Change-in-mean tests in long-memory time series: a review of recent developments

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may AbstractIt 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.

Revisiting Wti-Brent Spread and its Drivers

“…Applying their test, we rejected the null hypothesis of a constant mean with a d~1. We note, however, that simulation studies have shown that this test can be unreliable, even for mid-range values of d. In fact, Wenger et al [107] have shown that even for fractionally integrated white noise vectors, this test is biased toward rejection. As a workaround, we first checked via a Whittle estimator to have a clearer picture of the order of fractional integration.…”

Fixed-bandwidth CUSUM tests under long memory

“…The testing problem is addressed by several papers such as Wang (2008), Shao (2011), Dehling, Rooch, and Taqqu (2013), Iacone, Leybourne, and Taylor (2014), Betken (2016), and others, who employ a variety of competing testing principles. These are reviewed in Wenger, Leschinski, and Sibbertsen (2018). It is found that self-normalized tests are robust against size distortions in finite samples and the CUSUM testing principle tends to be the most powerful.…”

Divergence-Based Segmentation Algorithm for Heavy-Tailed Acoustic Signals with Time-Varying Characteristics

“…Complexity of segmentation may be different, from quite simple statistic based decision making, especially if differences in the data for different subprocesses are clear to notice (as a change of mean or variance) to very advanced techniques for a more complicated process. Interesting approaches used for the problem related to the changing of the location parameter (like mean) can be found in [33][34][35][36][37][38][39][40] while the methods for changing the scale parameter (like variance) are presented, for instance, in [33,[41][42][43][44][45][46][47][48]. A specific case is related to heavy-tailed processes [28][29][30][31] where we expect the impulsive behavior of the corresponding data.…”