A residual-based test for stochastic cointegration

Abstract

We consider the problem of hypothesis testing in a modified version of the stochastic integration and cointegration framework of Harris, McCabe, and Leybourne (2002, Journal of Econometrics 111, 363-384). This nonlinear setup allows for volatility in excess of that catered for by the standard integration/cointegration paradigm through the introduction of nonstationary heteroskedasticity. We propose a test for stochastic cointegration against the alternative of no cointegration and a secondary test for stationary cointegration against the heteroskedastic alternative. Asymptotic distributions of these tests under their respective null hypotheses are derived, and consistency under their respect..