Example 16.7
Forecasting Quarterly Sales at a
Pharmaceutical Company
Pharmaceutical Sales.xlsx
• This file contains quarterly sales data for a large
pharmaceutical company from first quarter 1998
through fourth quarter 2007 (in millions of dollars).
• The time series plot shown on the next slide
indicates a fairly consistent upward trend, with a
relatively small amount of noise.
• Can Holt’s method be used to provide reasonably
accurate forecasts of this series?
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Solution
• We illustrate how StatTools can be used to
implement Holt’s method on the sales data.
• This requires two steps: identifying the data set
and then doing the forecasting.
• StatTools works with data sets,
which you have to specify before
performing any statistical analysis.
The data in this file, shown here,
are in the range A1:B41.
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Solution -- continued
• To specify the data set, select the StatTools/Data
Set Manager menu item, fill out the resulting dialog
box as shown on the next slide, and click on OK.
• Now you are ready to perform a statistical analysis
on this data set.
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Applying Holt’s Method to
Forecast
• To apply Holt’s method, select Forecast from the Time Series &
Forecasting dropdown on the StatTools ribbon.
• There are three tabs on the resulting dialog box. The most important is
the Forecast Settings tab, which you should fill in as shown on the next
slide.
• This indicates that
–
–
–
–
Sales is the time series variable of interest
we want eight quarters of future forecasts
we are using Holt’s method,
we want to optimize the smoothing constants
• The other two tabs are straightforward and are not shown here.
• The Time Scale tab lets you indicate that these are quarterly data,
beginning with quarter 1 of 1998, and the Graphs to Display tab lets
you choose which of three graphs you want StatTools to create.
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Discussion of the Results
• The StatTools output for Holt’s method consists of
three sections: summary data, detailed data, and
charts. The summary data appears below.
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Discussion of the Results -continued
• They indicate that the best smoothing constants are 0.574
(for level) and 0.0 (for trend). These produce the error
measures shown.
• For example, MAPE is 4.40%. Although the smoothing
constants shown here minimize RMSE, you can experiment
with other smoothing constants in cells B9 and B10.
• For example, if you set both smoothing constants equal to
0.2, you will see that RMSE increases to 349.54 and MAPE
increases to 5.56%.
• Clearly, the choice of smoothing constants does make a
difference.
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Discussion of the Results -continued
• Two useful charts produced by StatTools appear on the
next two slides.
• The first of these superimposes the forecasts onto the
original series. It also shows the projected forecasts at the
right. We see that the forecasts track the series well, and
the future projections follow the clear upward trend.
• The second shows the series of forecast errors. If the
forecast method is working well, this chart should be
“random,” with no apparent patterns. The only suspicious
pattern evident here is that the zigzags appear to be
increasing in magnitude through time.
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Discussion of the Results -continued
• For our purposes, Holt’s method seems to be
doing very well with this data set. It tracks the
historical data closely, and it accurately projects
the upward trend.
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