Finite mixture and Markov-switching models generalize and, therefore, nest specifications featuring only one component. While specifying priors in the general (mixture) model and its special (single-component) case, it may be desirable to ensure that the prior assumptions introduced into both structures are compatible in the sense that the prior distribution in the nested model amounts to the conditional prior in the mixture model under relevant parametric restriction. The study provides the rudiments of setting compatible priors in Bayesian univariate finite mixture and Markov-switching models. Once some primary results are delivered, we derive specific conditions for compatibility in the case of three types of continuous priors commonly engaged in Bayesian modeling: the normal, inverse gamma, and gamma distributions. Further, we study the consequences of introducing additional constraints into the mixture model’s prior on the conditions. Finally, the methodology is illustrated through a discussion of setting compatible priors for Markov-switching AR(2) models.

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

This paper investigates the relative importance of cost, demand, financialand monetary shocks in driving real exchange rates in four CEE countries over2000–2018. A two-country New Keynesian open economy model is used as atheoretical framework. In the empirical part, a Bayesian SVAR model withMarkov switching heteroscedasticity is employed. The structural shocks areidentified on the basis of volatility changes and named with reference to the signrestrictions derived from the economic model. Main findings are fourfold. First,real and financial shocks have similar contributions to real exchange variability,whereas that of monetary shocks is small. Second, financial shocks amplifyexchange rate fluctuations stemming from real shocks. Third, even though theexchange rate gaps change over time, they remain quite similar across CEEcountries except for Slovakia. Fourth, Slovakia introduced the euro at the timeof a relatively large real overvaluation, which subsided after a lengthy adjustmentprocess.