Nonparametric multistep-ahead prediction in time series analysis
Rong Chen, Lijian Yang, Christian Hafner
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2004 · Volume 66 · Issue 3
DOI: 10.1111/j.1467-9868.2004.04664.x
Abstract
Summary.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, nonparametrick-step-ahead least squares prediction for non-linear autoregressive AR(d) models is done by estimatingE(Xt+k|Xt, …,Xt−d+1) via nonparametric smoothing ofXt+kon (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.
Keywords
Improvement ratio, Local polynomial, Multistage smoothing, Optimal bandwidth, Sunspot series
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