Nonparametric multistep-ahead prediction in time series analysis

We consider the problem of multistep-ahead prediction in time series analysis by using nonparametric smoothing techniques. Forecasting is always one of the main objectives in time series analysis. Research has shown that non-linear time series models have certain advantages in multistep-ahead forecasting. Traditionally, nonparametric "k"-step-ahead least squares prediction for non-linear autoregressive AR("d") models is done by estimating "E"("X"_"t"+"k" |"X"_"t", …,  "X"_{"t" - "d"+1}) via nonparametric smoothing of "X"_"t"+"k" on ("X"_"t", …, "X"_{"t" - "d"+1}) directly. We propose a multistage nonparametric predictor. We show that the new predictor has smaller asymptotic mean-squared error than the direct smoother, though the convergence rate is the same. Hence, the predictor proposed is more efficient. Some simulation results, advice for practical bandwidth selection and a real data example are provided. Copyright 2004 Royal Statistical Society.