An approach to increasing forecast-combination accuracy through VAR error modeling

Weigt Till, Wilfling Bernd

Abstract
We consider a situation in which the forecaster has available M individual forecasts of a univariate target variable. We propose a 3-step procedure designed to exploit the interrelationships among the M forecast-error series (estimated from a large time-varying parameter VAR model of the errors, using past observations) with the aim of obtaining more accurate predictions of future forecast errors. The refined future forecast-error predictions are then used to obtain M new individual forecasts that are adapted to the information from the estimated VAR. The adapted M individual forecasts are ultimately combined and any potential accuracy gains from the adapted combination forecasts analyzed. We evaluate our approach in an out-of-sample forecasting analysis, using a well established 7-country data set on output growth. Our 3-step procedure yields substantial accuracy gains (in terms of loss reductions of up to 18%) for the simple average and three time-varying-parameter combination forecasts.

Keywords
Bayesian VAR estimation; Dynamic model averaging; Forecast combinations; Forgetting factors; Large time-varying parameter VARs; State-space model