What results can we expect from rolling trace tests? A discussion based on the issue of stock market integration

This paper discusses pitfalls in the application of the rolling trace test. This procedure is based on the iterative calculation of Johansen's (1988) trace test for the rank of a cointegration system in windows of equal length that roll over the sample. Pitfalls lie in the selection of the window length and of the lag order for short-run coefficients as well as in the presence of stationary variables in some sub-periods. We give practical recommendations to solve these issues and demonstrate their implications when assessing the integration of four major European stock markets.