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A Fixed-b Test for a Break in Level at an unknown time under Fractional Integration

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JournalJournal of Time Series Analysis
DateE-pub ahead of print - 23 Oct 2013
DatePublished (current) - Jan 2014
Issue number1
Volume35
Number of pages15
Pages (from-to)40-54
Early online date23/10/13
Original languageEnglish

Abstract

In this paper we propose a test for a break in the level of a fractionally integrated process when the timing of the putative break is not known. This testing problem has received considerable attention in the literature in the case where the time series is weakly autocorrelated. Less attention has been given to the case where the underlying time series is allowed to be fractionally integrated.
Here, valid testing can only be performed if the limiting null distribution of the
level break test statistic is well-defined for all values of the fractional integration exponent considered. However, conventional sup-Wald type tests diverge
when the data are strongly autocorrelated. We show that a sup-Wald statistic which is standardized using a non-parametric kernel-based long run variance
estimator does possess a well-defined limit distribution, depending only on the
fractional integration parameter, provided the recently developed fixed-b asymptotic framework is applied. We give the appropriate asymptotic critical values for this sup-Wald statistic, and show that it has good finite sample size and power properties.

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