Size and power of some cointegration tests under structural breaks and heteroskedastic noise

In this paper we examine the power and size distortions of a number of representative cointegration tests in some large-scale Monte Carlo simulations, when the underlying system is subjected to regime shifts and conditional (ARCH-type) heteroskedasticity. Following the suggestion by Gregory and Hansen, we select the minimum (maximum for the Johansen test) value for the statistics evaluated over a set of tentative break points for the regime shifts. The performance of these statistics is compared to the corresponding ordinary statistics in the presence of regime shifts. We demonstrate that the size of the cointegration tests is severely distorted by conditional heteroskedasticity.