Stochastic model specification in Markov switching vector error correction models

Abstract

This paper proposes a hierarchical modeling approach to perform stochastic model specification in Markov switching vector error correction models. We assume that a common distribution gives rise to the regime-specific regression coefficients. The mean as well as the variances of this distribution are treated as fully stochastic and suitable shrinkage priors are used. These shrinkage priors enable to assess which coefficients differ across regimes in a flexible manner. In the case of similar coefficients, our model pushes the respective regions of the parameter space towards the common distribution. This allows for selecting a parsimonious model while still maintaining sufficient flexibility to control for sudden shifts in the parameters, if necessary. We apply our modeling approach to real-time Euro area data and assume transition probabilities between expansionary and recessionary regimes to be driven by the cointegration errors. The results suggest that the regime allocation is governed by a subset of short-run adjustment coefficients and regime-specific variance-covariance matrices. These findings are complemented by an out-of-sample forecast exercise, illustrating the advantages of the model for predicting Euro area inflation in real time.

Bayesian Markov switching model for BRICS currencies' exchange rates

“…As discussed, because the number of parameters to be calculated get proliferated substantially with an increase in the number of regimes, we use Bayesian techniques for calculating parameters. Based on Hauzenberger et al (2021), we first stack the parameters to be estimated in the vector form…”

“…As discussed, because the number of parameters to be calculated get proliferated substantially with an increase in the number of regimes, we use Bayesian techniques for calculating parameters. Based on Hauzenberger et al (2021), we first stack the parameters to be estimated in the vector form = , which is of dimension where and then vectorize it as . We also define for as a variance–covariance matrix of variances .…”

“…We set the values for as 1, 100, 0.04, and 0.01. These values make the prior fairly uninformative and reasonably good for estimating highly parameterized models (Hauzenberger et al, 2021; Huber & Zörner, 2019). The label switching issue described by Frühwirth‐Schnatter (2006) is addressed using an identification condition embedded in the iteration process by assuming that the conditional mean of the short‐run interest rate equation is higher in a scenario when the currency is depreciated and is implemented as a rejection step in the MCMC algorithm.…”

“…For the Bayesian estimation, this study adopts a mix of two shrinkage priors: the normal‐gamma (NG) prior introduced by Griffin and Brown (2010) and the Minnesota prior by Litterman (1979). Hauzenberger et al (2021) and Huber and Zörner (2019) demonstrate that these shrinkage priors provide the necessary flexibility for regime‐specific coefficient identification.…”

Hybrid SV‐GARCH, t‐GARCH and Markov‐switching covariance structures in VEC models—Which is better from a predictive perspective?

“…Particularly, to the best of our knowledge, there are only individual studies focused on predictive comparison of Bayesian cointegrated VAR models incorporating time‐varying volatility [see, e.g. Hauzenberger et al, 2021, who focus solely on VECs with Markov‐switching heteroskedasticity (MSH)]. Because both long‐term relationships and conditional heteroskedasticity need to be accounted for simultaneously (e.g.…”