Abstract
We show that the CUSUM-squared based test for a change in persistence by Leybourne et al. (J Time Ser Anal 28:408–433, 2007) is not robust against shifts in the mean. A mean shift leads to serious size distortions. Therefore, adjusted critical values are needed when it is known that the data generating process has a mean shift. These are given for the case of one mean break. Response curves for the critical values are derived and a Monte Carlo study showing the size and power properties under this general de-trending is given.
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Sibbertsen, P., Willert, J. Testing for a break in persistence under long-range dependencies and mean shifts. Stat Papers 53, 357–370 (2012). https://doi.org/10.1007/s00362-010-0342-5
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DOI: https://doi.org/10.1007/s00362-010-0342-5