Maximum likelihood estimation of skew-<i>t</i> copulas with its applications to stock returns

2018-05-16T17:14:15Z (GMT) by Toshinao Yoshiba
<p>The multivariate Student-<i>t</i> copula family is used in statistical finance and other areas when there is tail dependence in the data. It often is a good-fitting copula but can be improved on when there is tail asymmetry. Multivariate skew-<i>t</i> copula families can be considered when there is tail dependence and tail asymmetry, and we show how a fast numerical implementation for maximum likelihood estimation is possible. For the copula implicit in a multivariate skew-<i>t</i> distribution, the fast implementation makes use of (i) monotone interpolation of the univariate marginal quantile function and (ii) a re-parametrization of the correlation matrix. Our numerical approach is tested with simulated data with data-driven parameters. A real data example involves the daily returns of three stock indices: the Nikkei225, S&P500 and DAX. With both unfiltered returns and GARCH/EGARCH filtered returns, we compare the fits of the Azzalini–Capitanio skew-<i>t</i>, generalized hyperbolic skew-<i>t</i>, Student-<i>t</i>, skew-Normal and Normal copulas.</p>