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An empirical evaluation of fat-tailed distributions in modeling financial time series. (English) Zbl 1148.62316
Summary: There is substantial evidence that many financial time series exhibit leptokurtosis and volatility clustering. We compare the two most commonly used statistical distributions in empirical analysis to capture these features: the $t$ distribution and the generalized error distribution (GED). A Bayesian approach using a reversible-jump Markov chain Monte Carlo method and a forecasting evaluation method are adopted for the comparison. In the Bayesian evaluation of eight daily market returns, we find that the fitted $t$ error distribution outperforms the GED. In terms of volatility forecasting, models with $t$ innovations also demonstrate superior out-of-sample performance.
##### MSC:
 62P05 Applications of statistics to actuarial sciences and financial mathematics 62M10 Time series, auto-correlation, regression, etc. (statistics) 62F15 Bayesian inference 91B84 Economic time series analysis