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Nearest-neighbour methods for time series analysis. (English) Zbl 0615.62115

The paper shows the possibilities of the k(n)-nearest-neighbour (k-NN) method in the context of time series analysis (so far this method of nonparametric estimation has been applied mainly in the i.i.d. case). In the paper the k-NN method is used to infer the nonlinear regression function \(m(x)=E(X_{n+1}| X_ n=x)\), where \(\{X_ n\}\) is a stationary ergodic Markov time series. It is shown that under the \(G_ 2\) mixing condition by Rosenblatt the method converges at the Stone- optimal rate.
These results are extended briefly beyond the Markov assumption to a broader pattern-recognition context. The application of the method for the prediction in hydrology (rainfalls/runoff measurements) is presented in comparison with other standard methods.
Reviewer: T.Cipra

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M05 Markov processes: estimation; hidden Markov models
62G05 Nonparametric estimation
62J02 General nonlinear regression
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References:

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