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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. in statistics (GARCH)
62F15 Bayesian inference
91B84 Economic time series analysis
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