Cointegration is an important concept in the analysis of non-stationarytime-series, giving conditions under which a collection of non-stationaryprocesses has an underlying stationary (cointegration) relationship. In thispaper we present the first fully Bayesian residual-based test forcointegration, where we consider the whole space of possible cointegrationrelationships when testing for the presence of cointegration. We firstdemonstrate that such a test can be performed exactly in the case where theresidual process follows a first-order autoregressive process. We then extendthis test to include more complex residual processes, where we first consider asuitable cointegration test-statistic and then leverage Bayesian samplingtechniques to perform the necessary inference. We empirically demonstrate thatour Bayesian approach attains a superior classification accuracy than existingapproaches, all of which use a point estimate of the cointegration relationshipin their test. Finally, we demonstrate our approach on some real worldfinancial time-series data.
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