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.
Publié le : 2000-10-14
Classification:
detection of change-points,
long range dependence,
maximal inequality,
nonparametric spectral estimation,
penalized minimum contrast estimate,
quadratic forms,
Whittle likelihood
@article{1081282692,
author = {Lavielle, Marc and Lude\~na, Carenne},
title = {The multiple change-points problem for the spectral distribution},
journal = {Bernoulli},
volume = {6},
number = {6},
year = {2000},
pages = { 845-869},
language = {en},
url = {http://dml.mathdoc.fr/item/1081282692}
}
Lavielle, Marc; Ludeña, Carenne. The multiple change-points problem for the spectral distribution. Bernoulli, Tome 6 (2000) no. 6, pp. 845-869. http://gdmltest.u-ga.fr/item/1081282692/