Title: Hidden semi-Markov models with multivariate leptokurtic-normal components: Application to daily returns series
Authors: Luca Bagnato - Catholic University of the Sacred Heart (Italy) [presenting]
Antonio Punzo - University of Catania (Italy)
Antonello Maruotti - Libera Università Maria Ss Assunta (Italy)
Abstract: The recently proposed multivariate leptokurtic-normal (MLN) distribution is a heavy-tailed generalization of the multivariate normal distribution with an additional parameter governing/denoting excess kurtosis. Advantageously with respect to other multivariate heavy-tailed elliptical distributions, the MLN is directly parametrized according to the moments of interest, i.e. the mean vector, the covariance matrix, and the excess kurtosis. With the aim of modelling the distributional and dynamic properties of daily returns, we consider the MLN as emission distribution to build hidden Markov and semi-Markov models. We outline an EM algorithm for maximum likelihood estimation which exploits recursions developed within the hidden (semi-)Markov literature. As an illustration, we provide an example based on the analysis of a bivariate time series of stock market returns.