Traditional Problem Definition - Computational Intelligence in Time Series Forecasting - page 48

forecasting is closely linked with the term prediction . The earliest researchers
working on methods of determination of future values of empirical functions,
based on a set of collected values, coined the term prediction , rather than
forecasting. Forecasting is predominantly associated with the problem of time
series analysis. The term prediction, however, is still preferably used in systems
and control engineering.

2.9.1 Some Forecasting Issues

Forecasting the future values of a time series is defined in the following way:

x given a set of observed values x 1 , x 2 , x 3 , ..., x n of a time series, the future
value x n+ 1 , x n+ 2, …, should be estimated
x q-steps ahead prediction x n+q , calculated at time point n , is denoted by
(),

ˆ n q

where the integer q is called the lead time .

x

Generally, the forecasting approaches can be classified into

x objective forecasts , made on a subjective basis using judgement, intuition,
commercial knowledge and any other relevant information
x univariate forecasts , based entirely on fitting a one-dimensional model to
the collected data and on extrapolation of the time series pattern
x multivariate forecasts , based on simultaneous observation of two or more
variables and on models of multivariate time series.
In practice, a forecasting approach can include a combination of two of the above
approaches. For example, univariate forecasts - after being carried out - can be
adjusted subjectively. Or, put in another way, the marketing forecast based on
various predictions developed statistically from the past data can be combined with
the experience or knowledge of people deeply involved in the market. Finally, the
simplest way of more reliable forecasting takes into account the combination of
two or more weighted objective forecast estimations to calculate the final forecast
value (see Section 2.9.6).
Before selecting a forecasting method it is essential to consider how this is to
be used, what forecasting accuracy is expected, what computational resources are
available, how many items are to be forecast, how much data are available, and
how far ahead forecasts are needed. Furthermore, the forecasting method may
somehow depend on the required lead time, although in engineering it is mainly
short-term forecasts that are of interest, whereas in management it is mostly lead
time of nine months that may be of interest. For example, in stock control, the lead
time for which forecasts are required is the time between ordering an item and its
delivery, which is usually a few weeks or a few months.
Apart from this, some forecasting methods simply produce point forecasts. But
in some cases it is desirable to produce interval forecasts. Some procedures, such
as the one from Box-Jenkins, enable one to do this by addressing the upper and
lower limits on a subjective basis.
Basically, for all forecasting approaches, plotting the time series data is
recommended as the first step of data analysis. This is because much useful