ROBUSTNESS OF MAXIMUM-LIKELIHOOD-ESTIMATES FOR MULTISTEP PREDICTIONS - THE EXPONENTIAL SMOOTHING CASE

We extend the argument initiated by Cox (1961) that the exponential sm oothing formula can be made more robust for multi-step forecasts if th e smoothing parameter is adjusted as a function of the forecast horizo n l. The consistency property of the estimator which minimizes the sum of squares of the sample l-step ahead forecast errors makes the robus tness result useful in practice. We also generalize the consistency re sult to some other parsimonious nonstationary models which have been p opular in use. The asymptotic distribution of the estimated smoothing parameter adjusted for forecast horizon l leads to the development of diagnostic tools which are based on l-step forecasts.