Local Functional Exponential Smoothing
35 Pages Posted: 17 Aug 2005
Date Written: June 3, 2005
A generalization of the exponential smoothing (ES) model is proposed by making two new assumptions about the form that the ES forecast function takes. First, the smoothing coefficient is made a function of (possibly a lag of) the observed time series and, second, the one-step ahead forecast is allowed to be a weighted average of the last forecast and an unknown function of the last observation. These assumptions greatly enhance the usefulness and applicability of ES as a filtering and forecasting method, as they permit data-dependent updating of the smoothing coefficient and can handle nonlinearity. Neither of these features is available in the context of the standard ES model. The inference problem is nonparametric and the approximation parameters of the model are estimated by local nonlinear least squares. A model selection procedure, based on generalized cross-validation, is also given. The potential of the new model is illustrated using four real economic time series.
Keywords: Exponential smoothing, forecasting, nonlinear, nonparametric
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