On discriminating between long-range dependence and changes in mean

By István Berkes, Lajos Horv'ath, Piotr Kokoszka, Qi-Man Shao. 2006

156 citations recorded by the source corpus.

We develop a testing procedure for distinguishing between a long-range dependent time series and a weakly dependent time series with change-points in the mean. In the simplest case, under the null hypothesis the time series is weakly dependent with one change in mean at an unknown point, and under the alternative it is long-range dependent. We compute the CUSUM statistic T n , which allows us to construct an estimator k of a change-point. We then compute the statistic T n,1 based on the observations up to time k and the statistic T n,2 2 based on the observations after time k. The statistic M n = max[T n.1 , T n,2 ] converges to a well-known distribution under the null, but diverges to infinity if the observations exhibit long-range dependence. The theory is illustrated by examples and an application to the returns of the Dow Jones index.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/36e31f6c9df8860f73391768436ab44228682863

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Citations in the corpus

Testing equality of stationary autocovariances (2009, unknown): “Any truncation form should satisfy the hypotheses in Thm A.1 in Berkes et al. (2006).”
Non‐Parametric Change‐Point Tests for Long‐Range Dependent Data (2013, background): “Berkes et al. (2006) propose cusum type tests for discriminating between long-range dependence and changes in the mean of a weakly dependent process.”
Structural breaks in time series (2013, background): “…findings by Bhattacharya et al. (1983) and others were subsequently made rigorous by a number of authors, among them Giraitis et al. (2003), Berkes et al. (2006), Aue et al. (2009d), Harvey et al. (2010). aUniversity of California bUniversity of Utah Correspondence to: Alexander Aue…”
Optimal detection of changepoints with a linear computational cost (2011, background): “C penalty are shown as vertical lines in Figure 2. These results are consistent with previous studies on portions of the data; the 3rd week in March 1973 found by Hsu (1977) and October 1987 found by Berkes et al. (2006). The PELT method identiﬁes 82 changepoints and the Binary Segmentation method i”
Simple (but effective) tests of long memory versus structural breaks (2006, unknown): “k=0 Γ(−d̂ + k) Γ(−d̂)k! (Xt−k − μ̇(d̂)), (9) where μ̇(d̂) = w(d)n−1 ∑n t=1 Ẋt + (1 − w(d))Ẋ1.”
Exploring the ability of the Pettitt method for detecting change point by Monte Carlo simulation (2014, background): “In statistical literatures, the change point problems have been much investigated and studied (Giraitis et al. 1996; Berkes et al. 2006; Ling 2007; Antoch et al. 2008; Wang 2008; Spokoiny 2009; Zhao et al. 2010; Yamaguchi 2011; Kim and Lee 2011; Dehling et al. 2012; Hušková and Kirch 2012; Tan et…”
Extensions of some classical methods in change point analysis (2014, background): “It has been observed [cf. Aue et al. (2009b) and Berkes et al. (2006)] that CUSUM and the quasi-maximum likelihood tests reject the no change in the mean null hypothesis, even if the null hypothesis is correct, when the errors follow a random walk or there is long-range dependence between the…”
Detecting changes in the mean of functional observations (2009, methodology): “It is generally very difficult to determine on purely statistical grounds whether a change-point or a long-range dependent model is more suitable for any particular finite length record; see Berkes et al. (2006) and Jach and Kokoszka (2008) for recent methodology, discussion and references.”