N‐step combinations of forecasts

Abstract

While there is general agreement that a linear combination of forecasts can outperform the individual forecasts, there is controversy about the appropriateness of the combination method to be used in a given situation.Hence, in any given application it may be more beneficial to combine different sets of combined forecasts rather than picking one of them. This paper introduces the concept of N-step combinations of forecasts which involves combining the combined forecasts obtained from different combination procedures used at the preceding step. Using quarterly GNP data, evidence supporting the increase in the accuracy of the one-periodahead ex-ante forecasts as the combination step increases is provided. The MSE, MAE, MAPE and their corresponding standard deviations are used to evaluate the accuracy of the forecasts obtained.KEY WORDS Combining forecasts Accuracy of forecasts State space models ARCH models Gross National Product Regression with serially correlated errors Regression with linear constraints I t is known that a linear combination of forecasts obtained from models which may use different functional forms and/or information sets may sometimes outperform individual forecasts. Due to the existence of competing theories on the underlying causal relationships, data unavailability and cost considerations, forecasts of the same variable of interest are often based on different information sets. As a less costly alternative to obtaining a composite forecast by combining the models and the information sets themselves, a combination of these forecasts yields a forecast that is indirectly based on the union of these information sets. On the other hand, since any given forecasting technique makes specific assumptions on the stochastic process generating the particular series, and may use a different error-minimization criterion in parameter estimation, the models fit and the forecasts provided may capture certain characteristics of the series not captured by other forecasting techniques. Thus, a combination of forecasts based on different information sets and/or models may provide a combined forecast which is more accurate than any of the individual forecasts. After the pioneering works of Reid (1969) and of Bates and Granger (1969) in this area, various researchers have studied the procedures to be used for combining the individual forecasts and the statistical properties of the resulting combined forecasts. The combination 0277-6693/89/030253-15$07.50

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