Bayesian estimation of stochastic tail index from high-frequency financial data

Osman Doğan, Süleyman Taşpınar, Anil K. Bera

Research output: Contribution to journalArticlepeer-review


Tails of the return distribution of an asset are informative about the (financial) risk behavior of that asset. Stochastic tail index (STI) models are designed to quantify riskiness by estimating a time-varying tail index from the distribution of extreme values using high-frequency financial data. In this paper, we propose a computationally efficient Bayesian estimation method for STI models based on the recent advances in band and sparse matrix algorithms. We then show how the deviance information criterion (DIC) can be calculated from the integrated likelihood function for model comparison exercises. In a Monte Carlo study, we investigate the finite sample properties of the Bayesian estimator as well as the performance of two DIC measures. Our results show that the Bayesian estimator performs sufficiently well and the DIC measures based on the integrated likelihood function are useful for model selection exercises. In an empirical application, we illustrate calculation of the tail index using high-frequency data on IBM stock returns. Our estimation results indicate that the daily tail index of the return distribution of IBM stock has a time-varying feature: It tends to decline when there are large losses, whereas it tends to increase when there are small losses.

Original languageEnglish (US)
Pages (from-to)2685-2711
Number of pages27
JournalEmpirical Economics
Issue number5
StatePublished - Nov 2021


  • Bayesian inference
  • DIC
  • Extreme value theory
  • Extreme values
  • High-frequency data
  • MCMC
  • Stochastic tail index models
  • Stochastic volatility models
  • Tail index

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics


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