Volatility Dynamics Under Duration-Dependent Mixing

This paper proposes a new approach to modeling volatility changes and clustering. In particular, we use a parsimonious high-order Markov chain which allows for duration dependence. As in the standard 1st-order Markov-switching model, this structure can capture turning points and shifts in volatility due, for example, to policy changes or news events. However, unlike the 1st-order model, the duration-dependent Markov switching model is suited to exploiting the persistence associated with volatility clustering. To highlight the features of our model, we compare it to a popular benchmark, the GARCH model. Unlike the latter, the proposed parameterization allows time-varying persistence, includes a stochastic component for volatility, and incorporates anticipated discrete changes in the level of volatility. The empirical distribution generated by our proposed structure works well for the samples of data used in this paper. Implications for forecasts relevant for risk management are emphasized.