There are a number of techniques which provide a projection of a statistical series into the future and which rely entirely on analysis of the series. They are based on the assumption that past performance will be a guide to the future.Whether such an assumption is correct depends, of course, on many factors, including the age of the product, the point reached in its life cycle, and the length of time for which the forecast is made. There are many methods which are very valuable for short-term forecasts of a few months, but which are rarely accurate beyond this.One use of these methods is to gain perspective: to see where a trend might lead. If this projected position is patently impossible the forecaster will have learnt something about the data.
i.
Simple growth pattern
A commonly used method of forecasting is based on the average annual growth
rate calculated over a period, simply worked out by expressing the latest year
as an index of the earliest and working out the growth rate from a book of
compound interest tables. Variations on this theme include allowing for erratic
movements in the data or in a typical year. It may also be postulated that the
expected change is a particular percentage of the previous growth rate.
ii.
Moving averages
A moving average is a method of eliminating regular seasonal or cyclical
patterns from the data to indicate the underlying smoothed trend. (Having
calculated the trend, it then becomes possible to eliminate it statistically,
to enable a study to be made of the seasonal factors.) Each point in the moving
average is the mean of a number of consecutive points of the series: the number
of data points is chosen by judgement to give the period which best eliminates
the seasonal irregularities. The average used may be the arithmetic or
geometric means, or the median. Moving averages are rarely useful for long-term
forecasts. One of their disadvantages is that they always fall short of the
actual data available: any projection has to cover not only the future but also
some of the past.
iii.
Exponential smoothing
Another technique for short-term forecasting, which has a particular value for
inventory and production control systems, is exponential smoothing. The method
is based on a moving average which is exponentially weighted so that the more
recent data is given a greater weighting, and that the past forecasting error
is taken into account in each successive forecast. A full description of the
method is given by Coutie et al.5 Statistical confidence limits may also be
calculated.A more sophisticated variant of exponential smoothing is the
Box–Jenkins method which is even more accurate in short-term forecasting (up to
three months).
iv.
Mathematical trends
A number of mathematical formulae are available for calculating a trend line in
a time series and extending this line to some future point. The simplest, and
often a valuable starting position, is to fit a line on a graph by eye, using a
ruler so that the area on the graph under the trend line is approximately equal
to the area above it. By eye alone the line of ‘best fit’ is difficult to place
exactly, but may be calculated mathematically by the method of least squares.
An indication of the likely validity of a least squares trend line as a method
for predicting the future trend of a series of data can be obtained using the
Cartesian coordinate method. This will reveal whether the data has any
correlation or if it is completely dissociated. A full description of these
methods will be found in most books onelementary statistics, e.g. Moroney.