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 fo r the conditional probability of the next observation, given the infin ite past. Ornstein gave such a construction for the case that the valu es are from a finite set, and recently Algoet extended the scheme to t ime series with coordinates in a Polish space. The present study relat es 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.