Open Access
2012 Multiple breaks detection in general causal time series using penalized quasi-likelihood
Jean-Marc Bardet, William Kengne, Olivier Wintenberger
Electron. J. Statist. 6: 435-477 (2012). DOI: 10.1214/12-EJS680


This paper is devoted to the off-line multiple breaks detection for a general class of models. The observations are supposed to fit a parametric causal process (such as classical models AR(), ARCH() or TARCH()) with distinct parameters on multiple periods. The number and dates of breaks, and the different parameters on each period are estimated using a quasi-likelihood contrast penalized by the number of distinct periods. For a convenient choice of the regularization parameter in the penalty term, the consistency of the estimator is proved when the moment order r of the process satisfies r2. If r4, the length of each approximative segment tends to infinity at the same rate as the length of the true segment and the parameters estimators on each segment are asymptotically normal. Compared to the existing literature, we added the fact that a dependence is possible over distinct periods. To be robust to this dependence, the chosen regularization parameter in the penalty term is larger than the ones from BIC approach. We detail our results which notably improve the existing ones for the AR(), ARCH() and TARCH() models. For the practical applications (when n is not too large) we use a data-driven procedure based on the slope estimation to choose the penalty term. The procedure is implemented using the dynamic programming algorithm. It is an O(n2) complexity algorithm that we apply on AR(1), AR(2), GARCH(1,1) and TARCH(1) processes and on the FTSE index data.


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Jean-Marc Bardet. William Kengne. Olivier Wintenberger. "Multiple breaks detection in general causal time series using penalized quasi-likelihood." Electron. J. Statist. 6 435 - 477, 2012.


Published: 2012
First available in Project Euclid: 19 March 2012

zbMATH: 1337.62210
MathSciNet: MR2988415
Digital Object Identifier: 10.1214/12-EJS680

Primary: 62F12 , 62M10

Keywords: AR(∞) processes , ARCH(∞) processes , causal processes , change detection , model selection by penalized likelihood , quasi-maximum likelihood estimator

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society

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