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Nonparametric inference for ergodic, stationary time series. (English) Zbl 0855.62076

Summary: The setting is a stationary, ergodic time series. The challenge is to construct a sequence of functions, each based on only finite segments of the past, which together provide a strongly consistent estimator for the conditional probability of the next observation, given the infinite past. D. S. Ornstein [Israel J. Math. 30, 292-296 (1978; Zbl 0386.60032)] gave such a construction for the case that the values are from a finite set, and recently P. Algoet [Ann. Probab. 20, No. 2, 901-941 (1992; Zbl 0758.90006)] extended the scheme to time series with coordinates in a Polish space.
The present study relates a different solution to the challenge. The algorithm is simple and its verification is fairly transparent. Some extensions to regression, pattern recognition and on-line forecasting are mentioned.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G05 Nonparametric estimation
60G25 Prediction theory (aspects of stochastic processes)
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References:

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[22] TUCSON, ARIZONA 85721 1521 STOCZEK U. 2, BUDAPEST HUNGARY LASZLO Gy ORFI \' \' \" DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE TECHNICAL UNIVERSITY OF BUDAPEST 1521 STOCZEK U. 2, BUDAPEST HUNGARY
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