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Stat Papers (2012) 53:357370
DOI 10.1007/s00362-010-0342-5
REGULAR ARTICLE
Received: 2 September 2009 / Accepted: 12 May 2010 / Published online: 26 June 2010
Springer-Verlag 2010
Abstract We show that the CUSUM-squared based test for a change in persistence by Leybourne et al. (J Time Ser Anal 28:408433, 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.
Keywords Break in persistence Long memory Structural break Level shift
Mathematics Subject Classication (2000) C12 C22
1 Introduction
It is well known that structural breaks in the mean of a time series can easily be confused with long-range dependence. Shifts in the mean can heavily bias estimators for the memory parameter and therefore create misleading results. For an overview about the problem of spurious long memory due to mean shifts see Sibbertsen (2004). In the recent years a change of the persistence of a time series, this is a change of the order of integration, has come more and more into the focus of empirical and theoretical researchers. Beginning with Banerjee et al. (1992) several authors proposed tests for a change in persistence in the classical I (0)/I (1) framework. A popular stationarity test against a break in persistence was introduced by Kim (2000). Kims test has the
P. Sibbertsen (B) J. Willert
Institute of Statistics, Faculty of Economics and Management, Leibniz Universitt Hannover,
30167 Hannover, Germany
e-mail: [email protected]
Testing for a break in persistence under long-range dependencies and mean shifts
Philipp Sibbertsen Juliane Willert
123
358 P. Sibbertsen, J. Willert
disadvantage to reject the null if the data generating process is constantly I (1) during the whole sample what is theoretically correct but not desirable. Leybourne et al. (2007) suggest a CUSUM-squares based test to solve this problem. Sibbertsen and Kruse (2009) generalized this test to the long memory framework by allowing for fractional degrees of integration.
Belaire-Franch (2005) proved that Kims test is not robust...