A Bayesian Approach to Modelling Bivariate Time-Varying Cointegration and Cointegrating Rank

A bivariate 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 sub-models implied by alternative cointegrating matrix ranks and allows for transitions between stationarity and non-stationarity, and cointegrating and non-cointegrating relationships in accordance with the observed behaviour 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.