Nonparametric conditional predictive regions for time series. (English) Zbl 0990.62083
Summary: Several nonparametric predictors based on the Nadaraya–Watson kernel regression estimator have been proposed in the literature. They include the conditional mean, the conditional median, and the conditional mode. We consider three types of predictive regions for these predictors – the conditional percentile interval (CPI), the shortest conditional modal interval (SCMI), and the maximum conditional density region (MCDR). Further, we introduce a data-driven method for the choice of the optimal bandwidth. This method is based on the minimization of a cross-validation criterion given three different types of predictors.
When the underlying conditional distribution is multi-modal, we show that the MCDR is much shorter in length than the CPI or SCMI irrespective of the type of predictor used. This point is illustrated using both a simulated and a real data set.
When the underlying conditional distribution is multi-modal, we show that the MCDR is much shorter in length than the CPI or SCMI irrespective of the type of predictor used. This point is illustrated using both a simulated and a real data set.
MSC:
| 62M20 | Inference from stochastic processes and prediction |
| 62G08 | Nonparametric regression and quantile regression |
Keywords:
conditional mean; conditional median; conditional mode; cross-validation; kernel methods; Markovian processes; maximum conditional density region (MCDR); nonparametric prediction; shortest conditional modal interval (SCMI)References:
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