A Bayesian Residual-Based Test for Cointegration

Cointegration is an important concept in the analysis of non-stationary time-series, giving conditions under which a collection of non-stationary processes has an underlying stationary (cointegration) relationship. In this paper we present the first fully Bayesian residual-based test for cointegration, where we consider the whole space of possible cointegration relationships when testing for the presence of cointegration. We first demonstrate that such a test can be performed exactly in the case where the residual process follows a first-order autoregressive process. We then extend this test to include more complex residual processes, where we first consider a suitable cointegration test-statistic and then leverage Bayesian sampling techniques to perform the necessary inference. We empirically demonstrate that our Bayesian approach attains a superior classification accuracy than existing approaches, all of which use a point estimate of the cointegration relationship in their test. Finally, we demonstrate our approach on some real world financial time-series data.