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The information contained in the forecasts from two econometric models can be compared by regressing the actual change in the variable forecasted on the two forecasts of the change. We do such comparisons in this paper, where the forecasts are based only on information through the period prior to the ﬁrst period of the forecast. If a model’s forecast is statistically signiﬁcant in such a regression, we conclude that the model captures information not in the other model whose forecast is also included in the regression. The models studied include the Fair model, vector autoregressive (VAR) models estimated by ordinary least squares, vector autoregressive models estimated with Litterman priors, and a new class of models, which we call “autoregressive components: (AC) models. The AC models divide GNP into components and estimate an autoregressive equation for each component. Our results show that the Fair model’s forecasts contain information not in the forecasts of the VAR and AC models. The AC models contain no information not in the Fair model, which indicates that the Fair model uses all the useful information in the components. The VAR models contain information not in the Fair model for the four-quarter-ahead forecasts but not the one-quarter-ahead forecasts. The best AC model contains information not in the best VAR model, which indicates that there is useful information in the components that the VAR models are not using. The best VAR model contains information not in the best AC model for the four-quarter-ahead forecasts but not the one-quarter-ahead forecasts.
Fair, Ray C. and Shiller, Robert J., "Econometric Modeling as Information Aggregation" (1987). Cowles Foundation Discussion Papers. 1076.