Maximum likelihood estimation of the Markov-switching GARCH model

The frequency of regime switching in financial market volatility

“…Andreou & Ghysels (2002), among others, have argued that financial returns are known to exhibit sudden jumps in their volatility, a phenomenon caused essentially by structural breaks, and cannot be captured by regime-invariant parameters such as the single-state GARCH-type models. Abdymomunov (2013) and Augustyniak (2014) have confirmed that the volatility is indeed subject to two regimes: high and low (or normal), where the high risk regime is considered as a financial stress and closely related to periods of crisis. Alternatively, Hillebrand (2005) has affirmed that the nearly integrated behavior, generally observed in classical GARCH models, is the consequence of structural changes.…”

“…As pointed out by Hoffmann et al (2013), investors' risk perception fluctuates significantly during financial crisis, more than it does during normal non-crisis periods. Consequently, and in alignment with Abdymomunov (2013) and Augustyniak (2014), we suspect that during these high-stress periods, the volatility tends to be higher than during normal periods; hence, we see no reason to extend our analysis for more than two regimes.…”

Selection Criteria in Regime Switching Conditional Volatility Models

“…This experiment focuses on the traditional approach, the one adopted in [25]. Data are generated following Equation (12). The simulation procedure is the following.…”

“…There appear to be no findings on MS-GARCH models to date, nor on the asymptotic distribution of the Maximum Likelihood (ML) estimation. For example, Augustyniak [12] conducts an experiment which shows that Gray's method does not generate consistent estimates for the path-dependent MS-GARCH model. These 1 Some empirical studies have shown that the QML estimation of smooth transition models can cause problems in interpretation.…”

Markov Switching GARCH Models: Filtering, Approximations and Duality

“…Furthermore, Bayesian approaches based on Markov Chain Monte Carlo Gibbs technique for estimating MS GARCH can be found in [3], [4], [17] or [5]. Other works based on both Monte Carlo methods combined with expectation-maximization algorithm and importance sampling to evaluate Maximum Likelihood (ML) estimators are conducted by [1], [6], and [7]. Finally, a recent paper by [2] proposes estimation of MS GARCH models with a deterministic particle filter.…”