Nonparametric Time Series Prediction Through Adaptive ModelSelection

  • Authors:
  • Ron Meir

  • Affiliations:
  • Department of Electrical Engineering, Technion, Haifa 32000, Israel. rmeir@ee.technion.ac.it

  • Venue:
  • Machine Learning
  • Year:
  • 2000

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Abstract

We consider the problem of one-step ahead prediction for time seriesgenerated by an underlying stationary stochastic process obeying thecondition of absolute regularity, describing the mixing nature of process.We make use of recent results from the theory of empirical processes, andadapt the uniform convergence framework of Vapnik and Chervonenkis to theproblem of time series prediction,obtaining finite sample bounds. Furthermore, by allowing boththe model complexity and memory size tobe adaptively determined by the data, we derive nonparametric rates ofconvergence through an extension of the method of structural riskminimization suggested by Vapnik. All our results arederived for general L error measures, andapply to bothexponentially and algebraically mixing processes.