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Kernel regression smoothing of time series. (English) Zbl 0759.62016

The authors study the problem of choosing the smoothing parameter \(h\) for a Nadaraya-Watson-kernel estimator in nonparametric regression with \(\alpha\)-mixing, so dependent, data. They use a CV-method with a leave- one-out estimator to choose \(h\) and prove that the procedure is asymptotically optimal if the situation is nice enough. The method is applied to time series prediction \((Z_ n)\) estimating the autoregression function \(r_ s(z)=E(Z_{n+s}| Z_ n=z)\) nonparametrically, a problem which fits into the model above provided \((Z_ n)\) is \(\alpha\)-mixing as well.

MSC:

62G07 Density estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M20 Inference from stochastic processes and prediction
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