Abstract
We consider an estimator for the location of a shift in the mean of long-range dependent sequences. The estimation is based on the two-sample Wilcoxon statistic. Consistency and the rate of convergence for the estimated change point are established. In the case of a constant shift height, the $1/n$ convergence rate (with $n$ denoting the number of observations), which is typical under the assumption of independent observations, is also achieved for long memory sequences. It is proved that if the change point height decreases to $0$ with a certain rate, the suitably standardized estimator converges in distribution to a functional of a fractional Brownian motion. The estimator is tested on two well-known data sets. Finite sample behaviors are investigated in a Monte Carlo simulation study.
Highlights
MSC 2010 subject classifications: Primary 62G05, 62M10; secondary 60G15, 60G22
The Wilcoxon change point test can be applied. It rejects the hypothesis for large values of the Wilcoxon test statistic defined by kn
In this paper we shortly address the issue of estimating the change point location on the basis of the self-normalized Wilcoxon test statistic proposed in Betken (2016)
Summary
Under non-restrictive constraints on the dependence structure of the data-generating process (including long-range dependent time series) Kokoszka and Leipus (1998) prove consistency of kC,γ under the assumption of fixed as well as decreasing jump heights They establish the convergence rate of the change point estimator as a function of the intensity of dependence in the data if the jump height is constant. Determines the rate of convergence of the change point estimator and derives its asymptotic distribution These results are shown to hold for weakly dependent observations that satisfy a linear model and cover, for example, ARMA(p, q)-processes. Under the assumption of independent data Darkhovskh (1976) establishes an estimator for the location of a change in distribution based on the two-sample Mann-Whitney test statistic He obtains a convergence rate that has order.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
