Introduction

We have seen that there are several different methods of producing forecasts and also that, even when a particular method is selected, a forecaster still has to choose such things as the variables of interest, the functional form and the estimation procedure. As a result, we frequently have several, generally different, forecasts available for the same outcome. The question then is should just one particular forecast be chosen or should some form of average be taken? This has received much attention in the academic literature over the last few years. In this chapter we consider the main themes of this literature as well as reviewing some of the empirical contributions. In section 3.2 we determine the optimal way in which two unbiased forecasts can be combined. The weights are shown to depend on the variances and covariances of the forecast errors. A generalisation of this, which extends to include biased forecasts, is presented in section 3.3, and the problems caused by serially correlated errors are discussed in section 3.4. Other approaches to combining forecasts, including the use of the simple average are considered in section 3.5. The empirical evidence on how different combinations perform is reviewed in section 3.6 and some practical suggestions for deciding how to choose an appropriate combination are offered. We then consider the results of the Makridakis forecasting competition which compares a wide range of time-series forecasts, as well as some simple combinations.