Selecting the forgetting factor in subset autoregressive modelling

Conventional methods to determine the forgetting factors in autoregressive (AR) models are mostly based on arbitrary or personal choices. In this paper, we present two procedures which can be used to select the forgetting factor in subset AR modelling. The first procedure uses the bootstrap to determine the value of a fixed forgetting factor. The second procedure starts from this base and applies the time-recursive maximum likelihood estimation to a variable forgetting factor. In one illustration using real exchange rates, we demonstrate the effect of the forgetting factor in subset AR modelling on ex ante forecasting of non-stationary time series. In a second illustration, these two procedures are applied to time-update forecasts for a stock market index. Subset AR models not including a forgetting factor act as a set of benchmarks for assessing ex ante forecasting performance, and consistently improved forecasting performance is demonstrated for these proposed procedures.