Hidden Markov and semi-Markov models with multivariate leptokurtic-normal components for robust modeling of daily returns series

We introduce multivariate models for the analysis of stock market returns. Our models are developed under hidden Markov and semi-Markov settings to describe the temporal evolution of returns, whereas the marginal distribution of returns is described by a mixture of multivariate leptokurtic-normal (LN) distributions. Compared to the normal distribution, the LN has an additional parameter governing excess kurtosis and this allows us a better fit to both the distributional and dynamic properties of daily returns. We outline an expectation maximization 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.