A time series is a sequence of
observations of a periodic random variable. Examples are the
monthly demand for a product, the annual freshman enrollment
in a department of the university and the daily flows in a river.
Time series are important for operations research because they
are often the drivers of decision models. An inventory model
requires estimates of future demands, a course scheduling and
staffing model for a university department requires estimates
of future student inflow, and a model for providing warnings
to the population in a river basin requires estimates of river
flows for the immediate future.
Time series analysis provides tools for selecting a model that
describes the time series and using the model to forecast future
events. Modeling the time series is a statistical problem because
observed data is used in computational procedures to estimate
the coefficients of a supposed model. Models assume that observations
vary randomly about an underlying mean value that is a function
of time.
On these pages we restrict attention to using historical time
series data to estimate a time dependent model. The methods
are appropriate for automatic, short term forecasting of frequently
used information where the underlying causes of time variation
are not changing markedly in time. In practice, the forecasts
derived by these methods are subsequently modified by human
analysts who incorporate information not available from the
historical data.
Our primary purpose in this section is to present the equations
for the four forecasting methods used in the *Forecasting*
add-in: moving average, exponential smoothing, regression and
double exponential smoothing. These are called smoothing methods.
Methods not considered include qualitative forecasting, multiple
regression, and autoregressive methods (ARIMA). Those interested
in more extensive coverage should visit the *Forecasting
Principles* site or read one of the several excellent
books on the topic. We used the book *Forecasting*, by
Makridakis, Wheelwright and McGee, John Wiley & Sons, 1983.
To use the Excel Examples workbook, you must have the Forecasting
add-in installed. Choose the *Relink* command to establish
the links to the add-in. |