Abstract
M.Com. (Econometrics)
The main purpose of this study is the combining of forecasts with special reference to major macroeconomic series of South Africa. The study is based on econometric principles and makes use of three macro-economic variables, forecasted with four forecasting techniques. The macroeconomic variables which have been selected
are the consumer price index, consumer expenditure on durable and semi-durable products and real M3 money supply. Forecasts of these variables have been generated by applying the Box-Jenkins ARIMA technique, Holt's two parameter exponential smoothing, the regression approach and mUltiplicative decomposition. Subsequently,
the results of each individual forecast are combined in order to determine if forecasting errors can be minimized. Traditionally, forecasting involves the identification and application of the best forecasting model. However, in the search for this unique model, it often happens that some important independent information contained in one of the other models, is discarded. To prevent this from happening, researchers have investigated the idea of combining forecasts. A number of researchers used the results from different techniques as inputs into the combination of forecasts. In spite
of the differences in their conclusions, three basic principles have been identified in the combination of forecasts, namely: i The considered forecasts should represent the widest range of forecasting techniques possible. Inferior forecasts should be identified. Predictable errors should be modelled and incorporated into a new forecast series. Finally, a method of combining the selected forecasts needs to be chosen. The best way of selecting a m ethod is probably by experimenting to find the best fit over the historical data. Having generated individual forecasts, these are combined by
considering the specifications of the three combination methods. The first combination method is the combination of forecasts via weighted averages. The use of weighted averages to combine forecasts allows consideration of the relative accuracy of the individual methods and of the covariances of forecast errors among the methods. Secondly, the combination of exponential smoothing and Box-Jenkins is considered. Past errors of each of the original forecasts are used to determine the weights to attach to the two original forecasts in forming the combined forecasts. Finally, the regression approach is used to combine individual forecasts. Granger en Ramanathan (1984) have shown that weights can be obtained by regressing actual values of the variables of interest on the individual forecasts, without including a constant and with the restriction that weights add up to one. The performance
of combination relative to the individual forecasts have been tested, given that the efficiency criterion is the minimization of the mean square errors. The results of both the individual and the combined forecasting methods are acceptable. Although some of the methods prove to be more accurate than others, the conclusion can be made that
reliable forecasts are generated by individual and combined forecasting methods. It is up to the researcher to decide whether he wants to use an individual or combined method since the difference, if any, in the root mean square percentage errors (RMSPE)
are insignificantly small.