Structural Risk Minimization for Nonparametric Time Series Prediction
Ron Meir · 1997
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 tradeoff between approximation and estimation is discussed. A complexity regularization approach is outlined, based on Vapnik's method of Structural Risk Minimization, and shown to be applicable in the context of mixing stochastic processes. 1 Time Series Prediction and Mixing Processes A great deal of effort has been expended in recent years on the problem of deriving robust distribution-free error bounds for learning, mainly in the context of memoryless processes (e.g. [9]). On the other hand, an extensive amount of work has been devoted by statisticians and econometricians to the study of parametric (often linear) mo...