The concept of cointegration that enables the proper statistical analysis of long-run comovements between unit root processes has been of great interest to numerous economic investigators since it was introduced. However, investigation of short-run comovement between economic time series seems equally important, especially for economic decision-makers. The concept of common features and based on it the idea of two additional reduced rank structure forms in a VEC model (the strong and the weak one) may be of some help. The strong form reduced rank structure (SF) takes place when at least one linear combination of the first differences of the variables exists, which is white noise. However, when this assumption seems too strong, the weaker case can be considered. The weak form appears when the linear combination of first differences adjusted for long-run efects exists, which is white noise.

The main focus of this paper is a Bayesian analysis of the VEC models involving the weak form of reduced rank restrictions.

After the introduction and discussion of the said Bayesian model, the presented methods will be illustrated by an empirical investigation of the price – wage spiral in the Polish economy.

The paper aims at comparing forecast ability of VAR/VEC models with a non-changing covariance matrix and two classes of Bayesian Vector Error Correction – Stochastic Volatility (VEC-SV) models, which combine the VEC representation of a VAR structure with stochastic volatility, represented by the Multiplicative Stochastic Factor (MSF) process, the SBEKK form or the MSF-SBEKK specification.

Based on macro-data coming from the Polish economy (time series of unemployment, inflation and interest rates) we evaluate predictive density functions employing of such measures as log predictive density score, continuous rank probability score, energy score, probability integral transform. Each of them takes account of different feature of the obtained predictive density functions.

We propose a Bayesian approach to estimating productive capital stocks and depreciation rates within the production function framework, using annual data on output, employment and investment only. Productive capital stock is a concept related to the input of capital services to production, in contrast to the more common net capital stock estimates, representing market value of fixed assets. We formulate a full Bayesian model and employ it in a series of illustrative empirical examples. We find that parameters of our model, from which the time-path of capital is derived, are weakly identified with the data at hand. Nevertheless, estimation is feasible with the use of prior information on the production function parameters and the characteristics of productivity growth. We show how precision of the estimates can be improved by augmenting the model with an equation for the rate of return.

In this paper we present the Bayesian model selection procedure within the class of cointegrated processes. In order to make inference about the cointegration space we use the class of Matrix Angular Central Gaussian distributions. To carry out posterior simulations we use an alorithm based on the collapsed Gibbs sampler. The presented methods are applied to the analysis of the price – wage mechanism in the Polish economy.

The main goal of the paper is the Bayesian analysis of weak form polynomial serial correlation common features together with cointegration. In the VEC model the serial correlation common feature leads to an additional reduced rank restriction imposed on the model parameters.

After the introduction and discussion of the model, the methods will be illustrated with an empirical investigation of the price-wage nexus in the Polish economy.

Additionally, consequences of imposing such additional short-run restrictions for permanent-transitory decomposition will be discussed.

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.

In 1993 Engle and Kozicki proposed the notion of common features of which one example is a serial correlation common feature. We say that stationary, non-innovation processes exhibit common serial correlation when there exists at least one linear combination of them which is an innovation. Later on in 1993 Vahid and Engle combined the notions of cointegration among I(1) processes with common serial correlation within their first differences. It is commonly known that cointegrated time series have vector error correction (VEC) representation. The existence of common serial correlation leads to an additional reduced rank restriction imposed on the VEC model’s parameters. This type of restriction was later termed a strong form (SF) reduced rank structure, as opposed to a weak one introduced in 2006 by Hecq, Palm and Urbain.

The main aim of the present paper is to construct the Bayesian vector error correction model with these additional strong form restrictions.

The empirical validity of investigating both the short- and long-run co-movements between macroeconomic time series will be illustrated by the analysis of the price-wage nexus in the Polish economy.

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