We extend the monitoring of structural breaks in classic cointegration proposed by Wagner and Wied (2017) to explicitly allow for fractional cointegration and breaks in these fractional relations with possible deterministic trends. To estimate the parameters we use a fully modified OLS estimator and we estimate the integration order by the exact local whittle. In order to build the test statistic we establish a CUSUM test for a break in parameters or a break in the order of integration and derive the limiting distribution of the cumulative sum of the modified OLS residuals by using representations by Davidson and Hashimzade (2009) and Fox and Taqqu (1987). Using these limiting results we propose a detector and its limiting distribution as a function of fractional Brownian motions and prove the consistency of our procedure against fixed and local alternatives. The critical values for the monitoring are derived by bootstrap. In a Monte-Carlo study we show the finite sample behavior of our test and compare it to the one by Wagner and Wied (2017) in different scenarios of fractional cointegration. To conclude we show the applicability of the test by presenting the results of applying the test in the context of momentum investing.
