Bayesian Analysis of a Regime Switching In-Mean Effect for the Polish Stock Market

The study aims at a statistical verification of breaks in the risk-return relationship for shares of individual companies quoted at the Warsaw Stock Exchange. To this end a stochastic volatility model incorporating Markov switching in-mean effect (SV-MS-M) is employed. We argue that neglecting possible regime changes in the relation between expected return and volatility 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- or three-state Markov chain. The model is handled within Bayesian framework, which allows to fully account for the uncertainty of model parameters, latent conditional variances and state variables. MCMC methods, including the Gibbs sampler, Metropolis-Hastings algorithm and the forward-filtering-backward-sampling scheme are suitably adopted to obtain posterior densities of interest as well as marginal data density. The latter allows for a formal model comparison in terms of the in-sample fit and, thereby, inference on the 'adequate' number of the risk premium regimes.