Formalizing a postprocessing procedure for linear-convex combination forecasts

Monschang, Verena; Wilfling, Bernd

Abstract

We investigate mean-squared-forecast-error (MSE) accuracy improvements for linear-convex combination forecasts, whose components are pretreated by a postprocessing procedure called 'Vector Autoregressive Forecast Error Modeling' (VAFEM). Assuming that the forecast-error series of the individual forecasts are governed by a stable VAR process under classic conditions, we obtain the following results: (i) VAFEM treatment bias-corrects all individual and linear-convex combination forecasts. (ii) Any VAFEM-treated combination has a smaller theoretical MSE than its untreated analogue, if the VAR parameters are known. (iii) In empirical applications, VAFEM gains depend on (1) in-sample sizes, (2) out-of-sample forecast horizons, (3) the biasedness of the untreated forecast combination. We demonstrate the VAFEM capacity in simulations and for realized-volatility forecasting, using S&P 500 data.

Keywords
Combination forecasts; mean-squared-error loss; VAR forecast-error modeling; multivariate least squares estimation