Evaluating Density Forecasts with an Application to Stock Market Returns

Gabriela de Raaij () and Burkhard Raunig
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Gabriela de Raaij: Oesterreichische Nationalbank, Banking Analysis and Inspections Division, Otto-Wagner-Platz 3, POB 61, A-1011 Vienna, Austria, http://www.oenb.at

Working Papers from Oesterreichische Nationalbank (Austrian Central Bank)

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.

Keywords: Density forecasting; Forecast evaluation; Risk management; GARCH-models (search for similar items in EconPapers)
JEL-codes: C52 C53 G10 (search for similar items in EconPapers)
Pages: 39
Date: 2002-02-18
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (3)

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Working Paper: Evaluating Density Forecasts with an Application to Stock Market Returns (2002)
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