A CUSUM test for breaks in fractional cointegration

We propose a CUSUM type test for breaks in a fractional cointegration model. The test can be used to detect a break in the cointegrating vector and potentially for a break in the degree of integration. We establish the limiting distribution using different representations of stochastic integrals, which depend on the combined degree of integration of the series. Also, we prove consistency of the test under a break in the parameter. In a Monte-Carlo simulation we find good size and power levels for most combinations of fractional integration. • We propose a CUSUM test for breaks in a fractional cointegration model. • We introduce a new bootstrap procedure to generate critical values. • A non-trivial limit distribution is derived and consistency is proven. • In a Monte Carlo study, we find good size and power for most orders of integration.