A Multivariate Skew-in-mean GARCH Model

• Activity Number: 151
• Type: Topic Contributed
• Date/Time: Monday, August 9, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Giovanni De Luca*+ and Nicola Loperfido and Marc G. Genton
• Companies: University of Naples Parthenope and University of Urbino and North Carolina State University
• Keywords: skew-normal distribution ; stock returns ; volatility

Abstract

The distribution of a small capitalized market index return is usually influenced by the performance of some dominant market. Some inspection revealed that the behavior of the returns at time t of a set of European stock index is affected by the performance of the U.S. stock exchange at time t-1. Taking into account the dynamics of the conditional correlations among stock exchange returns, a multivariate framework is introduced. Empirical analyses show that the multivariate distribution of financial returns is usually far from being multinormal. In particular, using Mardia's measure of multivariate skewness it is possible to stress a feature usually neglected in the statistical analysis of returns. Starting from standard assumptions, we show that the multivariate distribution of a set of European stock index returns, conditionally on the performance of the one-day lagged American stock exchange expressed through its sign, turns out to be a multivariate skew-normal distribution which is an extension of the multivariate normal distribution allowing for an additional parameter to regulate skewness. The model, denoted as Multivariate Skew-in-Mean GARCH model, is applied.