Relatore: Andrew Harvey, University of Cambridge
Abstract
Beta-t-EGARCH models in which the dynamics of the logarithm of scale are driven by the conditional score are known to exhibit attractive theoret- ical properties for the t-distribution and general error distribution (GED). The generalized-t includes both as special cases. We derive the information matrix for the generalized-t and show that, when parameterized with the inverse of the tail index, it remains positive deÖnite as the tail index goes to inÖnity and the distribution becomes a GED. Hence it is possible to con- struct Lagrange multiplier tests of the null hypothesis of light tails against the alternative of fat tails. The full information matrix may be obtained for the model with dynamics. The distribution may be extended by allowing for skewness and asymmetry in the shape parameters and the asymptotic the- ory for the associated EGARCH models may be correspondingly extended. For positive variables, the GB2 distribution may be parameterized so that it goes to the generalised gamma in the limit as the tail index goes to in- Önity. Again dynamic volatility may be introduced and the full information matrix obtained. Overall the approach o§ers a uniÖed, áexible, robust and practical treatment of dynamic scale.
Organizzatore: Prof. Alessandra Luati