Nonparametric Time Series Prediction Through Adaptive Model Selection

We consider the problem of one-step ahead prediction for time series generated by an underlying stationary stochastic process obeying the condition of absolute regularity, describing the mixing nature of process. Wemakeuseofrecentresultsfromthetheoryofempiricalprocesses,andadapttheuniformconvergenceframework of Vapnik and Chervonenkis to the problem of time series prediction, obtaining finite sample bounds. Furthermore, by allowing both the model complexity and memory size to be adaptively determined by the data, we derive nonparametricratesofconvergencethroughanextensionofthemethodofstructuralriskminimizationsuggestedby Vapnik. All our results are derived for general L p error measures, and apply to both exponentially and algebraically mixing processes.

• Type: Journal
• Year: 2000
• Where: ML
• Authors: Ron Meir
• Keywords: Machine Learning, ML 2000, One-step Ahead Prediction, Stationary Stochastic Process, Time Series Prediction