Detecting abrupt changes of the long-range dependence or the self-similarity of a Gaussian process

Details Detecting abrupt changes of the long-range dependence or the self-similarity of a Gaussian process Detecting abrupt changes of the long-range dependence or the self-similarity of a Gaussian process

2007-12-10

arxiv.org/abs/0712.1456v2

Mathematics

Statistics Theory

Scientific paper

In this paper, an estimator of $m$ instants ($m$ is known) of abrupt changes of the parameter of long-range dependence or self-similarity is proved to satisfy a limit theorem with an explicit convergence rate for a sample of a Gaussian process. In each estimated zone where the parameter is supposed not to change, a central limit theorem is established for the parameter's (of long-range dependence, self-similarity) estimator and a goodness-of-fit test is also built. {\it To cite this article: J.M. Bardet, I. Kammoun, C. R. Acad. Sci. Paris, Ser. I 340 (2007).}

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