A Bayesian Residual-Based Test for Cointegration

TL;DR

This paper introduces the first fully Bayesian residual-based test for cointegration in non-stationary time-series, improving classification accuracy over existing methods by considering the entire space of cointegration relationships.

Contribution

It develops a novel Bayesian cointegration test that accounts for all possible relationships, extending to complex residual processes and demonstrating superior empirical performance.

Findings

Bayesian test outperforms existing methods in classification accuracy.

Exact testing possible for first-order autoregressive residuals.

Effective application demonstrated on real financial data.

Abstract

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.