## Bernoulli

- Bernoulli
- Volume 23, Number 2 (2017), 1408-1447.

### A robust approach for estimating change-points in the mean of an $\operatorname{AR}(1)$ process

S. Chakar, E. Lebarbier, C. Lévy-Leduc, and S. Robin

#### Abstract

We consider the problem of multiple change-point estimation in the mean of an $\operatorname{AR}(1)$ process. Taking into account the dependence structure does not allow us to use the dynamic programming algorithm, which is the only algorithm giving the optimal solution in the independent case. We propose a robust estimator of the autocorrelation parameter, which is consistent and satisfies a central limit theorem in the Gaussian case. Then, we propose to follow the classical inference approach, by plugging this estimator in the criteria used for change-points estimation. We show that the asymptotic properties of these estimators are the same as those of the classical estimators in the independent framework. The same plug-in approach is then used to approximate the modified BIC and choose the number of segments. This method is implemented in the R package AR1seg and is available from the Comprehensive R Archive Network (CRAN). This package is used in the simulation section in which we show that for finite sample sizes taking into account the dependence structure improves the statistical performance of the change-point estimators and of the selection criterion.

#### Article information

**Source**

Bernoulli, Volume 23, Number 2 (2017), 1408-1447.

**Dates**

Received: February 2015

Revised: October 2015

First available in Project Euclid: 4 February 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.bj/1486177403

**Digital Object Identifier**

doi:10.3150/15-BEJ782

**Mathematical Reviews number (MathSciNet)**

MR3606770

**Zentralblatt MATH identifier**

1378.62059

**Keywords**

auto-regressive model change-points model selection robust estimation of the $\operatorname{AR}(1)$ parameter time series

#### Citation

Chakar, S.; Lebarbier, E.; Lévy-Leduc, C.; Robin, S. A robust approach for estimating change-points in the mean of an $\operatorname{AR}(1)$ process. Bernoulli 23 (2017), no. 2, 1408--1447. doi:10.3150/15-BEJ782. https://projecteuclid.org/euclid.bj/1486177403