Model averaging for asymptotically optimal combined forecasts

We propose a model-averaging (MA) method for constructing an asymptotically optimal combination of a set of point forecast sequences generated from a class of predictive regressions. The asymptotic optimality is defined in terms of approximating an unknown conditional-mean sequence based on the local(-to-zero) asymptotics. Our method has the following essential features. First, it is more general than combining a set of single point forecasts. Second, the asymptotic optimality is generally dependent on the estimation scheme and the asymptotic ratio of the length of forecast sequence relative to the in-sample size. Third, the asymptotically optimal weights may be consistently estimated under suitable conditions, while it needs the time series to be sufficiently long. We also assess the forecasting performance of our method using simulation data and real data.