- Volume 6, Number 5 (2000), 845-869.
The multiple change-points problem for the spectral distribution
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.
Bernoulli, Volume 6, Number 5 (2000), 845-869.
First available in Project Euclid: 6 April 2004
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Lavielle, Marc; Ludeña, Carenne. The multiple change-points problem for the spectral distribution. Bernoulli 6 (2000), no. 5, 845--869. https://projecteuclid.org/euclid.bj/1081282692