of Michigan Index of Consumer Sentiment. How do we evaluate how well that forecast, or any other, actually works? One can not rely on a simple visual inspection of the actual values and
the predicted values in a graph such as Figure 1.7.
We need some way to evaluate the accuracy of forecasting models over a number of periods so that we can identify the model that generally works the best.
Among a number of possible criteria that could be used, seven common ones
are the mean error (ME), the mean absolute error (MAE), the mean percentage
error (MPE), the mean absolute percentage error (MAPE), the mean-squared
error (MSE), the root-mean-squared error (RMSE), and Theil’s U. We will focus
mainly on MAPE, which is widely used by professional business forecasters.
To illustrate how each of these is calculated, let
At = Actual value in period t
Ft = Forecast value in period t
n = Number of periods used in the calculation
1. The mean error is calculated as:
∑ (​A​  ​​ − ​Ft​  ​​)
ME = _______
​  tn ​
2. The mean absolute error is then calculated as:
∑ ​ ​​ ​A​  ​​ − ​Ft​  ​​​|​​
MAE = _______
​  | nt  ​
3. The mean percentage error is calculated as:
∑ [ (​At​  ​​ − ​Ft​  ​​) / ​At​  ​​ ]
__________
MPE =
​
n ​
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30 Chapter One
4. The mean absolute percentage error is calculated as:
∑ ​ ​​(​A​  ​​ − ​Ft​  ​​) / ​At​  ​​​|​​
MAPE = __________
​  | t n ​
5. The mean-squared error is calculated as:
2
∑ ​(​A​  ​​ − ​Ft​  ​​)​​  ​
MSE = _______
​  tn ​
6. The root-mean-squared error is:
________
2
∑ ​(A
​ t​  ​​ − ​Ft​  ​​)​​  ​
RMSE = √
​ _______
​
n ​ ​
7. Theil’s U can be calculated in several ways, two of which are shown here.
_________
__________
U = ​√ ∑ ​(A
​ t​  ​​ − ​Ft​  ​​)​​  2​ ​ ÷ ​√
∑ ​(A
​ t​  ​​ − ​A​ t−1​​)​​  2​ ​
​ ​  ​ ​ ​
​
​
U = RMSE (model) ÷ RMSE (no-change model)
The no-change model used in calculating Theil’s U is the basic naive forecast
model described above, in which Ft = At − 1.
For criteria one through six, lower values are preferred to higher ones. For
Theil’s U, a value of zero means that the model forecast perfectly (no error in
the numerator). If U < 1, the model forecasts better than the consecutive-period
no-change naive model; if U = 1, the model does only as well as the consecutiveperiod no-change naive model; and if U > 1, the model does not forecast as well
as the consecutive-period no-change naive model.
The MAPE for the forecast of the University of Michigan Index of Consumer
Sentiment is shown in Table 1.4 From this, we see that on average, there was an
error of 2.95 percent. Note that by using absolute values (values that ignore the
algebraic sign), positive and negative errors do not cancel each other out. There
could be a very bad forecast with a zero mean error since positive and negative
values could potentially add to zero. Because the MAPE is calculated with absolute values, this problem is averted.
This MAPE of 2.95 percent is neither good nor bad. It is just one commonly
used metric that allows us to compare different forecasts. Of course, a lower
MAPE is preferred to a higher MAPE.
Mean error (ME) and mean percentage error (MPE) are not often used as measures of forecast accuracy because large positive errors (At > Ft) can be offset by
large negative errors (At < Ft). In fact, a very bad model could have an ME or
MPE of zero. ME and MPE are, however, very useful as measures of forecast bias.
A negative ME or MPE suggests that, overall, the forecasting model overstates
the forecast, while a positive ME or MPE indicates forecasts that are generally
too low.
The other measures (MAE, MAPE, MSE, RMSE, and Theil’s U) are best used
to compare alternative forecasting models for a given series. Because of different
units used for various series, only MAPE and Theil’s U should be interpreted
across series. For example, a sales series may be in thousands of units, while the
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Introduction to Business Forecasting and Predictive Analytics 31
TABLE 1.4 Calculation of the Mean Absolute Percentage Error (MAPE) (c1t4)
Date
UMICS = A
Naive
Forecast = F
NA
Absolute
Error
Absolute
% Error (Absolute
Error/ A)*100
NA
NA
NA
Error (A − F)
Jan-2016
92
Feb-2016
91.7
92
−0.3
0.3
0.33
Mar-2016
91
91.7
−0.7
0.7
0.77
Apr-2016
89
91
−2
2
2.25
May-2016
94.7
89
5.7
5.7
6.02
Jun-2016
93.5
94.7
−1.2
1.2
1.28
Jul-2016
90
93.5
−3.5
3.5
3.89
Aug-2016
89.8
90
−0.2
0.2
0.22
Sep-2016
91.2
89.8
1.4
1.4
1.54
Oct-2016
87.2
91.2
4
4.59
Nov-2016
93.8
87.2
6.6
6.6
7.04
Dec-2016
98.2
93.8
4.4
4.4
4.48
Jan-2017
NA
98.2
NA
−4
NA
NA
MAPE = 2.95
prime interest rate is a percentage. Thus, MAE, MSE, and RMSE would be lower
for models used to forecast the prime rate than for those used to forecast sales.
Throughout this text, we will focus on the mean absolute percentage error
(MAPE) to evaluate the relative accuracy of various forecasting methods. The
MAPE is easy for most people to interpret because of its simplicity and it is one
of the most commonly used measures of forecast accuracy.
All quantitative forecasting models are developed on the basis of historical
data. When measures of accuracy, such as MAPE, are applied to the historical period, they are often considered measures of how well various models fit the data
(i.e., how well they work “in sample”). To determine how accurate the models
are in actual forecasts (“out of sample”), a holdout period is often used for evaluation. It may be that the best model “in sample” may not hold up as the best “out
of sample.” It is common to test models for their accuracy by preparing forecasts
for which actual values are known and see how the MAPE (or other metric) compares when calculated on data that was not used in developing the forecast. For
example, if one has eight years of quarterly data, they might not use (hold out)
the last four quarters and use those values as a true test of the forecast model’s accuracy. Once they find the model that works best for the out of sample data, they
would redo the forecast using all eight years of quarterly data. This helps us in
selecting an appropriate model.
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32
Chapter One
USING MULTIPLE FORECASTS
When forecasting sales or some other business or economic variable, it is usually a good idea to consider more than one model. We know it is unlikely that
one model will always provide the most accurate forecast for any series. Thus,
it makes sense to “hedge one’s bets,” in a sense, by using two or more forecasts.
This may involve making a “most optimistic,” a “most pessimistic,” and a “most
likely” forecast. Suppose that we have two forecasts. We could take the forecast with the lowest MAPE as the most optimistic, the forecast with the highest
MAPE as the most pessimistic, and the average value as the most likely. The latter can be calculated as the mean of the two other forecast values in each month.
That is:
UMICSF1 + UMICSF2
Most likely forecast = ​ ________________
​
2
In making a final
forecast, we again
stress the importance
of using well-reasoned
judgments based on
expertise regarding
the series under
consideration.
This is the simplest way to combine forecasts. Actually, it is unlikely that the
simple mean will provide the best combination of forecasts. Later we will see
one way of determining the optimal weights for each forecast in the combination.
The purpose of a number of studies has been to identify the best way to combine forecasts to improve overall accuracy. After we have covered a wider array of
forecasting models, we will come back to this issue of combining different forecasts (see the appendix to Chapter 5 ). For now, we just want to call attention to the
desirability of using more than one method in developing any forecast. In making
a final forecast, we again stress the importance of using well-reasoned judgments
based on expertise regarding the series under consideration.
SOURCES OF DATA
The quantity and type of data needed in developing forecasts can vary a great deal
from one situation to another. Some forecasting techniques require only the data
series that is to be forecast. These methods include the naive method discussed
above, as well as more sophisticated time-series techniques such as time-series
decomposition, exponential smoothing, and ARIMA models, which will be discussed in subsequent chapters of this text. On the other hand, multiple-regression
methods require a data series for each variable included in the forecasting model.
This may mean that a large number of data series must be maintained to support
the forecasting process.
The most obvious sources of data are the internal records of the organization
itself. Such data include unit product sales histories, employment and production
records, total revenue, shipments, orders received, inventory records, and so forth.
However, it is surprising how often an organization fails to keep historical data in
a form that facilitates the development of forecasting models. Another problem
with using internal data is getting the cooperation necessary to make them available both in a form that is useful and in a timely manner. As better information
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Introduction to Business Forecasting and Predictive Analytics 33
systems are developed and made available, internal data will become more useful
in the preparation of forecasts.
For many types of forecasts, the necessary data come from outside the firm.
Various trade associations are a valuable source of such data, which are usually
available to members at a nominal cost and sometimes to nonmembers for a fee.
But the richest sources of external data are various governmental and syndicated
services (such as Prevedere, discussed in Chapter 5).
You will find a wealth of data available on the Internet.23 Using various search
engines, you can uncover sources for most macroeconomic series that are of interest to forecasters.
FORECASTING TOTAL NEW HOUSES SOLD
In each chapter of the text where new forecasting techniques are developed, we will
apply at least one of the new methods to preparing a forecast of total new houses
sold in the United States (TNHS). As you will see, there is a fair amount of variability in how well different methods work for this very important economic series.
The data we will be using are shown graphically in Figure 1.8. As you see from the
graph, we have monthly TNHS from January 2010 through December 2016. The
data represent sales in thousands of units and have not been seasonally adjusted.
In Figure 1.9, you see how a naive forecast looks for total new houses sold in
the United States. At first, you might think it looks pretty good because the actual
and forecast lines appear to be fairly close. The problem is that our eyes can be
deceiving. We may only see the horizontal difference between the lines. However,
the errors are the vertical distances between the lines at each observation. Looking
at the graph this way, we see that the errors are quite large. When data are seasonal, such as TNHS, a naive model will typically make for very poor forecasts.
FIGURE 1.8 Total new houses sold (TNHS). This graph shows TNHS in thousands of
units per month from January 2010 through December 2016. (c1f8)
Total New Houses Sold (000)
60
50
40
30
20
10
Ja
nM 10
ay
-1
Se 0
p1
Ja 0
nM 11
ay
-1
Se 1
p1
Ja 1
n1
M 2
ay
-1
Se 2
p1
Ja 2
nM 13
ay
-1
Se 3
p1
Ja 3
nM 14
ay
-1
Se 4
p1
Ja 4
nM 15
ay
-1
Se 5
p1
Ja 5
n1
M 6
ay
-1
Se 6
p16
0
23
We encourage students to explore the data available on http://www.economagic.com.
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34
Chapter One
FIGURE 1.9 Total new houses sold (TNHS) and a naive forecast. This graph shows
TNHS in thousands of units per month from January 2010 through December 2016, along with a
naive forecast. (c1f9)
TNHS and a Naive Forecast
60
50
40
30
20
TNHS (000)
Naïve Forecast (000)
10
Ja
nM 10
ay
-1
Se 0
p1
Ja 0
nM 11
ay
-1
Se 1
p1
Ja 1
nM 12
ay
-1
Se 2
p1
Ja 2
nM 13
ay
-1
Se 3
p1
Ja 3
nM 14
ay
-1
Se 4
p1
Ja 4
nM 15
ay
-1
Se 5
p1
Ja 5
n1
M 6
ay
-1
Se 6
p1
Ja 6
n17
0
STEPS TO BETTER TIME SERIES FORECASTS
Judgmental or qualitative forecasts rarely are as good as forecasts based on quantitative methods. Figure 1.10 shows a hierarchy of time series forecast methods
starting at the bottom with the methods that are least likely to provide good forecasts. As one moves up and to the right, the methods become more sophisticated
and generally can provide better forecasts when applied to data series for which
they are appropriate. In Chapter 2, we provide more guidance about selection of
appropriate methods.
FIGURE 1.10
Steps to improving
forecasts of time
series data.
STEPS TO IMPROVED TIME SERIES FORECASTS
Aim to be here.
Even better forecasters
are here.
Causal Models
Multiple Regression
Higher Level
Exponential Smoothing
Holt’s and Winters’
Simple Quantitative
Moving Averages & Simple
Exponential Smoothing
Better forecasters are here.
Naïve (+)
Judgmental
Some forecasters are still here.
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Introduction to Business Forecasting and Predictive Analytics 35
INTEGRATIVE CASE: FORECASTING SALES OF THE GAP
Background of the Gap and Gap Sales
We will be using The Gap sales in an integrative case at the end of most chapters.
In these chapters, concepts from the chapter will be applied to this sales series.
In this chapter, we provide an overview of the company as well as of applying a
forecasting concept.
The first Gap store was opened in 1969 by founder Donald Fisher, who decided
to open a store after he had a problem exchanging a pair of Levi’s jeans that were
an inch too short. He felt that there was a need for a store that would sell jeans
in a full array of sizes. He opened his first store in San Francisco and advertised
that it had “four tons” of Levi’s. The store was an instant success, and The Gap
stores were on their way to national prominence. Levi’s were the mainstay of The
Gap’s business, and due to Levi Strauss & Company’s fixed pricing, Fisher originally maintained a 50 percent margin on the sales of these jeans. This changed
in 1976, however, when the Federal Trade Commission prohibited manufacturers
from dictating the price that retailers could charge for their products. There was
suddenly massive discounting on Levi’s products, which drastically cut The Gap’s
margins. Fisher recognized the need to expand his product offerings to include
higher-margin items and therefore began to offer private-label apparel.
In 1983, Fisher recruited Millard Drexler as president, with his objective being
to revamp The Gap. Drexler did this by liquidating its existing inventories and
focusing on simpler, more classic styles that offered the consumer “good style,
good quality, good value.” The Gap started to design its own clothes to fit into
this vision. The Gap already had formed strong relationships with manufacturers
from its earlier entry into the private-label business. This enabled it to monitor
manufacturing closely, which kept costs low and quality high. The Gap’s strategy
didn’t end with high-quality products. Drexler paid equally close attention to the
visual presence of the stores. He replaced the old pipe racks and cement floors with
hardwood floors and attractive tables and shelves with merchandise neatly folded,
which made it easier for the customers to shop. As new merchandise came in, store
managers were given detailed “plannograms,” which told them precisely where the
items would go. With this control, Drexler ensured that each Gap store would have
the same look and would therefore present the same image to the customer.
Drexler’s retailing prowess also became evident when he turned around the
poor performance of the Banana Republic division. In 1983, The Gap bought
Banana Republic, which featured the then-popular safari-style clothing. This trend
toward khakis had been brought on by the popularity of movies such as Raiders
of the Lost Ark and Romancing the Stone. By 1987, Banana Republic’s sales had
reached $191 million. Then the safari craze ended, and this once-popular division
lost roughly $10 million in the two years that followed. Banana Republic was
repositioned as a more upscale Gap, with fancier decor as well as more updated
fashions that offered a balance between sophistication and comfort.
In the early 1990s, the market became flooded with “Gap-like” basics. Other
retailers were also mimicking their presentation strategy and started folding
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36
Chapter One
large-volume commodity items such as jeans, T-shirts, and fleece, some selling
them at substantially lower prices. Drexler and his team recognized that several
major changes were taking place in the retailing environment and they needed to
identify ways to respond to this competition if they were to continue to grow.
One way The Gap responded to increasing competition was to revise its merchandise mix. Customers were shifting away from the basics toward more fashion
items in gender-specific styles. To respond to this trend, The Gap took advantage
of aggressive changes already under way in its inventory management programs,
which gave it faster replenishment times. This enabled The Gap to reduce its inventories in basics by as much as 40 percent, giving it more room for hot-selling,
high-profit items. In addition to shifting to more fashion, The Gap also fine-tuned
its product mix so that merchandise would be more consistent between stores.
Another way that The Gap responded to increased competition and changing
retailing trends was by entering into strip malls. Many strip malls offer their customers easier access to stores and more convenient parking than they could in
larger indoor mall locations.
Gap launched the Old Navy Clothing Co. in April 1994 to target consumers
in households with lower to middle incomes. Old Navy stores carry a different
assortment of apparel than traditional Gap stores. They differentiated themselves
from The Gap stores by offering alternative versions of basic items, with different
fabric blends that enable them to charge lower retail prices. To help keep costs
down, it also scaled down the decor of these stores, with serviceable concrete
floors and shopping carts instead of the hardwood floors found in The Gap. Old
Navy stores further positioned themselves as one-stop-shopping stores by offering
clothing for the whole family in one location.
With its current mix of stores, The Gap has successfully carved out a position
for itself in many retail clothing categories. Table 1.5 shows the distribution of
store types by geographic regions. Although there have been some hurdles along
TABLE 1.5
The Gap Store Count
Source: http://www.gapinc.
com/content/gapinc/html/
investors/realestate.html (click
on Historical Store Count by
country).
Stores
As of 2017
Gap North America
Gap Asia
Gap Europe
Old Navy North America
Old Navy Asia
Banana Republic North America
Banana Republic Asia
Banana Republic Europe
Athleta North America
Intermix North America
Company-Operated Stores
Franchise
844
311
164
1,043
13
601
48
1
132
43
3,200
459
Total
3,659
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Introduction to Business Forecasting and Predictive Analytics 37
the way, Gap has proven that it has the ability to respond to changes in the retail
environment and has, therefore, managed to stay in the race.
Gap’s quarterly sales are shown in Table 1.6 and in Figure 1.11 . Table 1.6 and
Figure 1.11 also have a modified naive forecast for The Gap sales using a fourquarter lag.
TABLE 1.6 The Gap Sales and a Modified Naive Forecast (Forecast = Sales [−4])
(c1t6&f11).
The Gap sales data are in thousands of dollars by quarter.
The months indicated in the date columns represent the end month in The Gap’s
financial quarter.
The first quarter of Gap’s fiscal year includes February, March, and April.
Gap data from ycharts.com.
Date
Apr-06
Jul-06
Oct-06
Jan-07
Apr-07
Jul-07
Oct-07
Jan-08
Apr-08
Jul-08
Oct-08
Jan-09
Apr-09
Jul-09
Oct-09
Jan-10
Apr-10
Jul-10
Oct-10
Jan-11
Apr-11
Jul-11
Oct-11
Jan-12
Gap Sales
($M)
3,441
3,714
3,851
4,919
3,549
3,685
3,854
4,675
3,384
3,499
3,561
4,082
3,127
3,245
3,589
4,236
3,329
3,317
3,654
4,364
3,295
3,386
3,585
4,283
Gap Sales
Modified
Naïve
Forecast
(M$)
Date
3,441
3,714
3,851
4,919
3,549
3,685
3,854
4,675
3,384
3,499
3,561
4,082
3,127
3,245
3,589
4,236
3,329
3,317
3,654
4,364
Apr-12
Jul-12
Oct-12
Jan-13
Apr-13
Jul-13
Oct-13
Jan-14
Apr-14
Jul-14
Oct-14
Jan-15
Apr-15
Jul-15
Oct-15
Jan-16
Apr-16
Jul-16
Oct-16
Jan-17
Apr-17
Jul-17
Oct-17
Jan-18
Gap Sales
($M)
3,487
3,575
3,864
4,725
3,729
3,868
3,976
4,575
3,774
3,981
3,972
4,708
3,657
3,898
3,857
4,385
3,438
3,851
3,798
4,429
Gap Sales
Modified
Naïve
Forecast
(M$)
3,295
3,386
3,585
4,283
3,487
3,575
3,864
4,725
3,729
3,868
3,976
4,575
3,774
3,981
3,972
4,708
3,657
3,898
3,857
4,385
3,438
3,851
3,798
4,429
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38
Chapter One
FIGURE 1.11 The Gap sales in thousands of dollars and a modified naive forecast. The data are
quarterly, so a four-quarter lag was used for a modified naive forecast. (c1t6&f11)
Gap Sales and Modified Naive Forecast (M$)
6,000
5,000
4,000
3,000
2,000
Gap Sales ($M)
Gap Sales Modified
Naïve Forecast (M$)
1,000
O
A
pr
-0
6
ct
-0
A 6
pr
-0
O 7
ct
-0
A 7
pr
-0
O 8
ct
-0
A 8
pr
-0
O 9
ct
-0
A 9
pr
-1
O 0
ct
-1
A 0
pr
-1
O 1
ct
-1
A 1
pr
-1
O 2
ct
-1
A 2
pr
-1
O 3
ct
-1
A 3
pr
-1
O 4
ct
-1
A 4
pr
-1
O 5
ct
-1
A 5
pr
-1
O 6
ct
-1
A 6
pr
-1
O 7
ct
-1
7
0
Case
Questions
1. Based on the tabular and the graphic presentations of The Gap sales data, what do you
think explains the seasonal pattern in its sales data?
2. Why do you think a modified naive forecasting method, rather than the simple naive
method, was used for Gap sales? Using Excel with only Gap data from April 2005
through January 2016, make your own forecast of The Gap sales for the four quarters
from April 2016 through January 2017. Based on inspection of your graph, what is your
expectation in terms of forecast accuracy?
3. Calculate the MAPE for your forecast of those four quarters, given the actual sales that
are in a bold font shown in Table 1.6.
Solutions
to Case
­Questions
Data are in the c1t6&f11 file.
1. The seasonal pattern is one in which sales typically have a modest increase from the
first to the second quarter, followed by another similar increase in the third quarter, then
a large increase in the fourth quarter. The increase in the fourth quarter is caused by the
holiday shopping season.
2. The model would be: GAPF = GAPSALES(−4). GAPF represents the forecast values, while GAPSALES(−4) is the actual value four periods earlier. An inspection
of The Gap sales series would lead us to expect that a naive forecasting model with
a lag of four periods would pick up the seasonality as well as the downward trend
in The Gap sales. This can be seen in the graph of actual and predicted values in
Figure 1.10.
3. The actual and predicted values for April 2016 through January 2017 are shown below.
The MAPE for these four quarters is: MAPE = 2.5 percent.
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Introduction to Business Forecasting and Predictive Analytics 39
Gap Sales
($M)
Gap Sales
Modified Naive
Forecast
Error
Absolute
Error
April 2016
3,438
3,657
−219
219
6.4
July 2016
3,851
3,898
−47
47
1.2
October 2016
3,798
3,857
−59
59
1.6
January 2017
4,429
4,385
44
44
1.0
Date
Absolute
%Error
MAPE = 2.5%
Case
References
http://www.gapinc.com
http://money.cnn.com/2005/02/23/news/fortune500/Gap/?cnn5yes
AN INTRODUCTION TO FORECASTXTM
ForecastXTM is a family of forecasting tools capable of performing the most complex forecast methods and requires only a brief learning curve that facilitates immediate, simple,
and accurate operation regardless of user experience.
Forecasting with the ForecastX Wizard™
The following provides a brief description of some features of the ForecastX Wizard™
and how to use them while forecasting. A complete manual can be found in the “Wizard
Users Guide.pdf” file, which is in the Help subfolder of the ForecastX™ folder within the
Programs folder (or wherever you have installed the software). You will get instructions on
how to download the software from your instructor,
Open the “Gap Practice Data” file by clicking on c1 Gap Practice Data.
When the spreadsheet opens, click in any cell that contains data; for example, B4.
Click the ForecastX Wizard™ icon
to start the Wizard.
USING THE FIVE MAIN TABS ON THE OPENING
FORECASTXTM SCREEN
Use The Gap sales data you have opened, and follow the directions in the following screen
shots to get a first look at how ForecastX™ works.
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40
Chapter One
The Data Capture Tab
This tab appears when you first start ForecastX™.
Source: John Galt Solutions
The purpose of the Data Capture screen is to tell ForecastX™ about your data.
When the ForecastX Wizard™ captures your data, the Intelligent Data Recognizer determines the following:
a. Organization: Indicates whether the data is in rows or columns.
b. Data to Be Forecast: Specifies the range of the data to be forecasted.
c. Dates: Specifies whether the data has dates and the periodicity of the dates.
d. Labels: Indicates the number of rows of descriptive labels in the data.
e. Parameters: Indicates the number of DRP (Distribution Resource Planning) fields in
your data. For the purposes of this text, you will not need to use this functionality.
f. Seasonality: You can either select the seasonality of the data or allow ForecastX™ to
determine it. Here you see that ForecastX™ correctly identified the data as quarterly. It
is almost always correct. These fields must follow the labels information in your underlying data.
g. Forecast Periods: Set the number of periods to forecast out into the future. The default
is 12.
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Introduction to Business Forecasting and Predictive Analytics 41
Forecast Method Tab
The ForecastX Wizard™ allows you to select individual forecasting techniques and their
parameters. To select a Forecasting Technique:
Source: John Galt Solutions
From the Forecasting Technique drop-down menu, select a particular method from over 20
forecasting techniques. For this example, select “Holt Winters,” as shown above. Later you
will understand why you would select this method.
The Group By Tab
In this text, we only discuss forecasting a single series, so you will not need this tab. However, should you want to forecast product groups, see the “Wizard Users Guide.pdf” file.
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42
Chapter One
The Statistics Tab
Source: John Galt Solutions
The ForecastX Wizard™ allows you to select statistical analyses to include on the Audit
Trail report. ForecastX™ supports more than 40 statistics from both descriptive and accuracy measurement categories. For this example, just select the MAPE, as shown above.
The “More Statistics” option offers advanced statistics. The Root Mean Squared Error
(RMSE) and many other metrics are available. Statistics for regression models are located
in this dialog box. To access the Advanced Statistics dialog, click the “More Statistics”
button on the Statistics screen.
The Reports Tab
Source: John Galt Solutions
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Introduction to Business Forecasting and Predictive Analytics 43
The ForecastX Wizard™ offers five report choices with specific options for each. Checking any of the report boxes in the upper grouping of check boxes automatically includes it
in the output. You may check more than one if desired. Each type of report will produce its
own Excel workbook but may contain several series within one workbook. In this text, we
will use only the “Audit” and “Standard” reports. Detailed information about all these tabs
can be found in the “Wizard Users Guide.pdf” file.
Standard Report
The Standard Report is built for speed and handling of large volumes of data. It produces
a side-by-side report listing the actual values compared to the forecasted values. It also
includes selected metrics and statistics: Mean Absolute Percentage Error (MAPE), RSquared Value, and Standard Deviation.
Audit Report
The Audit Report produces the most detailed analysis of the forecast. Those who need to
justify their forecasts with statistics generally use the Audit Trail report. A partial section
of the Audit Trail report that you have generated by following these instructions is shown
below. (see c1Gap Gap Practice Data)
6,000
Gap Sales ($M)
5,000
4,000
3,000
2,000
Actual
Forecast
Fitted Values
1,000
Ju
Ja
n-
20
1
l-2 1
01
Ja
n- 1
20
Ju 12
l-2
0
Ja 12
n20
Ju 13
l-2
0
Ja 13
n20
Ju 14
l-2
0
Ja 14
n20
Ju 15
l-2
0
Ja 15
n20
Ju 16
l-2
0
Ja 16
n20
Ju 17
l-2
0
Ja 17
n20
Ju 18
l-2
0
Ja 18
n20
Ju 19
l-2
01
9
0
Forecast – Holt-Winters Selected
Forecast
Date
Quarterly
Annual
Jan-2017
4,396.35
Apr-2017
3,510.72
Jul-2017
3,867.98
Oct-2017
3,798.00
15,573.05
Jan-2018
4,396.35
Apr-2018
3,510.72
Jul-2018
3,867.98
Oct-2018
3,798.00
15,573.05
Jan-2019
4,396.35
Apr-2019
3,510.72
Jul-2019
3,867.98
Oct-2019
3,798.00
15,573.05
Accuracy Measures
MAPE
Value
2.52%
Note: Throughout the text you may find some situations in which the standard calculations that we show do not match exactly with the ForecastX™ results. This is because
they, at times, invoke proprietary alterations from the standard calculations. The results
are always very close but sometimes do not match perfectly with “hand” calculations.
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44
Chapter One
Suggested
Readings and
Web Sites
Adams, F. Gerard. The Business Forecasting Revolution. New York: Oxford University
Press, 1986.
Armstrong, J. Scott. “Forecasting for Environmental Decision Making.” In Tools to
Aid Environmental Decision Making, eds. V. H. Dale and M. E. English. New York:
Springer-Verlag, 1999, pp. 192–225.
Armstrong, J. Scott; Kesten C. Green; and Andreas Graefe. “Golden Rule of
Forecasting.” Journal of Business Research, 68, no. 8 (August 2015). pp. 1717–1731.
Armstrong, J. Scott. Principles of Forecasting: A Handbook for Researchers and
Practitioners. Norwell, MA: Kluwer Academic Publishers: The Netherlands, 2001.
Blessington, Mark. “Sales Quota Accuracy and Forecasting,” Foresight, 40, (Winter
2016), pp. 44–49.
Byrne, Teresa M. McCarthy. “Omnichannel: How Will It Impact Retail Forecasting and
Planning Processes?” Journal of Business Forecasting 35, no. 4 (Winter 2016–2017), pp. 4–9.
Chase, Charles W. Jr. Demand-Driven Forecasting. 2nd ed. Hoboken, NJ: John Wiley &
Sons, 2013.
Duguay, Andrew. “The Top 10 External Factors That Impact Forecast Accuracy.” www.
prevedere.com, (January 21, 2016), pp. 1–3.
Ellis, Joseph H. Ahead of the Curve: A Commonsense Guide to Forecasting Business and
Market Cycles. Boston, MA.: Harvard Business School Press, 2005.
Goodwin, P. “Predicting the Demand for New Products,” Foresight, no. 9 (2008), pp. 8–10.
Kahn, Kenneth B.; and John Mello. “Lean Forecasting Begins with Lean Thinking on
the Demand Forecasting Process.” Journal of Business Forecasting 23, no. 4 (Winter
2004–05), pp. 30–40.
Lapide, Larry. “Execution Needs the S&OP Plans.” Journal of Business Forecasting 35,
no. 1 (Spring 2016). pp. 19–22.
Meade, N. “Evidence for the Selection of Forecasting Methods.” Journal of Forecasting
19, no. 6 (2000), pp. 515–35.
Shore, H.; and D. Benson-Karhi (2007) “Forecasting S-Shaped Diffusion Processes via
Response Modeling Methodology,” Journal of the Operational Research Society, 58,
pp. 720–28.
Wagner, Rich. “Why External Data Are Vital to Demand Forecasts.” Journal of Business
Forecasting 35, no. 1 (Spring 2016). pp. 30–34.
Wilson, J. Holton; and Deborah Allison-Koerber. “Combining Subjective and Objective
Forecasts Improves Results.” Journal of Business Forecasting 11, no. 3 (Fall 1992), pp. 12–16.
http://www.economagic.com
http://www.forecasters.org
http://www.forecastingprinciples.com
http://www.johngalt.com
www.ibf.org
Exercises
1. Describe the three phases of the evolution of forecasting/prediction.
2. How does the organization of the material in this book relate to the stages of the evolution of prediction?
3. Write a paragraph in which you compare what you think are the advantages and disadvantages of subjective forecasting methods. How do you think the use of quantitative
methods relates to these advantages and disadvantages?
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Introduction to Business Forecasting and Predictive Analytics 45
4. Explain how forecasting relates to having an efficient supply chain.
5. The process of forecasting new products is difficult. Why? How can new products be
forecast?
6. In this chapter, you saw an example of a naive forecast. Why do you think it is given
that name? Describe how the naive forecast is developed.
7. In the chapter, you learned about many metrics that can be used to evaluate forecast
accuracy. The MAPE was one of those that may be the most common in use. Explain
what the MAPE tells a forecaster.
8. Suppose that you work for a U.S. senator who is contemplating writing a bill that would
put a national sales tax in place. Because the tax would be levied on the sales revenue of
retail stores, the senator has asked you to prepare a forecast of retail store sales for year
8, based on data from year 1 through year 7. The data are:
(c1p8)
Year
Retail Store Sales
1
2
3
4
5
6
7
$ 1,225
1,285
1,359
1,392
1,443
1,474
1,467
a. Use the naive forecasting model presented in this chapter to prepare a forecast of
retail store sales for each year from 2 through 8.
b. Prepare a time-series graph of the actual and forecast values of retail store sales for
the entire period. (You will not have a forecast for year 1 or an actual value for year 8.)
c. Calculate the MAPE for your forecast series using the values for year 2 through year 7.
9. Suppose that you work for a major U.S. retail department store that has outlets nationwide.
The store offers credit to customers in various forms, including store credit cards, and over
the years has seen a substantial increase in credit purchases. The manager of credit sales
is concerned about the degree to which consumers are using credit and has started to track
the ratio of consumer installment credit to personal income. She calls this ratio the credit
percent, or CP, and has asked that you forecast that series for year 8. The available data are:
(c1p9)
Year
CP
1
2
3
4
5
6
7
12.96
14.31
15.34
15.49
15.70
16.00
15.62
a. Use the first naive model presented in this chapter to prepare forecasts of CP for years
2 through 8.
b. Plot the actual and forecast values of the series for the years 1 through 8. (You will
not have an actual value for year 8 or a forecast value for year 1.)
c. Calculate the MAPE for your forecasts for years 2 through 7.
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46
Chapter One
10. Go to the library and look up annual data for population in the United States from 2000
through the most recent year available. This series is available at a number of Internet
sites, including http://www.economagic.com. Plot the actual data along with the forecast you would get by using the basic naive model discussed in this chapter.
11. CoastCo Insurance, Inc., is interested in developing a forecast of larceny thefts in the
United States. It has found the following data:
(c1p11)
Year
Larceny Thefts*
Year
Larceny Thefts*
1
4,151
10
7,194
2
4,348
11
7,143
3
5,263
12
6,713
4
5,978
13
6,592
5
6,271
14
6,926
6
5,906
15
7,257
7
5,983
16
7,500
8
6,578
17
7,706
9
7,137
18
7,872
Plot this series in a time-series plot and make a naive forecast for years 2 through 19.
Calculate the MAPE for years 2 through 18. On the basis of these measures and what
you see in the plot, what do you think of your forecast? Explain.
12. As the world’s economy becomes increasingly interdependent, various exchange rates
between currencies have become important in making business decisions. For many
U.S. businesses, the Japanese exchange rate (in yen per U.S. dollar) is an important
decision variable. This exchange rate (EXRJ) is shown in the following table by month
for a two-year period:
(c1p12)
Period
EXRJ
Year 1
Period
EXRJ
Year 2
M1
127.36
M1
144.98
M2
127.74
M2
145.69
M3
130.55
M3
153.31
M4
132.04
M4
158.46
M5
137.86
M5
154.04
M6
143.98
M6
153.70
M7
140.42
M7
149.04
M8
141.49
M8
147.46
M9
145.07
M9
138.44
M10
142.21
M10
129.59
M11
143.53
M11
129.22
M12
143.69
M12
133.89
Prepare a time-series plot of this series, and use the naive forecasting model to forecast
EXRJ for each month from year 1 M2 (February) through year 3 M1 (January). Calculate the MAPE for the period from year 1 M2 through year 2 M12.
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