Principles of Business Forecasting by Keith Ord & Robert Fildes

Author:Keith Ord & Robert Fildes
Language: eng
Format: mobi
Publisher: Cengage Textbook
Published: 2012-07-19T04:00:00+00:00

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Chapter 9

Model Building

Introduction

Even the simplest business process is likely to be driven by a large number of different fac-

tors. Many of these will have only a minor impact. Our objective in statistical modeling is to

identify the key elements and then to be prepared to ascribe the remaining variation to the

random or unexplained error term that appears in all our models. In Chapters 7 and 8 we listed

our key assumptions, and the model will be effective only if those assumptions are satisfied,

at least approximately. In Section 8.5, we saw how to examine some of these assumptions by

graphical means. In this chapter, guided by these diagnostic procedures, we develop more

accurate forecasting models. However, we should always remember two things:

• Our forecasts rely on the future being governed by the same rules and relationships

as in the past;

• Our conclusions about the behavior of processes are based upon sample data and

can never be definitive.

The model specified in Assumptions R1 and R2 in Section 8.5 assumes that we have iden-

tified all of the relevant variables; however, key variables may have been omitted, includ-

ing possible changes in conditions (e.g., seasonal effects or changes in legal requirements).

Some of the possible departures from the basic assumptions about the error process are the

presence of (auto)correlation, the lack of constancy in the variance, and a nonnormal dis-

tribution, possibly caused by outliers. We explore each of these issues in turn. In Section 9.1, we introduce indicator (or dummy) variables and show how these tools can be used to

address various problems, including seasonal patterns. In Section 9.2, we consider the

introduction of lagged values of the dependent variable into the model in order to account

for autocorrelation. A natural extension is to combine lagged values of the dependent variable

with other variables, and this option is explored in Section 9.3.

In principle, we might consider a large number of predictor variables and incorporate lags

of various orders for each of these input variables. If we are guided by strong theoretical con-

siderations, such steps can be very valuable. More commonly, we are guided only by the vague

intuition or fond hope that some of these variables might be useful. Without clear guidelines,

we may arrive at a plethora of variables and no strong reason to prefer one set of inputs over

another. We therefore need to develop methods that identify plausible models from among the

many alternatives; we refer to these methods as variable selection methods and introduce them

in Section 9.4. An additional problem arising from an increased number of inputs is that we

may find that some or all of the variables are very highly correlated. This finding would have

two undesirable effects: (1) Our estimates of the individual slope coefficients may become

highly unstable, to the point that identifying the “best” forecasting model becomes difficult,

and (2) the magnitudes of the estimated effects may be unrealistic. We refer to the condition

in which two or more of the variables are highly correlated as multicollinearity among the inputs. In Section 9.5, we consider how to check for the presence of multicollinearity and use

variable selection methods as one way to handle the difficulty.

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