Formalizing a Postprocessing Procedure for Linear–Convex Combination Forecasts

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 analog, if the VAR parameters are known. (iii) In empirical applications, VAFEM gains depend on (1) in‐sample sizes, (2) out‐of‐sample forecast horizons, and (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.