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Strategies for sequential prediction of stationary time series

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Abstract

We present simple procedures for the prediction of a real valued sequence. The algorithms are based on a combination of several simple predictors. We show that if the sequence is a realization of a bounded stationary and ergodic random process then the average of squared errors converges, almost surely, to that of the optimum, given by the Bayes predictor. We offer an analog result for the prediction of stationary gaussian processes.

Suggested Citation

  • László Györfi & Gábor Lugosi, 2000. "Strategies for sequential prediction of stationary time series," Economics Working Papers 507, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:507
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    Cited by:

    1. Gérard Biau & Kevin Bleakley & László Györfi & György Ottucsák, 2010. "Nonparametric sequential prediction of time series," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(3), pages 297-317.
    2. Sancetta, A., 2005. "Forecasting Distributions with Experts Advice," Cambridge Working Papers in Economics 0517, Faculty of Economics, University of Cambridge.
    3. Sancetta, Alessio, 2007. "Online forecast combinations of distributions: Worst case bounds," Journal of Econometrics, Elsevier, vol. 141(2), pages 621-651, December.

    More about this item

    Keywords

    Sequential prediction; ergodic process; individual sequence; gaussian process;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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