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Evaluating Density Forecasts with an Application to Stock Market Returns

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  • Raunig, Burkhard
  • de Raaij, Gabriela

Abstract

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.

Suggested Citation

  • Raunig, Burkhard & de Raaij, Gabriela, 2002. "Evaluating Density Forecasts with an Application to Stock Market Returns," Discussion Paper Series 1: Economic Studies 2002,08, Deutsche Bundesbank.
  • Handle: RePEc:zbw:bubdp1:4173
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    More about this item

    Keywords

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

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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