Volatility dynamics under duration-dependent mixing

This paper proposes a discrete-state stochastic volatility model with duration-dependent mixing. The latter is directed by a high-order Markov chain with a sparse transition matrix. As in the standard first-order Markov switching (MS) model, this structure can capture turning points and shifts in volatility, due for example, to policy changes or news events. However, the duration-dependent Markov switching model (DDMS) can also exploit the persistence associated with volatility clustering. To evaluate the contribution of duration dependence, we compare with a benchmark Markov switching-ARCH (MS-ARCH) model. The empirical distribution generated by our proposed structure is assessed using interval forecasts and density forecasts. Implications for areas of the distribution relevant to risk management are also assessed.