FINITE-SAMPLE BOUNDS FOR TIME-SERIES PREDICTION

The problem of time series prediction is studied within the uniform co nvergence framework of Vapnik and Chervonenkis. The dependence inheren t in the temporal structure is incorporated into the analysis, thereby generalizing the available theory for memoryless processes. Finite sa mple bounds are calculated in terms of covering numbers of the approxi mating class, and the trade-off between approximation and estimation i s discussed. A sketch of a complexity regularization approach is outli ned and shown to be applicable in the context of mixing stochastic pro cesses. Finally; a comparison of the method with other recent approach es to non-parametric time series prediction is briefly discussed.