@TechReport{dp-728,
  author   = {Dierkes, Maik and Fitter, Krischan and Sibbertsen, Philipp},
  astring  = {Maik Dierkes, Krischan Fitter and Philipp Sibbertsen}
  title    = {Monitoring Breaks in Fractional Cointegration},
  month    = {November},
  year     = {2024},
  pages    = {22},
  number   = {728},
  size     = {486},
  language = {en},
  keywords = {long-memory time series, fractional cointegration, structural change, monitoring},
  jelclass = {C32, C12, C52},
  abstract = {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.}
}