Common Trends and Common Cycles – Bayesian Approach

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.