A Bayesian Approach to Modeling Time-Varying Cointegration and Cointegrating Rank

A multivariate model that allows for both a time-varying cointegrating matrix and time-varying cointegrating rank is presented. The model addresses the issue that, in real data, the validity of a constant cointegrating relationship may be questionable. The model nests the submodels implied by alternative cointegrating matrix ranks and allows for transitions between stationarity and nonstationarity, and cointegrating and noncointegrating relationships in accordance with the observed behavior of the data. A Bayesian test of cointegration is also developed. The model is used to assess the validity of the Fisher effect and is also applied to equity market data.