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Evaluating Density Forecasts with an Application to Stock Market Returns


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  • Raunig, Burkhard
  • de Raaij, Gabriela
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    Density forecasts have become quite important in economics and finance. For example, such forecasts play a central role in modern financial risk management techniques like Value at Risk. This paper suggests a regression based density forecast evaluation framework as a simple alternative to other approaches. In simulation experiments and an empirical application to in- and out-of-sample one-step-ahead density forecasts of daily returns on the S&P 500, DAX and ATX stock market indices, the regression based evaluation strategy is compared with a recently proposed methodology based on likelihood ratio tests. It is demonstrated that misspecifications of forecasting models can be detected within the proposed regression framework. It is further demonstrated that the likelihood ratio methodology without additional misspecification tests has no power in many practical situations and therefore frequently selects incorrect forecasting models. The empirical results provide some evidence that GARCH-t models provide good density forecasts. The results further suggest that extensions of statistical models with fat-tailed conditional distributions to models that incorporate higher order conditional moments beyond the conditional variance might be appropriate to capture the empirical regularities in financial time series in some cases. -- Die Voraussagen von Dichten ist in verschiedenen ökonomischen Fragestellungen sehr wichtig geworden. Solche Voraussagen spielen zum Beispiel eine wichtige Rolle bei modernen Methoden des Risikomanagements im Finanzsektor. Dieses Papier schlägt vor, Dichte-Prognosen mithilfe einer Methode zu beurteilen, die auf einem Regressionsansatz beruht. In Simulationsexperimenten und empirischen Anwendungen auf Dichte-Prognosen für tägliche Erträge verschiedener Aktienindices (S&P 500, DAX, ATX) wird diese Methode mit einer verglichen, die auf likelihood ratio Tests beruht und die erst neulich vorgeschlagen wurde. Es zeigt sich, dass Fehlspezifikationen der Prognosemodelle mithilfe der hier vorgeschlagenen Methode entdeckt werden können. Dagegen hat die Methode, die auf likelihood ratio Test beruht, ohne zusätzliche Tests auf Fehlspezifikation in vielen praktischen Fällen keine Macht. Die empirischen Ergebnisse deuten darauf hin, dass GARCH-t-Modelle gute Dichte-Prognosen liefern. Weiterhin wird gezeigt, dass Erweiterungen von statistischen Modellen mit Verteilungen mit dicken Enden zu Modellen, die höhere Momente einbeziehen, geeignet sein können, um in manchen Fällen empirische Regelmäßigkeiten in Finanzzeitreihen abzubilden.

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    Bibliographic Info

    Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 1: Economic Studies with number 2002,08.

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    Date of creation: 2002
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    Handle: RePEc:zbw:bubdp1:4173

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    Related research

    Keywords: Density forecasting; Forecast evaluation; Risk management; GARCH-models;

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