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Testing for a break in persistence under long‐range dependencies
Author(s) -
Sibbertsen Philipp,
Kruse Robinson
Publication year - 2009
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2009.00611.x
Subject(s) - mathematics , estimator , consistency (knowledge bases) , range (aeronautics) , cusum , asymptotic distribution , algorithm , statistics , discrete mathematics , materials science , composite material
. We show that tests for a break in the persistence of a time series in the classical I (0)/ I (1) framework have serious size distortions when the actual data‐generating process (DGP) exhibits long‐range dependencies. We prove that the limiting distribution of a CUSUM of squares‐based test depends on the true memory parameter if the DGP exhibits long memory. We propose adjusted critical values for the test and give finite sample response curves that allow easy implementation of the test by the practitioner and also ease in computing the relevant critical values. We furthermore prove the consistency of the test for a simple breakpoint estimator also under long memory. We show that the test has satisfying power properties when the correct critical values are used.