Stylized facts of financial time series and hidden semi-Markov models

Hidden Markov models reproduce most of the stylized facts about daily series of returns. A notable exception is the inability of the models to reproduce one ubiquitous feature of such time series, namely the slow decay in the autocorrelation function of the squared returns. It is shown that this stylized fact can be described much better by means of hidden semi-Markov models. This is illustrated by examining the fit of two such models to 18 series of daily sector returns.