An empirical evaluation of fat-tailed distributions in modeling financial time series

  • Authors:

  • Mike K. P. So;Cathy W. S. Chen;Jen-Yu Lee;Yi-Ping Chang

  • Affiliations:

  • Department of Information and Systems Management, The Hong Kong University of Science and Technology, Hong Kong;Graduate Institute of Statistics and Actuarial Science, Feng Chia University, Taiwan;Graduate Institute of Statistics and Actuarial Science, Feng Chia University, Taiwan;Department of Business Mathematics, Soochow University, Taiwan

  • Venue:
  • Mathematics and Computers in Simulation
  • Year:
  • 2008

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Abstract

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.