Component-Driven Regime-Switching Volatility

We develop a new class of regime-switching volatility models that are characterized by high-dimensional state spaces, parsimonious transition matrices, and ARMA dynamics for the log volatility process. This combination of features is achieved by assuming that we can decompose the Markov chain that describes regime dynamics into a number of two-state component chains that evolve independently through time. Using daily data for S&P 500 index and IBM shares, we show that our component-driven regime-switching (CDRS) models are capable of outperforming GARCH, component GARCH, regime-switching GARCH, and Markov-switching multifractal models in forecasting realized variances out of sample. Interestingly, we find that CDRS models with simple AR(1) dynamics perform well across the board.