Change point estimation based on the Wilcoxon test in the presence of long-range dependence
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Date
2016
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Abstract
We consider an estimator, based on the two-sample Wilcoxon statistic, for the location of a
shift in the mean of long-range dependent sequences. Consistency and the rate of convergence for the
estimated change point are established. In particular, 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 in case of a constant shift height. It is proved that after a suitable normalization
the estimator converges in distribution to a functional of a fractional Brownian motion, if the change point
height decreases to 0 with a certain rate. The estimator is tested on two well-known data sets. Finite sample
behaviors are investigated in a Monte Carlo simulation study.
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Keywords
change point estimation, self-normalization, Wilcoxon test, long-range dependence