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Model Selection for Weakly Dependent Time Series Forecasting

Author

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  • Pierre Alquier

    (Crest)

  • Olivier Wintenberg

    (Crest)

Abstract

Observing a stationary time series, we propose a two-step procedure for the predictionof the next value of the time series. The first step follows machine learning theory paradigmand consists in determining a set of possible predictors as randomized estimators in (possiblynumerous) different predictive models. The second step follows the model selection paradigmand consists in choosing one predictor with good properties among all the predictors of the firststeps. We study our procedure for two different types of observations: causal Bernoulli shifts andbounded weakly dependent processes. In both cases, we give oracle inequalities: the risk of thechosen predictor is close to the best prediction risk in all predictive models that we consider. Weapply our procedure for predictive models such as linear predictors, neural networks predictorsand non-parametric autoregressive predictors.

Suggested Citation

  • Pierre Alquier & Olivier Wintenberg, 2010. "Model Selection for Weakly Dependent Time Series Forecasting," Working Papers 2010-39, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2010-39
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    References listed on IDEAS

    as
    1. Doukhan, Paul & Wintenberger, Olivier, 2008. "Weakly dependent chains with infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 1997-2013, November.
    2. Lacour, Claire, 2008. "Nonparametric estimation of the stationary density and the transition density of a Markov chain," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 232-260, February.
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