The Annals of Statistics
- Ann. Statist.
- Volume 24, Number 1 (1996), 370-379.
Nonparametric inference for ergodic, stationary time series
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. Ornstein gave such a construction for the case that the values are from a finite set, and recently Algoet 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.
Ann. Statist., Volume 24, Number 1 (1996), 370-379.
First available in Project Euclid: 26 September 2002
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Morvai, Gusztáv; Yakowitz, Sidney; Györfi, László. Nonparametric inference for ergodic, stationary time series. Ann. Statist. 24 (1996), no. 1, 370--379. doi:10.1214/aos/1033066215. https://projecteuclid.org/euclid.aos/1033066215