WEAKLY CONVERGENT NONPARAMETRIC FORECASTING OF STATIONARY TIME-SERIES

The conditional distribution of the next outcome given the infinite pa st of a stationary process can be inferred from finite but growing seg ments of the past, Several schemes are known for constructing pointwis e consistent estimates, but they all demand prohibitive amounts of inp ut data. In this paper we consider real-valued time series and constru ct conditional distribution estimates that make much more efficient us e of the input data, The estimates are consistent in a weak sense; and the question whether they are pointwise-consistent is still open, For finite-alphabet processes one may rely on a universal data compressio n scheme like the Lempel-Ziv algorithm to construct conditional probab ility mass function estimates that are consistent in expected informat ion divergence. Consistency in this strong sense cannot be attained in a universal sense for all stationary processes with values in an infi nite alphabet, but weak consistency can, Some applications of the esti mates to on-line forecasting, regression, and classification are discu ssed.