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Journal Article

The Multiple Change-Points Problem for the Spectral Distribution

Marc Lavielle and Carenne Ludeña
Bernoulli
Vol. 6, No. 5 (Oct., 2000), pp. 845-869
DOI: 10.2307/3318759
Stable URL: http://www.jstor.org/stable/3318759
Page Count: 25
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The Multiple Change-Points Problem for the Spectral Distribution
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Abstract

We consider the problem of detecting an unknown number of change-points in the spectrum of a second-order stationary random process. To reach this goal, some maximal inequalities for quadratic forms are first given under very weak assumptions. In a parametric framework, and when the number of changes is known, the change-point instants and the parameter vector are estimated using the Whittle pseudo-likelihood of the observations. A penalized minimum contrast estimate is proposed when the number of changes is unknown. The statistical properties of these estimates hold for strongly mixing and also long-range dependent processes. Estimation in a nonparametric framework is also considered, by using the spectral measure function. We conclude with an application to electroencephalogram analysis.

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