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. Ž . 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. Ž . However, the duration-dependent Markov switching model DDMS can also exploit the persistence associated with volatility clustering. To evaluate the contribution of duration Ž . 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. q 2000 Elsevier Science B.V. All rights reserved.