Forecasting is the estimation of the value of a variable (or set of variables) at some future point in time. In this note we will consider some methods for forecasting. A forecasting exercise is usually carried out in order to provide an aid to decision-making and in planning the future. Typically all such exercises work on the premise that if we can predict what the future will be like we can modify our behaviour now to be in a better position, than we otherwise would have been, when the future arrives. Applications for forecasting include:

inventory control/production planning - forecasting the demand for a product enables us to control the stock of raw materials and finished goods, plan the production schedule, etc
investment policy - forecasting financial information such as interest rates, exchange rates, share prices, the price of gold, etc. This is an area in which no one has yet developed a reliable (consistently accurate) forecasting technique (or at least if they have they haven't told anybody!)
economic policy - forecasting economic information such as the growth in the economy, unemployment, the inflation rate, etc is vital both to government and business in planning for the future.

1. Types of forecasting problems/methods

One way of classifying forecasting problems is to consider the timescale involved in the forecast i.e. how far forward into the future we are trying to forecast. Short, medium and long-term are the usual categories but the actual meaning of each will vary according to the situation that is being studied, e.g. in forecasting energy demand in order to construct power stations 5-10 years would be short-term and 50 years would be long-term, whilst in forecasting consumer demand in many business situations up to 6 months would be short-term and over a couple of years long-term. The table below shows the timescale associated with business decisions.

The basic reason for the above classification is that different forecasting methods apply in each situation, e.g. a forecasting method that is appropriate for forecasting sales next month (a short-term forecast) would probably be an inappropriate method for forecasting sales in five years time (a long-term forecast). In particular note here that the use of numbers (data) to which quantitative techniques are applied typically varies from very high for short-term forecasting to very low for long-term forecasting when we are dealing with business situations.

Forecasting methods can be classified into several different categories:

qualitative methods - where there is no formal mathematical model, often because the data available is not thought to be representative of the future (long-term forecasting)
regression methods - an extension of linear regression where a variable is thought to be linearly related to a number of other independent variables
multiple equation methods - where there are a number of dependent variables that interact with each other through a series of equations (as in economic models)
time series methods - where we have a single variable that changes with time and whose future values are related in some way to its past values.

We shall consider each of these methods in turn.

1.1. Regression methods

You have probably already met linear regression where a straight line of the form Y = a + bX is fitted to data. It is possible to extend the method to deal with more than one independent variable X. Suppose we have k independent variables X₁, X₂, ..., X_k then we can fit the regression line

Y = a + b₁X₁ + b₂X₂ + ... + b_kX_k

This extension to the basic linear regression technique is known as multiple regression. Plainly knowing the regression line enables us to forecast Y given values for the X_i i=1,2,...,k.

1.2. Time series methods/analysis

Methods of this type are concerned with a variable that changes with time and which can be said to depend only upon the current time and the previous values that it took (i.e. not dependent on any other variables or external factors). If Y_t is the value of the variable at time t then the equation for Y_t is

Y_t = f(Y_t-1, Y_t-2, ..., Y₀, t)

i.e. the value of the variable at time t is purely some function of its previous values and time, no other variables/factors are of relevance. The purpose of time series analysis is to discover the nature of the function f and hence allow us to forecast values for Y_t.

Time series methods are especially good for short-term forecasting where, within reason, the past behaviour of a particular variable is a good indicator of its future behaviour, at least in the short-term. The typical example here is short-term demand forecasting. Note the difference between demand and sales - demand is what customers want - sales is what we sell, and the two may be different.

1.3. More advanced time series forecasting

Time series forecasting methods more advanced than those considered in our simple package do exist. These are based on AutoRegressive Integrated Moving Average (ARIMA) models. Essentially these assume that the time series has been generated by a probability process with future values related to past values, as well as to past forecast errors. To apply ARIMA models the time series needs to be stationary. A stationary time series is one whose statistical properties such as mean, variance and autocorrelation are constant over time. If the initial time series is not stationary it may be that some function of the time series, e.g. taking the differences between successive values, is stationary.

In fitting an ARIMA model to time series data the framework usually used is a Box-Jenkins approach. It does however have the disadvantage that whereas a number of time series techniques are fully automatic, in the sense that the forecaster has to exercise no judgement other than in choosing the technique to use, the Box-Jenkins technique requires the forecaster to make judgements and consequently its use requires experience and "expert judgement" on the part of the forecaster. Some forecasting packages do exist that make these "expert choices" for you.

Conclusion

We have given just an overview of the types of forecasting methods available. The key in forecasting nowadays is to understand the different forecasting methods and their relative merits and so be able to choose which method to apply in a particular situation (for example consider how many time series forecasting methods the package has available).

All forecasting methods involve tedious repetitive calculations and so are ideally suited to be done by a computer. Forecasting packages, many of an interactive kind (for use on pc's) are available to the forecaster.

Literature

http://people.brunel.ac.uk/~mastjjb/jeb/or/forecast.html
http://www.freepatentsonline.com/6032125.html
http://safety.fhwa.dot.gov/PED_BIKE/ped/psol_forecast.htm

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