Management Science: The Art of
Modeling with Spreadsheets, 2e
Chapter 9: Short-Term Forecasting
S.G. Powell
K.R. Baker
© John Wiley and Sons, Inc.
PowerPoint Slides Prepared By:
Alan Olinsky
Bryant University
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9-1
Introduction
 Regression analysis can sometimes be useful
in short-term forecasting.
 A better approach is to base the forecast of a
variable on its own history, thereby avoiding
the need to specify a causal relationship and
to predict the values of explanatory variables.
 Our focus in this chapter is on time series
methods for forecasting.
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Forecasting with Time-Series
Models
 We make use of historical data for the phenomenon
we wish to forecast.
 We seek a routine calculation that may be applied
to a large number of cases and that may be
automated, without relying on any qualitative
information about the underlying phenomena.
 Short-term forecasts are often used in situations that
involve forecasting many different variables at
frequent intervals.
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Hypothesized Models
 The major components of such a model are
usually the following:



a base level
a trend
cyclic fluctuations
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Three Components of Time
Series Behavior
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The Moving Average Model
 The n-period moving average builds a forecast
by averaging the observations in the most
recent n periods:
At = (xt + xt–1 + … + xt–n+1) / n
 where xt represents the observation made in
period t, and At denotes the moving average
calculated after making the observation in
period t.
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Convention
 We adopt the following convention for the
steps in forecasting:



Make the observation in period t
Carry out the necessary calculations
Use the calculations to forecast period (t + 1)
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Worksheet for Calculating
Moving Averages
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Number of Periods to Include in
Moving Average
 There is no definitive answer to this question, but there is a
trade-off to consider.
 Suppose the mean of the underlying process remains stable:
If we include very few data points, then the moving average
exhibits more variability than if we include a larger number
of data points. In that sense, we get more stability from
including more points.
 Suppose there is an unanticipated change in the mean of the
underlying process:
If we include very few data points, our moving average will
tend to track the changed process more closely than if we
include a larger number of data points. In that case, we get
more responsiveness from including fewer points.
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Moving Average Calculations in
a Stylized Example
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Comparison of 4-week and 6week Moving Averages
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Measures of Forecast Accuracy
 MSE: the Mean Squared
Error between forecast and
actual
 MAD: the Mean Absolute
Deviation between forecast
and actual
 MAPE: the Mean Absolute
Percent Error between
forecast and actual
v
1
MSE =
( Ft  xt )2

(u  v  1) t u
v
1
MAD =
 Ft  xt
(u  v  1) t u
v
1
Ft  xt
MAPE =

(u  v  1) t u xt
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Comparison of Measures of
Forecast Accuracy
 The MAD calculation and the MAPE
calculation are similar: one is absolute, the
other is relative.
 We usually reserve the MAPE for
comparisons in which the magnitudes of two
cases are different.
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Excel Tip: Moving Average
Calculations
 Excel’s Data Analysis tool (Tools►Data
Analysis►Moving Average) contains an option for
calculating moving averages.
 Excel assumes that the data appear in a single
column, and the tool provides an option of
recognizing a title for this column, if it is included
in the data range.
 Other options include a graphical display of the
actual and forecast data and a calculation of the
standard error after each forecast.
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The Exponential Smoothing Model
 Exponential smoothing weighs recent
observations more than older ones.
St = xt + (1 – )St–1
 The parameter a is some number between zero
and one, called the smoothing constant.
 We refer to St as the smoothed value of the
observations, and we can think of it as our “best
guess” as to the value of the mean.
 Our forecasting procedure sets the forecast Ft+1
= St.
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Comparison of Weights Placed
on k-year-old Data
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Worksheet for Exponential
Smoothing Calculations
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Comparison of Smoothed and
Averaged Forecasts
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Exponential Smoothing Calculations
in a Stylized Example
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Excel Tip: Implementing
Exponential Smoothing
 Excel’s Data Analysis tool contains an option for
calculating forecasts using exponential smoothing.
 The Exponential Smoothing module resembles the
Moving Average module, but instead of asking for
the number of periods, it asks for the damping
factor, which is the complement of the smoothing
factor, or (1 – a).
 Again, there is an option for chart output and an
option for a calculation of the standard error.
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Exponential Smoothing with a
Trend
St = xt + (1 – )St–1
Tt = (St – St–1) + (1 – )Tt–1
where St is the smoothed value after the observation has been made
in period t, and Tt is the estimated trend.
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Trend Model Calculations with a
Trend in the Data
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Holt’s Method
 This more flexible procedure uses two smoothing
constants, as shown in the following formulas:
St = xt + (1 – )(St–1 + Tt–1)
Tt =  (St – St–1) + (1 –  )Tt–1
Ft+1 = St + Tt
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Holt's Method with a Trend in
the Data
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Exponential Smoothing with Trend
and Cyclic Factors
 We can take the exponential smoothing
model further and include a cyclical (or
seasonal) factor.
 For a cyclical effect, there are two types of
models: an additive model and a
multiplicative model.
 See text for formulas.
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*Using CB Predictor
 CB Predictor is an alternative to constructing
spreadsheet formulas for the specific purposes of
short-term forecasting.
 CB Predictor also provides a number of analyses
and reports automatically, whereas we might view
the time required to add such reports to our own
spreadsheet models counterproductive.
 Thus, for certain kinds of applications, it may make
sense to rely on CB Predictor rather than our own
custom spreadsheet models.
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*CB Predictor:
Alternative Forecasting Procedures
 Nonseasonal data with no trend
 Single Moving Average
 Single Exponential Smoothing
 Nonseasonal data with a trend
 Double Moving Average
 Double Exponential Smoothing
 Seasonal data with no trend
 Seasonal Additive
 Seasonal Multiplicative
 Seasonal data with a trend
 Holt-Winters’ Additive
 Holt-Winters’ Multiplicative
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*CB Preditor:
Single Moving Average
Data for the Curtis Distributors example
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CB Predictor Window: Input
Data Tab
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CB Predictor Window: Data
Attributes Tab
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CB Predictor Window: Method
Gallery Tab
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Single Moving Average Window
in CB Predictor
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CB Predictor: Results Tab
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CB Predictor:
Single Exponential Smoothing
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Advanced Options Window in
CB Predictor
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Preferences Window in CB
Predictor
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A Portion of the Report from CB
Predictor
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Summary
 Moving averages and exponential smoothing are
widely used for routine short-term forecasting.
 By making projections from past data, these
methods assume that the future will resemble the
past.
 However, the exponential smoothing procedure is
sophisticated enough to permit representations of a
linear trend and a cyclical factor in its calculations.
 Exponential smoothing procedures are adaptive.
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Summary
 Implementing an exponential smoothing procedure
requires that initial values be specified and a
smoothing factor be chosen.
 The smoothing factor should be chosen to trade off
stability and responsiveness in an appropriate
manner.
 Although Excel contains a Data Analysis tool for
calculating moving-average forecasts and
exponentially-smoothed forecasts, the tool does not
accommodate the most powerful version of
exponential smoothing, which includes trend and
cyclical components.
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