Detecting multiple change-points in general causal time series using penalized quasi-likelihood

Abstract : This paper is devoted to the off-line multiple change-point detection in a semiparametric framework. The time series is supposed to belong to a large class of models including AR($\infty$), ARCH($\infty$), TARCH($\infty$),... models where the coefficients change at each instant of breaks. The different unknown parameters (number of changes, change dates and parameters of successive models) are estimated using a penalized contrast built on conditional quasi-likelihood. Under Lipshitzian conditions on the model, the consistency of the estimator is proved when the moment order $r$ of the process satisfies $r\geq 2$. If $r\geq 4$, the same convergence rates for the estimators than in the case of independent random variables are obtained. The particular cases of AR($\infty$), ARCH($\infty$) and TARCH($\infty$) show that our method notably improves the existing results.
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Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2012, 6, pp.435-477
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  • HAL Id : hal-00507759, version 1
  • ARXIV : 1008.0054

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Jean-Marc Bardet, William Charky Kengne, Olivier Wintenberger. Detecting multiple change-points in general causal time series using penalized quasi-likelihood. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2012, 6, pp.435-477. 〈hal-00507759〉

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