It is well known that standard tests for a mean shift are invalid in long-range dependent time series. Therefore, several long-memory robust extensions of standard testing principles for a change-in-mean have been proposed in the literature. These can be divided into two groups: those that utilize consistent estimates of the long-run variance and self-normalized test statistics. Here, we review this literature and complement it by deriving a new long-memory robust version of the sup-Wald test. Apart from giving a systematic review, we conduct an extensive Monte Carlo study to compare the relative performance of these methods. Special attention is paid to the interaction of the test results with the estimation of the long-memory parameter. Furthermore, we show that the power of self-normalized test statistics can be improved considerably by using an estimator that is robust to mean shifts.
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We thank an anonymous referee for pointing this out.
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Financial support of the Deutsche Forschungsgesellschaft (DFG) is gratefully acknowledged. We would like to thank the anonymous referees for their reviews. We highly appreciate their comments and suggestions.
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Wenger, K., Leschinski, C. & Sibbertsen, P. Change-in-mean tests in long-memory time series: a review of recent developments. AStA Adv Stat Anal 103, 237–256 (2019). https://doi.org/10.1007/s10182-018-0328-5
- Fractional integration
- Structural breaks
- Long memory