O'Reilly logo

Analysis of Financial Time Series, Third Edition by RUEY S. TSAY

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

10.8 Multivariate t Distribution

Empirical analysis indicates that the multivariate Gaussian innovations used in the previous sections may fail to capture the kurtosis of asset returns. In this situation, a multivariate Student-t distribution might be useful. There are many versions of the multivariate Student-t distribution. We give a simple version here for volatility modeling.

A k-dimensional random vector inline has a multivariate Student-t distribution with v degrees of freedom and parameters u = 0 and inline (the identity matrix) if its probability density function (pdf) is

10.41 10.41

where Γ(y) is the gamma function; see Mardia, Kent, and Bibby (1979, p. 57). The variance of each component xi in Eq. (10.41) is v/(v − 2), and hence we define inline as the standardized multivariate Student-t distribution with v degrees of freedom. By transformation, the pdf of inline is

10.42 10.42

For volatility modeling, we write ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required