Multiple breaks detection in general causal time series using penalized quasi-likelihood

By Jean‐Marc Bardet, William Kengne, Olivier Wintenberger. 2012

52 citations recorded by the source corpus.

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 r≥2. If r≥4, 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.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/254c387a40fa94c1f3641e73f65592e7a228171c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. C. L'evy-Leduc
2. Stéphane Robin
3. Pengyu Liu
4. I. Macneill
5. É. Lebarbier
6. Stergios B. Fotopoulos
7. Venkata K. Jandhyala
8. S. Chakar

In Statistics and Probability

1. Stéphane Robin
2. É. Lebarbier
3. S. Chakar
4. Stergios B. Fotopoulos
5. Venkata K. Jandhyala
6. Pengyu Liu
7. I. Macneill
8. C. L'evy-Leduc

Citations in the corpus

• A robust approach for estimating change-points in the mean of an AR(1) process (2014, methodology): “[5] proposed a methodology for estimating the change-points of a nonstationary time series built from a general class of models having piecewise constant parameters.”
• Inference for single and multiple change‐points in time series (2013, background): “Recently, Bardet et al. (2012) considered a penalized conditional quasi-likelihood function for estimating the number of change-points and their locations in a general causal time series that includes such time series as AR(1), ARCH(1) and TARCH(1).”