BUSINESS FORECASTING ASSIGNMENT
DUE DATE: OCTOBER 24, 2011
INSTRUCTIONS:
This is a group assignment. .
All answers and analysis should be neatly typed (double spaced) and labeled
properly. Summarize and attach your computer output to your analysis as
appendices.
Grading will be based on the following:
 Demonstration of the understanding and use of forecasting
analytical tools 65%
 Clarity of presentation of report, organization, format and writing
skills 20% (Clarity of report and simplification of results so that the
average person may understand the report will be rewarded)
 Relevance of conclusions drawn 10%
 Support of analysis with referenced materials 5%
There are 3 cases in total. You are required to complete two cases. Case #1 is
mandatory..
CASE #1 (you must complete this case)
This case introduces you to short term forecasting models applied to forecasting
rates of return on stocks. Specifically, it introduces you to
 Accessing data in FORECASTXTM (the program that came with the
textbook)
 Plotting and Interpreting time-series plots
 Testing for stationarity in data series
 Applying transformation to non-stationary data
 Generating short term forecasting using various models and ForecastX
 Judging the relative accuracy of the forecasting models
 Testing random walk hypothesis on the stock market
The spreadsheet for this problem is SP500.XLS. It contains the following data:
Variable: SPCOM
Data range: December 2002 – August 2011
The series, SPCOM, is the monthly S&P500 composite Index (at close, not
adjusted for dividend and splits)
REQUIRED:
1.
Create a time series plot of the data and comment on it.
2.
Using ForecastX, test for stationarity by estimating the autocorrelation
function and the related correlogram. Comment on the
Autocorrelation coefficients and the correlogram.
Financial theory centers on rates of return rather than actual stock prices.
Accordingly,
REQUIRED:
Transform your series into a new series labeled %SPCOM i.e. create a new
column with the new variable name %SPCOM. % SPCOM is the percentage
change in the composite index over the period. Use the formula
𝑺𝑷𝑪𝑶𝑴𝒕
= 𝒍𝒏 (𝑺𝑷𝑪𝑶𝑴
𝒕−𝟏
).
(You should end up with one less observation)
This is a transformation that will convert your data into continuously compounded
rates. This practice is common in Finance rather than annual or discrete
compounding
3.
Plot the %SPCOM series and comment on the plot
TESTING THE RANDOM WALK THEORY
The theory of efficient market states that stock prices reflect all relevant
information immediately and therefore there is no useful information in past stock
prices. This implies that the best forecast of today’s rate of return conditional on
current information is yesterday’s actual return (basic naïve model). All
adjustments in stock prices to new information occur immediately (random walk
model)  basic naïve model is consistent with the random walk model. If, on the
other hand, stock prices take time to adjust to new information, then data in the
distant past may be useful (adjusted naïve model).
REQUIRED:
4.
Using the last 4 months (May – August 2011) data of the %SPCOM
series as the holdout period, crudely test the random walk theory by
using both the basic naïve method and the adjusted naïve model to
forecast the holdout period.
5.
Calculate, but do not limit to, the ME, MAPE, MSE, RMSE for both the
fit and the forecast for each model
6.
Using the original data series (not %SPCOM), and the same
procedures , generate forecast and several accuracy statistics for each
of the following 5 models:
Single Exponential Smoothing (select the optimal smoothing constant,
)
Adaptive Exponential Smoothing
Brown’s Double model
Holt’s 2- parameter model
Winter’s 3- parameter model
7.
On the basis of the accuracy statistics, pick the superior model (fit and
forecast) and speculate as to why this model forecast the data better
than the others. What is the implication of your selection regarding the
random walk hypothesis?
8.
Plot the forecasts series and the actual returns for the “holdout period”
(May – August 2011) for the ‘best’ method and the naïve method. (If
the naïve method is the best, then plot the naïve and the second best
method) and comment on your plot
(4 lines)
9.
Based on the most superior model chosen above, use the entire data,
Dec 2002 – August 2011, to generate a one period ahead forecast
(only one forecast) for September 2011. How does your data compare
to the actual data for September 2011? (The actual data for
September 2011 can be obtained from Yahoo Finance (the close index
for S&P 500 for the month )
10.
What are the implications of your forecasts on international business?
CASE #2
This assignment is designed to test your knowledge about dealing with time
series decomposition in the context of forecasting. Specifically,
 Deseasonalizing Data
 Performing Trend curve Analysis
 Generating Time Series Decomposition Forecasts using FORECASTXTM
 Comparing Decomposition Forecast with Expert Selection Forecasts using
Procast
CASE
Gerona Matthews owns a Used Clothing Export business in the Vancouver area.
Gerona is aware that her business is seasonal and would like to measure the
seasonal effect for two reasons. The first reason is to assist her in managing her
business and the second is to use it in a loan repayment negotiation with her
banker. Though Gerona feels good about the future of her business, she has not
done any concrete forecasting of future sales. Her creditors are a bit queasy
about her claim that “the future looks great” without any numbers to back her
statement. The monthly sales figures from all her stores were collected and
recorded in the Excel file SALES.XLS. (fictitious data)
Gerona has hired you to perform the following:
a.
Decomposition of her monthly sales figures
b.
Forecast her sales for the next six months based on this
decomposition.
REQUIRED
1.
What behavior characterizes the sales data? Plot her sales data and
comment.
2.
Using the classic Decomposition method, find the Trend and seasonal
indexes for Gerona’s sales, for the period October 2003 – September
2011. (You could try various trend curves and pick the best one) (Do
not generate any forecasts yet!).
3.
The forecast of national and local experts call for a slow improvement
in business in the future. Following this forecast, she has decided to
use the following C (cyclical factors) for her forecast (of the next six
months) : 1.03, 1.04, 1.04,.1.09, 1.10. 1.11. Turning to the irregular (I)
component for these months, she does not foresee any unusual events
except for December 2011. In that month, she plans to have an open
house along with reduced rates in most of her stores to be
accompanied by TV and radio advertisements. She expects this
promotion to lead to 15% increase in overall salesIrregular (I)
component for December 2011 would be 1.15
Using the entire data and her forecast of C and I, generate a forecast for the
next six months sales (October 2011 – March 2005) and make a
recommendation to Gerona’s creditors about the future of her business. (hint
combine forecasts of your trend and seasonal index in 2 above with her
forecast of C and I)
4.
What are the implications of your forecast on her business?
Case #3
Beer Sales Forecasting
Ace Brewery is one of the major breweries with sales in all parts of Canada. The
management of Ace Brewery has asked its Budget and Planning Department to
present a formal model to explain and predict beer sales.
In discussing the assignment with the whole management team at a recent
meeting, the head of the Budget and Planning Department, Ms. Angie Foster,
determined that management is divided on their beliefs about the determinants of
beer sales.
She discovered that there were two main ‘Schools of thought’ based on the
theories advanced at this meeting. School 1 believes that unemployment rate
and weather conditions are responsible for most of the short-run variations in
beer consumption.
The main advocate of School 1, Ms. Paris Labatts, was heard to remark “When it
is hot people drink more, when people are unemployed, they drink less beer, it’s
that simple”.
Ms. Barbara Heineken, leader of the second group, eloquently argued that beer
sales have no causal factors except patterns based on past sales and that
whatever model is developed should be one that strictly predicts future sales
based on the patterns in the past data.
One issue that all the groups agreed on was the seasonal nature of beer sales
but not whether a trend exists in the seasonality.
Management wants Ms. Foster and her team to test these theories and develop
a model for projecting and forecasting beer sales. In particular, they want a
model to forecast beer sales for the next 4 months. If the model is successful,
they plan to use it through out the year in the planning process for projecting
budgets, financing needs and balance sheets.
Management wants the study confined to one area; since unemployment and
weather conditions vary so much across the country, there is no point in
developing a single country wide model for beer sales. It is management’s
opinion that a number of models should be developed—one for each major
selling area—and the total sales forecast calculated as the sum of the area
forecasts.
Ms. Foster has hired your group to undertake this project. She has provided you
with monthly historical sales data from the Vancouver area, the average monthly
temperatures and the monthly unemployment rates in Vancouver. These data
are presented in the file Beer.xls.
REQUIRED:
Part I
Write a report of no more than 800 words to Ms. Foster analyzing the data based
on your forecasting methods (models). This report would serve as a source for a
‘smaller’ report that Ms. Foster will be presenting to the Management team at a
later date.
a.
In this report be sure to
 detail your forecasting methodology, accuracy measures, errors and
confidence levels of your forecasts
 examine the forecasting abilities (accuracy) of the models.
b.
Based on your comparison, select the most appropriate forecasting
methodology for this company and provide beer sales forecasts for the
next four months (Feb 2006 – May 2006).
c.
Discuss any assumptions, impediments and challenges you may have
faced that may impact your forecasting
Guidelines: Your analysis of this case SHOULD begin with
exploring the Sales data to determine the characteristics and nature of the
data. This is important because it would give the Board a visual
representation of what is happening to their bottom-line.
This should be done through graphical plots and ACF analysis
The following graphs will be most helpful: Actual Data, Detrended Data,
Seasonally- adjusted Data, Detrended and Seasonally adjusted Data.
Description and analysis of the charts will give Ms. Forster an idea of the
nature of the Sales data. Is there a trend? Is it seasonal? Is there a trend
in the seasonality? etc. etc. A brief ACF analysis and brief explanation to
confirm the eye-ball analysis above will help cement the findings from the
charts
In addition:
Your model should be a multiple regression of Sales on Unemployment and
Temperature. You should report and interpret their regression equation paying
particular attention to the signs of the coefficient and discussing if the signs
conform to theory. You should report/interpret some ‘goodness of fit’ measures
such as adjusted Rsquared. Perform some diagnostic test of the model by
testing for multicollinearity and serial correlation (with the DW statistics).
Significance test on the coefficients, t-test is required.
You can try to improve on this model by including 11 dummies to represent the
months and include seasonality in the model.
Compare these two models (original regression and the one with the dummies)
and determine if the inclusion of the dummies actually does improve this model.
Using whatever model is finally chosen; present a forecast of sales for the next 4
months.
A graph showing this forecast will greatly enhance any presentation.
Conclusion should include challenges and problems encountered working with
the data provided and suggestion for improvements. Technical Issues: what is
the best approach, Information issues: inadequate historical data, missing
variables etc.