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

Kim, Jaeho (2015): Bayesian Inference in a Non-linear/Non-Gaussian Switching State Space Model: Regime-dependent Leverage Effect in the U.S. Stock Market.

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Abstract

This paper provides a Bayesian algorithm 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 algorithm that are built upon the novel idea of ancestor sampling is robust to small numbers of particles. Moreover, the algorithm is 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.

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