Stochastic volatility models: conditional normality versus heavy-tailed distributions

• Published in: Journal of applied econometrics (Chichester, England) Vol. 15; no. 2; pp. 137 - 160
• Main Authors: Liesenfeld, Roman, Jung, Robert C.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.03.2000; John Wiley & Sons; John Wiley and Sons, Ltd; Wiley Periodicals Inc
• Subjects: American dollar; Autocorrelation; Econometrics; Economic models; Estimates; Exchange rates; Foreign exchange rates; Gaussian distributions; Hypotheses; Kurtosis; Maximum likelihood estimation; Modeling; Normal distribution; Parametric models; Prices; Securities markets; Statistical variance; Stochastic models; Stochastic processes; Stock prices; Stock returns; Studies; T distribution; Volatility
• ISSN: 0883-7252; 1099-1255
• DOI: 10.1002/(SICI)1099-1255(200003/04)15:2<137::AID-JAE546>3.0.CO;2-M

Most of the empirical applications of the stochastic volatility (SV) model are based on the assumption that the conditional distribution of returns, given the latent volatility process, is normal. In this paper, the SV model based on a conditional normal distribution is compared with SV specifications using conditional heavy-tailed distributions, especially Student's t-distribution and the generalized error distribution. To estimate the SV specifications, a simulated maximum likelihood approach is applied. The results based on daily data on exchange rates and stock returns reveal that the SV model with a conditional normal distribution does not adequately account for the two following empirical facts simultaneously: the leptokurtic distribution of the returns and the low but slowly decaying autocorrelation functions of the squared returns. It is shown that these empirical facts are more adequately captured by an SV model with a conditional heavy-tailed distribution. It also turns out that the choice of the conditional distribution has systematic effects on the parameter estimates of the volatility process.