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Additive time series: The kernel integration method. (English) Zbl 1008.62039
Summary: We consider additive models in a nonparametric multivariate regression context for which estimators are constructed by a kernel integration method. We first give asymptotic normality and mean square convergence for estimators of the additive components, and then we get the mean square rate of convergence for the multivariate regression estimator, which is the same as in a univariate nonparametric setting. Our results are proved under a general dependence condition, a $$\beta$$-mixing condition, and they are therefore directly applicable in time series prediction problems.

MSC:
 62G08 Nonparametric regression and quantile regression 62M20 Inference from stochastic processes and prediction 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)