The reliability and precision of the weights used in combining individual forecasts, irrespective of the method of combination, is important in evaluating a combined forecast. The objective of this study is not to suggest the 'best' method of combining individual forecasts, but rather to propose exploratory procedures, that make use of all available sample information contained in the covariance matrix of individual forecast errors, to (1) detect if the weights used in combining forecasts are 'reliable' (and 'stable' if it is known that the covariance matrix of forecast errors is stationary over time) and (2) test for 'insignificant' individual forecasts used in forming a combined forecast. We present empirical applications using two-year sales and individual forecast data provided by a major consumer durables manufacturer to illustrate the feasibility of our proposed procedures.
KEY WORDS Forecasting Combined forecasts Reliability of weights Evaluation of forecasts
Alternative forecasting systems (e.g. systems that employ econometric methods, time-series analysis, or subjective expert opinion) usually contain unique and independent information about the process to be forecast (e.g. product sales and market shares) since they utilize different data and model specifications. In theory, the best forecast (as measured, say, by low forecast error variance) is a 'combination' of existing alternative forecasts that makes use of all available information. An extensive theoretical and empirical literature exists on combining forecasts (see Moriarty, 1990; Clemen, 1989; Granger and Ramanathan, 1984) which strongly suggests that almost any 'reasonable' combination of alternative forecasts, including linear combinations, is more accurate than any single alternative forecast. As stated in Lilien and Kotler (1983, p. 327): 'For many companies, flexibility is emerging as, perhaps, the most distinguishing feature of their forecasting program ... . the primary mission has become that of finding and applying the right combination of methods for the particular forecasting job at hand'.