Finite sample bounds for time series prediction

Abstract

Abstract The problem of time series prediction is studied within the uniform convergence framework of Vapnik and Chervonenkis. The dependence inherent in the temporal structure is incorporated into the analysis, thereby generalizing the available theory for memoryless processes. Finite sample bounds are calculated in terms of covering numbers of the approximating class, and the trade-off between approximation and estimation is discussed. A sketch of a complexity regularization approach is outlined and shown to be applicable in the context of mixing stochastic processes. Finally, a comparison of the method with other recent approaches to non-parametric time series prediction is briefly discussed.