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 regimechanging nature of the relation between the current volatility (conditional standard deviation) and asset return within an ordinary SV-M specication may lead to spurious insignicance of the risk premium parameter (as being ‛averaged out’ over the regimes). Therefore, we allow the volatility-in-mean eect to switch over dierent regimes according to a discrete homogeneous two-state Markov chain. We treat the new specication 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 eect substantially enhances the model t to the data, as measured by the value of the marginal data density.
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 regime