Frequentist Averaging

Abstract

This chapter summarises the recent approaches to optimal forecast combination from a frequentist perspective. The availability of big data leads to the development of many different models of the same macroeconomic variables. The challenge is to seek the best way to combine all relevant information from big data to create optimal forecast. Forecast combination provides one plausible approach. This chapter discusses the practical aspects of combining forecasts optimally and theoretical properties of the combination both for point forecasts and density forecasts. Specifically, the chapter derives the asymptotic distributions of the estimated optimal weight under two of the most popular forecasting criteria: Mean Squared Forecast Error and Mean Absolute Deviation. This chapter also revisits the insights of the so-called forecast combination puzzle, which shows that in practice a simple average of forecasts outperforms more complex weighting strategies. These theoretical results help address the puzzle by providing a mean to test statistically the difference between the estimated optimal weight and the simple average. The optimal weights obtained from minimising the Kullback–Leibler Information Criterion (KLIC) are discussed in the context of density forecast combination. This chapter also proposes a novel Generalized Method of Moments approach for density forecast combination. The connection between the proposed approach and the conventional approach by minimising KLIC is also investigated in some details.