Performance bounds for nonlinear time series prediction

Abstract

We consider the problem of time series prediction within the uniform convergence framework pioneered by Vapnik and Chervonenkis. In order to incorporate the dependence inherent in the temporal structure, recent results from the theory of empirical processes are utilized whereby, for certain classes of mixing processes, dependent sequences are mapped into independent ones by an appropriate blocking scheme. Finite sample bounds are calculated in terms of covering numbers of the approximating class and the trade-off between approximation and estimation is discussed. Finally, we sketch how Vapnik's theory of structural risk minimization (aka complexity regularization) may be applied in the context of mixing stochastic processes. A comparison of the method with other recent approaches to nonparametric time series prediction is also discussed.