| Forecasting
Statistical forecasting
takes two different forms. Time series models are used
to forecast future values based on the history of the
variable being forecasted alone. Common approaches
include time series decomposition, exponential smoothing
and ARIMA models. While sometimes sufficient, time
series models often have forecast error too large to be
useful. A second approach often provides more precise
forecasts. This approach uses additional variables
which historically have high correlation to the variable
being forecasted. In the case of order forecasting for
a business, there may be several economic variables
which have shown a strong relationship to the historic
orders. It is particularly helpful to find economic
variables which are leading indicators. A leading
indicator is a variable which when offset in time has a
strong correlation to the variable being forecasted.
For example, suppose the series for semiconductor test
equipment sales could be shifted two time periods and
still have a high correlation to a particular test
product’s orders. This would mean that orders could be
forecasted two time periods ahead using observed data
for semiconductor test equipment sales.
Econometric forecast models which use two or more
economic variables to forecast a response variable of
interest can be developed using several statistical
methods. The most intuitive is perhaps multiple
regression. The problem with multiple regression models
is that there is an assumption of independence among the
regressor variables. This is likely not the case when
the regressor variables are economic factors each
correlated to the variable to be forecasted. While
there are some methods which can be used to reduce the
dependence among regressor variables, multiple
regression is often not a viable approach for
constructing an econometric forecast model.
An
alternative which has been used to good effect is
principal components regression. Here the economic
variables are first passed through a principal
components routine. Principal components are a way to
reduce the dimensionality of a potentially large set of
variables. They have the property of being independent
of each other while accounting for all the variation in
the original variables. Multiple regression is then
applied to the primary principal components rather than
the original econometric variables. Many econometric
variables can conceivably be included in the model.
Principal component regression has been effectively used
to forecast orders for product lines on a quarterly
basis. One drawback is that the resulting forecast
model is not as easy to interpret.
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