Markov Switching In-Mean Effect. Bayesian Analysis in Stochastic Volatility Framework

In the study we introduce an extension to a stochastic volatility in mean model (SV-M), allowing for discrete regime switches in the risk premium parameter. The logic behind the idea is that neglecting a possibly regime changing nature of the relation between the current volatility (conditional standard deviation) and asset return within an ordinary SV-M specification may lead to spurious insignificance of the risk premium parameter (as being 'averaged out' over the regimes). Therefore, we allow the volatility-in-mean effect to switch over different regimes according to a discrete homogeneous two-state Markov chain. We treat the new specification within the Bayesian framework, which allows to fully account for the uncertainty of model parameters, latent conditional variances and hidden Markov chain state variables. Standard Markov Chain Monte Carlo methods, including the Gibbs sampler and the Metropolis-Hastings algorithm, are adapted to estimate the model and to obtain predictive densities of selected quantities. Presented methodology is applied to analyse series of the Warsaw Stock Exchange index (WIG) and its sectoral subindices. Although rare, once spotted the switching in-mean effect substantially enhances the model fit to the data, as measured by the value of the marginal data density.