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Nonparametric multistep-ahead prediction in time series analysis. (English) Zbl 1046.62099

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 nonlinear time series models have certain advantages in multistep-ahead forecasting. Traditionally, nonparametric \(k\)-step-ahead least squares prediction for nonlinear autoregressive AR\((d)\) models is done by estimating \(E(X_{t+k}\mid X_t,\dots,X_{t-d+1})\) via nonparametric smoothing of \(X_{t+k}\) on \((X_t,\dots,X_{t-d+1})\) 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.

MSC:

62M20 Inference from stochastic processes and prediction
62G07 Density estimation
62G05 Nonparametric estimation
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