Robustness of Maximum Likelihood Estimates for Multi-Step Predictions: The Exponential Smoothing Case
研究了指数平滑法在多步预测中通过调整平滑参数提高稳健性，证明了最小化样本l步预测误差平方和的估计量的一致性，并推广到其他简约非平稳模型。
We extend the argument initiated by Cox (1961) that the exponential smoothing formula can be made more robust for multi-step forecasts if the smoothing parameter is adjusted as a function of the forecast horizon l. The consistency property of the estimator which minimizes the sum of squares of the sample l-step ahead forecast errors makes the robustness result useful in practice. We also generalize the consistency result to some other parsimonious nonstationary models which have been popular 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.