Testing the null of cointegration with a structural break: optimal kernel and bandwidth selection

Structural breaks in relationships between macroeconomic and financial time series are likely a result of financial crises or local reforms. If such structural breaks exist, cointegration tests have to take them into account. Arai and Kurozumi (2007), Carrion-i-Silvestre and Sanso (2006) and Kejriwal (2008) propose a test for the null of cointegration with structural breaks against the alternative of no cointegration (ACK test). In this paper, we systematically examine the ACK test along several dimensions: sample size, kernel selection, bandwidth selection, the maximum value of the first order autocorrelation coefficient allowed in the automated bandwidth estimators proposed by Andrews (1991) and break height. We then compare statistical error frequencies to those of the test proposed by Gregory and Hansen (1996) for the null of no cointegration against the alternative of cointegration with a structural break. We find that the ACK test performs better than the Gregory and Hansen (1996) test in some cases, especially when the data generating process does not contain a cointegration vector. If there is a cointegration vector, the ACK test usually leads to larger statistical error frequencies. The ACK test should hence be used in combination with other tests for cointegration.