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On Out-of-Sample Statistics for Time-Series


  • Yoshua Bengio
  • François Gingras
  • Claude Nadeau


This paper studies an out-of-sample statistic for time-series prediction that is analogous to the widely used R2 in-sample statistic. We propose and study methods to estimate the variance of this out-of-sample statistic. We suggest that the out-of-sample statistic is more robust to distributional and asymptotic assumptions behind many tests for in-sample statistics. Furthermore we argue that it may be more important in some cases to choose a model that generalizes as well as possible rather than choose the parameters that are closest to the true parameters. Comparative experiments are performed on a financial time-series (daily and monthly returns of the TSE300 index). The experiments are performed for varying prediction horizons and we study the relation between predictibility (out-of-sample R2), variability of the out-of-sample R2 statistic, and the prediction horizon. Cet article étudie une statistique hors-échantillon pour la prédiction de séries temporelles qui est analogue à la très utilisée statistique R2 de l'ensemble d'entraînement (in-sample). Nous proposons et étudions une méthode qui estime la variance de cette statistique hors-échantillon. Nous suggérons que la statistique hors-échantillon est plus robuste aux hypothèses distributionnelles et asymptotiques pour plusieurs tests faits pour les statistiques sur l'ensemble d'entraînement (in-sample). De plus, nous affirmons qu'il peut être plus important, dans certains cas, de choisir un modèle qui généralise le mieux possible plutôt que de choisir les paramètres qui sont le plus proches des vrais paramètres. Des expériences comparatives furent réalisées sur des séries financières (rendements journaliers et mensuels de l'indice du TSE300). Les expériences réalisées pour plusieurs horizons de prédictions, et nous étudions la relation entre la prédictibilité (hors-échantillon), la variabilité de la statistique R2 hors-échantillon, et l'horizon de prédiction.

Suggested Citation

  • Yoshua Bengio & François Gingras & Claude Nadeau, 2002. "On Out-of-Sample Statistics for Time-Series," CIRANO Working Papers 2002s-51, CIRANO.
  • Handle: RePEc:cir:cirwor:2002s-51

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    References listed on IDEAS

    1. Francis X. Diebold & Jose A. Lopez, 1995. "Forecast evaluation and combination," Research Paper 9525, Federal Reserve Bank of New York.
    2. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    3. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
    4. Francis X. Diebold & Lutz Kilian, 2001. "Measuring predictability: theory and macroeconomic applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(6), pages 657-669.
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