Non parametric multistep-ahead prediction in time series analysis

Abstract

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\Xt,...,Xt-d+1) via nonparametric smoothing of Xt+k on (Xt,.,Xt-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. Improvement ratio; Local polynomial; Multistage smoothing; Optimal bandwidth; Sunspot series.