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This paper provides two Bayesian algorithms to efficiently estimate non-linear/non-Gaussian switching state space models by extending a standard Particle Markov chain Monte Carlo (PMCMC) method. Instead of iteratively running separate PMCMC steps using conventional approaches, the proposed methods generate continuous-state and discrete-regime indicator variables together from their joint smoothing distribution in one Gibbs block. The proposed Bayesian algorithms that are built upon the novel ideas of ancestor sampling and particle rejuvenation are robust to small numbers of particles and degenerate state transition equations. Moreover, the algorithms are applicable to any switching state space models, regardless of the Markovian property. The difficulty in conducting Bayesian model comparisons is overcome by adopting the Deviance Information Criterion (DIC). For illustration, a regime-dependent leverage effect in the U.S. stock market is investigated using the newly developed methods. A conventional regime switching stochastic volatility model is generalized to encompass the regime-dependent leverage effect and is applied to Standard and Poor’s 500 and NASDAQ daily return data. The resulting Bayesian posterior estimates indicate that the stronger (weaker) financial leverage effect is associated with a high (low) volatility regime.

Bayesian Inference in a Non-Linear/Non-Gaussian Switching State Space Model: Regime-Dependent Leverage Effect in the U.S. Stock Market