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Nonparametric regression for nonstationary processes

This paper develops recursive kernel estimators for the probability density and the regression function of nonlinear and nonstationary time series. The resulting method is characterized by two smoothing coefficients (the bandwidth and the discounting rate of observations) that may be selected with a prediction error criterion. Statistical properties are investigated under a null hypothesis of stationarity and asymptotic elimination of the discounting. Simulation experiments on complex processes show the ability of the method in estimating time-varying nonlinear regression functions.