Stochastic volatility models: conditional normality versus heavy-tailed distributions

Abstract

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. Copyright © 2000 John Wiley & Sons, Ltd.

Comparing Conditional Variance Models: Theory and Empirical Evidence

“…with normal conditional distribution as a thick-tailed model. However, Liesenfeld and Jung (2000) show that for the persistence values most likely in empirical applications, i.e., with φ > 0.9, the normal SV model does not fit well enough to capture the entire unconditional kurtosis, this being consistent with results obtained by Geweke (1994), Terasvirta (1996), Gallant et al (1997), among others. So, for the SV as well, it is necessary to adopt heavy-tailed conditional distributions.…”

Stochastic volatility in mean models with scale mixtures of normal distributions and correlated errors: A Bayesian approach

“…Although the basic SV model offers great flexibility in modeling data with time-varying variances, it can suffer from a lack of robustness in the presence of extreme outlying observations (see, e.g., Liesenfeld and Jung, 2000;Abanto-Valle et al, 2010, among others). The volatility of daily stock returns has been estimated with SV models, but the results have relied on an extensive pre-modeling of these series to avoid the problem of simultaneous estimation of the mean and variance.…”

Robustness of Some Portmanteau Correlation Tests in Financial Time Series

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