Forecasting; Chapter3
Department of Business Administration
FALL 2010-2011
I see that you will
get an A this semester.
MGMT 405, POM, 2010/11. Lec Notes
Chapter 3: Forecasting
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Outline: What You Will Learn . . .
Forecasting; Chapter 3
 List the elements of a good forecast.
 Outline the steps in the forecasting process.
 Describe at least three qualitative forecasting techniques and
the advantages and disadvantages of each.
 Compare and contrast qualitative and quantitative approaches
to forecasting.
 Briefly describe averaging techniques, trend and seasonal
techniques, and regression analysis, and solve typical
problems.
 Describe two measures of forecast accuracy.
 Describe two ways of evaluating and controlling forecasts.
 Identify the major factors to consider when choosing a
forecasting technique
2
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Forecasting; Chapter 3
What is meant by Forecasting and Why?
 Forecasting is the process of estimating a variable,
such as the sale of the firm at some future date.
 Forecasting is important to business firm,
government, and non-profit organization as a
method of reducing the risk and uncertainty
inherent in most managerial decisions.
 A firm must decide how much of each product to
produce, what price to charge, and how much to
spend on advertising, and planning for the growth
of the firm.
3
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Forecasting; Chapter 3
The aim of forecasting
 The aim of forecasting is to reduce the risk or
uncertainty that the firm faces in its short-term
operational decision making and in planning for its
long term growth.
 Forecasting the demand and sales of the firm’s
product usually begins with macroeconomic forecast
of general level of economic activity for the economy
as a whole or GNP.
4
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Forecasting; Chapter 3
The aim of forecasting
 The firm uses the macro-forecasts of general economic
activity as inputs for their micro-forecasts of the
industry’s and firm’s demand and sales.
 The firm’s demand and sales are usually forecasted on
the basis of its historical market share and its planned
marketing strategy (i.e., forecasting by product line
and region).
 The firm uses long-term forecasts for the economy and
the industry to forecast expenditure on plant and
equipment to meet its long-term growth plan and
strategy.
5
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Forecasting; Chapter 3
Forecasting Process Map
Statistical
Model
Demand
History
Sales
Marketing
Causal
Factors
Product
Production &
Executive
Management
Inventory
Management
& Finance
Control
Consensus
Process
Consensus
Forecast
6
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Uses of Forecasts
Accounting
Cost/profit estimates
Finance
Cash flow and funding
Human Resources
Hiring/recruiting/training
Marketing
Pricing, promotion, strategy
MIS
IT/IS systems, services
Operations
Schedules, MRP, workloads
Product/service design
New products and services
Forecasting; Chapter 3
7
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Features of Forecasts
Forecasting; Chapter 3
 Assumes causal system
past ==> future
 Forecasts rarely perfect
because of randomness
I see that you will
get an A this semester.
 Forecasts more accurate for
groups vs. individuals
 Forecast accuracy decreases
as time horizon increases
8
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Forecasting; Chapter 3
Elements of a Good Forecast
Timely
Reliable
Accurate
Written
9
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Forecasting; Chapter 3
Steps in the Forecasting Process
“The forecast”
Step 6 Monitor the forecast
Step 5 Make the forecast
Step 4 Obtain, clean and analyze data
Step 3 Select a forecasting technique
Step 2 Establish a time horizon
Step 1 Determine purpose of forecast
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Forecasting; Chapter 3
Forecasting Techniques
 A wide variety of forecasting methods are
available to management. These range from the
most naïve methods that require little effort to
highly complex approaches that are very costly in
terms of time and effort such as econometric
systems of simultaneous equations.
 Mainly these techniques can break down into three
parts: Qualitative approaches (Judgmental
forecasts) and Quantitative approaches (Timeseries forecasts) and Associative model forecasts).
11
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Forecasting; Chapter 3
Forecasting Techniques
Judgmental - uses subjective inputs
such as opinion from consumer surveys,
sales staff etc..
Time series - uses historical data
assuming the future will be like the past
Associative models - uses explanatory
variables to predict the future
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Forecasting; Chapter 3
Qualitative Forecasts or Judgmental Forecasts
 Survey Techniques
Some of the best-know surveys
Planned Plant and Equipment Spending
Expected Sales and Inventory Changes
Consumers’ Expenditure Plans
 Opinion Polls
Business Executives
Sales Force
Consumer Intentions
13
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Forecasting; Chapter 3
What are qualitative forecast ?
 Qualitative forecast estimate variables at some
future date using the results of surveys and opinion
polls of business and consumer spending intentions.
 The rational is that many economic decisions are
made well in advance of actual expenditures.
 For example, businesses usually plan to add to plant
and equipment long before expenditures are actually
incurred.
14
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Forecasting; Chapter 3
Qualitative Forecasts or Judgmental Forecasts
 Surveys and opinion pools are often used to make
short-term forecasts when quantitative data are not
available
 Usually based on judgments about causal factors that
underlie the demand of particular products or services
 Do not require a demand history for the product or
service, therefore are useful for new products/services
 Approaches vary in sophistication from scientifically
conducted surveys to intuitive hunches about future
events
 The approach/method that is appropriate depends on a
product’s life cycle stage
15
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Forecasting; Chapter 3
Qualitative Forecasts or Judgmental Forecasts
 Polls can also be very useful in supplementing
quantitative forecasts, anticipating changes in
consumer tastes or business expectations about future
economic conditions, and forecasting the demand for
a new product.
 Firms conduct opinion polls for economic activities
based on the results of published surveys of
expenditure plans of businesses, consumers and
governments.
16
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Forecasting; Chapter 3
Qualitative Forecasts or Judgmental Forecasts


Survey Techniques– The rationale for forecasting
based on surveys of economic intentions is that many
economic decisions are made in advance of actual
expenditures (Ex: Consumer’s decisions to purchase
houses, automobiles, TV sets, furniture, vocation,
education etc. are made months or years in advance
of actual purchases)
Opinion Polls– The firm’s sales are strongly
dependent on the level of economic activity and sales
for the industry as a whole, but also on the policies
adopted by the firm. The firm can forecast its sales
by pooling experts within and outside the firm.
17
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Forecasting; Chapter 3
Qualitative Forecasts or Judgmental Forecasts
 Executive Polling- Firm can poll its top
management from its sales, production,
finance for the firm during the next quarter or
year.
 Bandwagon effect (opinions of some experts
might be overshadowed by some dominant
personality in their midst).
 Delphi Method – experts are polled
separately, and then feedback is provided
without identifying the expert responsible for
a particular opinion.
18
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Forecasting; Chapter 3
Qualitative Forecasts or Judgmental Forecasts
 Consumers intentions polling Firms selling automobiles, furniture, etc. can
pool a sample of potential buyers on their
purchasing intentions. By using results of the
poll a firm can forecast its sales for different
levels of consumer’s future income.
 Sales force polling –
 Forecast of the firm’s sales in each region and
for each product line, it is based on the opinion
of the firm’s sales force in the field (people
working closer to the market and their opinion
about future sales can provide essential
information to top management).
19
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Forecasting; Chapter 3
Quantitative Forecasting Approaches
 Based on the assumption, the “forces” that generated
the past demand will generate the future demand, i.e.,
history will tend to repeat itself.
 Analysis of the past demand pattern provides a good
basis for forecasting future demand.
 Majority of quantitative approaches fall in the
category of time series analysis.
20
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Forecasting; Chapter 3
Time Series Analysis
 A time series (naive forecasting) is a set of numbers
where the order or sequence of the numbers is
important, i.e., historical demand
 Attempts to forecasts future values of the time series
by examining past observations of the data only. The
assumption is that the time series will continue to
move as in the past
 Analysis of the time series identifies patterns
 Once the patterns are identified, they can be used to
develop a forecast
21
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Forecasting; Chapter 3
Forecast Horizon
 Short term
 Up to a year
 Medium term
 One to five years
 Long term
 More than five years
22
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Forecasting; Chapter 3
Reasons for Fluctuations in Time Series Data
 Secular Trend are noted by an upward or downward sloping
line- long-term movement in data (e.g. Population shift, changing
income and cultural changes).
 Cycle fluctuations is a data pattern that may cover several
years before it repeats itself- wavelike variations of more
than one year’s duration (e.g. Economic, political and agricultural
conditions).
 Seasonality is a data pattern that repeats itself over the
period of one year or less- short-term regular variations in
data (e.g. Weekly or daily restaurant and supermarket experiences).
 Irregular variations caused by unusual circumstances (e.g.
Severe weather conditions, strikes or major changes in a product or
service).
 Random influences (noise) or variations results from
random variation or unexplained causes. (e.g. residuals)
MGMT 405, POM, 2010/11. Lec Notes
23
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Forecasting; Chapter 3
Forecast Variations
Irregular
variatio
n
Trend
Cycles
90
89
88
Seasonal variations
24
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Forecasting; Chapter 3
Uses for Naïve Forecasts
Stable time series data
F(t) = A(t-1)
Seasonal variations
F(t) = A(t-n)
Data with trends
F(t) = A(t-1) + (A(t-1) – A(t-2))
25
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Forecasting; Chapter 3
Techniques for Averaging
Moving average
Weighted moving average
Exponential smoothing
26
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Forecasting; Chapter 3
Moving Averages
 Moving average – A technique that averages a
number of recent actual values, updated as new
values become available.
Ft = MAn=
At-n + … At-2 + At-1
n
n= number of period
Weighted moving average – More recent values
in a series are given more weight in computing
the forecast.
wnAt-n + … wn-1At-2 + w1At-1
Ft = WMAn=
n=total amount of number of weights
MGMT 405, POM, 2010/11. Lec Notes
n
27
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Forecasting; Chapter 3
Simple Moving Average
Actual
MA5
47
45
43
41
39
37
MA3
35
1
2
3
4
5
6
7
8
9
10 11 12
At-n + … At-2 + At-1
Ft = MAn=
n
28
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Forecasting; Chapter 3
Simple Moving Average
 An averaging period (AP) is given or selected
 The forecast for the next period is the arithmetic
average of the AP most recent actual demands
 It is called a “simple” average because each period
used to compute the average is equally weighted
 It is called “moving” because as new demand data
becomes available, the oldest data is not used
 By increasing the AP, the forecast is less responsive
to fluctuations in demand (low impulse response and
high noise dampening)
 By decreasing the AP, the forecast is more responsive
to fluctuations in demand (high impulse response and
low noise dampening)
29
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Forecasting; Chapter 3
Exponential Smoothing
Ft = Ft-1 + (At-1 - Ft-1)
Ft = forecast for period t
Ft-1 = forecast for the previous period
= smoothing constant
At-1 = actual data for the previous period
 Premise--The most recent observations might have
the highest predictive value. Therefore, we should
give more weight to the more recent time periods
when forecasting.
 Weighted averaging method based on previous
forecast plus a percentage of the forecast error
 A-F is the error term,  is the % feedback
30
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Forecasting; Chapter 3
Exponential Smoothing Forecasts
The weights used to compute the forecast
(moving average) are exponentially distributed.
The forecast is the sum of the old forecast and
a portion (a) of the forecast error (A t-1 - Ft-1).
The smoothing constant, , must be between
0.0 and 1.0.
A large  provides a high impulse response
forecast.
A small  provides a low impulse response
forecast.
31
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Forecasting; Chapter 3
Example-Moving Average
Central Call Center (CCC)
wishes to forecast the number of
incoming calls it receives in a day
from the customers of one of its
clients, BMI.
CCC schedules the appropriate
number of telephone operators
based on projected call volumes.
CCC believes that the
most recent 12 days of call
volumes (shown on the next
slide) are representative of
the near future call volumes.
32
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Example-Moving Average
Forecasting; Chapter 3
Moving Average
Use the moving average method with an AP = 3
days to develop a forecast of the call volume in
Day 13 (The 3 most recent demands)
 compute a three-period average forecast given
scenario above:
F13 = (168 + 198 + 159)/3 = 175.0 calls
33
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Forecasting; Chapter 3
Example-Weighted Moving Average
 Weighted Moving Average (Central Call Center )
 Use the weighted moving average method with an AP = 3
days and weights of .1 (for oldest datum), .3, and .6 to
develop a forecast of the call volume in Day 13.
 compute a weighted average forecast given scenario
above:

F13 = .1(168) + .3(198) + .6(159) = 171.6 calls
1
 Note: The WMA forecast is lower than the MA forecast
because Day 13’s relatively low call volume carries
almost twice as much weight in the WMA (.60) as it does
in the MA (.33).
34
MGMT 405, POM, 2010/11. Lec Notes
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Forecasting; Chapter 3
Example-Exponential Smoothing
 Exponential Smoothing (Central Call Center)
 Suppose a smoothing constant value of .25 is used and
the exponential smoothing forecast for Day 11 was
180.76 calls.
 what is the exponential smoothing forecast for Day 13?
 F12 = 180.76 + .25(198 – 180.76) = 185.07
 F13 = 185.07 + .25(159 – 185.07) = 178.55
35
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Forecasting; Chapter 3
Example 2-Exponential Smoothing
Period
Actual
1
2
3
4
5
6
7
8
9
10
11
12
Alpha = 0.1 Error
42
40
43
40
41
39
46
44
45
38
40
42
41.8
41.92
41.73
41.66
41.39
41.85
42.07
42.36
41.92
41.73
Alpha = 0.4 Error
-2.00
1.20
-1.92
-0.73
-2.66
4.61
2.15
2.93
-4.36
-1.92
42
41.2
41.92
41.15
41.09
40.25
42.55
43.13
43.88
41.53
40.92
-2
1.8
-1.92
-0.15
-2.09
5.75
1.45
1.87
-5.88
-1.53
 Exponential Smoothing (Actual Demand forecasting )
 Suppose a smoothing constant value of .10 is used and the exponential
smoothing forecast for the previous period was 42 units (actual demand
was 40 units).
 what is the exponential smoothing forecast for the next periods?
 F3 = 42 + .10(40 – 42) = 41.8
 F4 = 41.8 + .10(43 – 41.8) = 41.92
MGMT 405, POM, 2010/11. Lec Notes
36
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example 2-Exponential Smoothing
Graphical presentation
Actual
Demand
50
 = .4
45
 = .1
40
35
1
2
3
4
5
6
7
8
9 10 11 12
Period
37
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Forecasting; Chapter 3
Trend Projection
 The simplest form of time series is projecting the
past trend by fitting a straight line to the data either
visually or more precisely by regression analysis.
 Linear regression analysis establishes a relationship
between a dependent variable and one or more
independent variables.
 In simple linear regression analysis there is only one
independent variable.
 If the data is a time series, the independent variable
is the time period.
 The dependent variable is whatever we wish to
forecast.
38
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Forecasting; Chapter 3
Linear Trend Equation
Ft
Ft = a + bt
0 1 2 3 4 5
t
 Ft = Forecast for period t
 t = Specified number of time periods
 a = Value of Ft at t = 0
 b = Slope of the line
39
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Forecasting; Chapter 3
Trend Projection
 Linear Trend:
St = S 0 + b t
b = Growth per time period
 Constant Growth Rate
St = S0 (1 + g)t
g = Growth rate
 Estimation of Growth Rate
ln St = ln S0 + t ln (1 + g)
40
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Forecasting; Chapter 3
Trend Projection- Simple Linear Regression
 Regression Equation

This model is of the form:

Y = a + bX
 Y = dependent variable (the value of time series to be
forecasted for period t)
 X = independent variable ( time period in which the time
series is to be forecasted)
 a = y-axis intercept (estimated value of the time series, the
constant of the regression)
 b = slope of regression line (absolute amount of growth per
period)
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Forecasting; Chapter 3
Trend Projection- Calculating a and b
 Constants a and b
 The constants a and b are
computed using the equations
given:
 Once the a and b values are
computed, a future value of X
can be entered into the
regression equation and a
corresponding value of Y (the
forecast) can be calculated.
x  y- x xy

a=
n  x -( x)
2
2
b=
2
n xy- x y
n x -( x)
2
2
42
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© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Trend Projection- Calculating a and b
Or If formula b is used first, it may be used
formula a in the following format:
b=
n xy- x y
n x -( x)
2
2
Y  b X

a=
n
43
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© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example 1 for Trend Projection- Electricity sales

Suppose we have the data show electricity
sales in a city between 1997.1 and 2000.4. The
data are shown in the following table. Use time
series regression to forecast the electricity
consumption (mn kilowatt) for the next four
quarters.

Do not forget to use the formulae a and b
44
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Forecasting; Chapter 3
Example1 for Trend Projection
TP
1997Q1
1997Q2
1997Q3
1997Q4
1998Q1
1998Q2
1998Q3
1998Q4
1999Q1
1999Q2
1999Q3
1999Q4
2000Q1
2000Q2
2000Q3
2000Q4
T
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Q
11
15
12
14
12
17
13
16
14
18
15
17
15
20
16
19
sq ( T )
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
Qx T
11
30
36
56
60
102
91
128
126
180
165
204
195
280
240
304
sum
x
136
y
244
sq x
1496
xy
2208
a
b
11.9
0.394118
MGMT 405, POM, 2010/11. Lec Notes
a=
b=
2
x
  y- x xy
n x2 -( x)2
n xy- x y
n x2 -( x)2
sq sum x
18496
45
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example1 for Trend Projection
Y = 11.90 + 0.394X
Y17 = 11.90 + 0.394(17) = 18.60 in the first quarter of 2001
Y18 = 11.90 + 0.394(18) = 18.99 in the second quarter of 2001
Y19 = 11.90 + 0.394(19) = 19.39 in the third quarter of 2001
Y20 = 11.90 + 0.394(20) = 19.78 in the fourth quarter of 2001
Note: Electricity sales are expected to increase
by 0.394 mn kilowatt-hours per quarter.
46
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example 2 for Trend Projection
 Estimate a trend line using regression analysis

Year
Time
Period
(t)
Sales
(y)
2003
2004
2005
2006
2007
2008
1
2
3
4
5
6
20
40
30
50
70
65
Use time (t) as the
independent variable:
yˆ = b0  b1t
47
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example 2 for Trend Projection
(continued)
 The linear trend model is:
2003
2004
2005
2006
2007
2008
1
2
3
4
5
6
Sales
(y)
20
40
30
50
70
65
yˆ = 12.333  9.5714 t
Sales trend
sales
Year
Time
Period
(t)
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
Year
48
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example 2 for Trend Projection
(continued)
 Forecast for time period 7:
Sales
(y)
2003
2004
2005
2006
2007
2008
2009
1
2
3
4
5
6
7
20
40
30
50
70
65
??
yˆ = 12.333  9.5714 (7)
= 79.33
Sales
sales
Year
Time
Period
(t)
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
Year
49
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example for Trend Projection using-Non linear form
St = S0 (1 + g)t
 Running the regression above in the form of logarithms:
ln St = ln S0 + t ln (1 + g) to construct the equation
which has coefficients a and b.
 Antilog of 2.49 is 12.06 and Antilog of 0.026 is 1.026.
Coefficients
Standard Error t Stat
Intercept 2.486914 0.062793 39.60489
T
0.026371 0.006494 4.060874
St = 12.06(1.026)t
50
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example for Trend Projection using
St = S0 (1 + g)t
 S17= 12.06(1.026)17 = 18.66 in the first quarter of 2001
 S18= 12.06(1.026)18 = 19.14 in the second quarter of 2001
 S19= 12.06(1.026)19 = 19.64 in the third quarter of 2001
 S20= 12.06(1.026)20= 20.15 in the fourth quarter of 2001
These forecasts are similar to those obtained by
fitting a linear trend
51
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Evaluating Forecast-Model Performance
 Accuracy
 Accuracy is the typical criterion for judging the
performance of a forecasting approach
 Accuracy is how well the forecasted values match the
actual values
 Accuracy of a forecasting approach needs to be monitored to
assess the confidence you can have in its forecasts and
changes in the market may require reevaluation of the
approach
 Accuracy can be measured in several ways
 Standard error of the forecast (SEF)
 Mean absolute deviation (MAD)
 Mean squared error (MSE)
 Mean absolute percent error (MAPE)
 Root mean squared error (RMSE)
52
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Forecast Accuracy
Error - difference between actual value and
predicted value
Mean Absolute Deviation (MAD)
Average absolute error
Mean Squared Error (MSE)
Average of squared error
Mean Absolute Percent Error (MAPE)
Average absolute percent error
Root Mean Squared Error (RMSE)
Root Average of squared error
MGMT 405, POM, 2010/11. Lec Notes
53
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
MAD, MSE, and MAPE
=
MAD
 Actual
 forecast
n
MSE
=
 ( Actual
 forecast)
2
n -1
MAPE =
RMSE =
( Actual
 forecas
t
n
/ Actual*100)
2
(
A

F
)
 t t
MGMT 405, POM, 2010/11. Lec Notes
n
54
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
MAD, MSE and MAPE
 MAD
 Easy to compute
 Weights errors linearly
 MSE
 Squares error
 More weight to large errors
 MAPE
 Puts errors in perspective
 RMSE
 Root of Squares error
 More weight to large errors
55
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example-MAD, MSE, and MAPE
Compute MAD, MSE and MAP for the following data showing actual and the
predicted numbers of account serviced.
Period
1
2
3
4
5
6
7
8
MAD=
MSE=
MAPE=
Actual
217
213
216
210
213
219
216
212
2.75
10.86
1.28
Forecast
215
216
215
214
211
214
217
216
(A-F)
2
-3
1
-4
2
5
-1
-4
-2
|A-F|
2
3
1
4
2
5
1
4
22
(A-F)^2 (|A-F|/Actual)*100
4
0.92
9
1.41
1
0.46
16
1.90
4
0.94
25
2.28
1
0.46
16
1.89
76
10.26
22/8=2.75
76/8-1=10.86
10.26/8=1.28 %
56
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example: Central Call Center-Forecast Accuracy - MAD
Which forecasting method (the AP = 3
moving average or the a = .25 exponential
smoothing) is preferred, based on the MAD
over the most recent 9 days? (Assume that
the exponential smoothing forecast for Day 3
is the same as the actual call volume.)
57
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
E AP4 = 161-187.3=26.3
EEXP4 = 161-186=25.0
Forecasting; Chapter 3
Example: Central Call Center-Forecast Accuracy - MAD
F4MA = (186 + 217 + 159)/3 = 187.33 calls
F4EXP = 186 + .25(186 – 186) = 186.00 calls
MGMT 405, POM, 2010/11. Lec Notes
MADMA = 20.5/9 = 2.27
MADEXP = 18.0/9= 2.0
58
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example-For MA Techniques
Electricity sales data from 2000.1 to 2002.4 (t=12)-Forecast Accuracy - RMSE
1
2
Quarter Firm's ams (A)
1
20
2
22
3
23
4
24
5
18
6
23
7
19
8
17
9
22
10
23
11
18
12
23
13
3
Tqmaf (F)
4
A-F
21.6666667
23
21.6666667
21.6666667
20
19.6666667
19.3333333
20.6666667
21
2.333333
-5
1.333333
-2.66667
-3
2.333333
3.666667
-2.66667
2
total
5
6
sq(A-F) Fqmaf (F)
5.444444
25
1.777778
7.111111
9
5.444444
13.44444
7.111111
4
78.33333
21.3333333
AP = 3 moving average
MGMT 405, POM, 2010/11. Lec Notes
21.4
22
21.4
20.2
19.8
20.8
19.8
7
A-F
8
sq(A-F)
1.6
-3
-4.4
1.8
3.2
-2.8
3.2
total
2.56
9
19.36
3.24
10.24
7.84
10.24
62.48
20.6
AP = 5 moving average
59
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example-For MA Techniques
Electricity sales data from 2000.1 to 2002.4 (t=12)-Forecast Accuracy - RMSE
RMSE =
(A  F )
t
2
t
n
RMSE for 3-qma=2.95 Sqroot of 78.33/9=2.95
RMSE for 5-qma=2.99
Sqroot of 62.48/7=2.98
Thus three-quarter moving average forecast is marginally
better than the corresponding five- moving average
forecast.
60
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
(20+22+...23)/12=21=F1
Ft 1 = wAt  (1  w) Ft
Forecasting; Chapter 3
Example-Exponential Smoothing Forecast Accuracy - RMSE
1
2
3
QuarterFirm's ams (A)(F) w=0.3
1
20
21
2
22
20.7
3
23
21.09
4
24
21.663
5
18
22.3641
6
23
21.05487
7
19
21.63841
8
17
20.84689
9
22
19.69282
10
23
20.38497
11
18
21.16948
12
23
20.21864
13
21
4
A-F
-1
1.3
1.91
2.337
-4.3641
1.94513
-2.63841
-3.84689
2.30718
2.615026
-3.16948
2.781363
total
5
sq(A-F)
1
1.69
3.6481
5.461569
19.04537
3.783531
6.961202
14.79853
5.323078
6.838359
10.04562
7.735978
87.19
6
(F) w=0.5
21
20.5
21.25
22.125
23.0625
20.53125
21.76563
20.38281
18.69141
20.3457
21.67285
19.83643
8
sq(A-F)
1
2.25
3.0625
3.515625
25.62891
6.094727
7.648682
11.44342
10.94679
7.045292
13.48984
10.0082
101.5
21.5
F2= 0.3 (20)+(1-0.3) 21=20.7 with w=0.3
F2= 0.5 (20)+(1-0.5) 21=20.5 with w=0.5
MGMT 405, POM, 2010/11. Lec Notes
7
A-F
-1
1.5
1.75
1.875
-5.0625
2.46875
-2.76563
-3.38281
3.308594
2.654297
-3.67285
3.163574
total
61
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example-Exponential Smoothing Forecast Accuracy - RMSE
F2= 0.3 (20)+(1-0.3) 21=20.7 with w=0.3
F2= 0.5 (20)+(1-0.5) 21=20.5 with w=0.5
RMSE =
RMSE with w=0.3 is 2.70
2
(
A

F
)
 t t
n
RMSE with w=0.5 is 2.91
Both exponential forecasts are better than the
previous techniques in terms of average values.
62
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Seasonal Variation
63
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Seasonal Variation
Ratio to Trend Method
Actual
Trend Forecast
Ratio =
Seasonal
Adjustment =
Adjusted
Forecast
=
Average of Ratios for
Each Seasonal Period
Trend
Forecast
Seasonal
Adjustment
64
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Seasonal Variation
Ratio to Trend Method:
Example Calculation for Quarter 1
Trend Forecast for 2001.1 = 11.90 + (0.394)(17) = 18.60
Seasonally Adjusted Forecast for 2001.1 = (18.60)(0.887) = 16.50
YEAR Forecasted
1997Q1
12.29
1998Q1
13.87
1999Q1
15.45
2000Q1
17.02
Actual
11
12
14
15
AV
Act/Forec
0.895037
0.865177
0.906149
0.881316
0.88692
0.887
Deseasonalize data=actual sales/seasonal relative (index)
MGMT 405, POM, 2010/11. Lec Notes
65
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Seasonal Variation
 Select a representative historical data set.
 Develop a seasonal index for each season.
 Use the seasonal indexes to deseasonalize the data.
 Perform linear regression analysis on the
deseasonalized data.
 Use the regression equation to compute the
forecasts.
 Use the seasonal indexes to reapply the seasonal
patterns to the forecasts.
66
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example: Computer Products Corp.
 Seasonalized Times Series Regression Analysis
 An analyst at CPC wants to develop next year’s quarterly
forecasts of sales revenue for CPC’s line of Epsilon
Computers. The analyst believes that the most recent 8
quarters of sales (shown on the next slide) are representative of
next year’s sales. Calculate the seasonal indexes
67
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example: Computer Products Corp.
68
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Example: Computer Products Corp.
69
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Unseasonalized vs. Seasonalized
1
2
3
4
5
6
7
8
9
10
11
…
Seasonal
Index
Deseasonalized
Sales
23
40
25
27
32
48
33
37
37
50
40
0.825
1.310
0.920
0.945
0.825
1.310
0.920
0.945
0.825
1.310
0.920
…
27.88
30.53
27.17
28.57
38.79
36.64
35.87
39.15
44.85
38.17
43.48
…
27.88 =
23
0.825
Sales: Unseasonalized vs. Seasonalized
Sales
Quarter
Seasonalized
Sales
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
11
Quarter
Sales
Deseasonalized Sales
70
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Deflating a Time Series
 Observed values can be adjusted to base year
equivalent
 Allows uniform comparison over time
 Deflation formula:
y adj t
yt
=
(100)
It
where
yadj t
= adjusted time series value at time t
yt = value of the time series at time t
It = index value at time t
71
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Deflating a Time Series: Example
 Which movie made more money (in real terms)?
Movie
Title
Total Gross
$
1939
Gone With the
Wind
199
1977
Star Wars
461
1997
Titanic
601
Year
(Total Gross $ = Total domestic gross ticket receipts in $millions)
72
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Deflating a Time Series: Example
Movie
Title
Total
Gross
(base year = 1984)
Gross adjusted
to 1984 dollars
1939
Gone With
the Wind
199
13.9
1431.7
1977
Star Wars
461
60.6
760.7
1997
Titanic
601
160.5
374.5
Year
GWTW adj 1984 =
CPI
199
(100) = 1431.7
13.9
MGMT 405, POM, 2010/11. Lec Notes
 GWTW made about twice as
much as Star Wars, and about
4 times as much as Titanic
when measured in equivalent
dollars
73
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.
Forecasting; Chapter 3
Thanks
74
MGMT 405, POM, 2010/11. Lec Notes
© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved.