# A robust approach for estimating change-points in the mean of an AR(p) process

@article{Chakar2014ARA, title={A robust approach for estimating change-points in the mean of an AR(p) process}, author={Souhil Chakar and 'Emilie Lebarbier and C'eline L'evy-Leduc and St{\'e}phane Robin}, journal={arXiv: Methodology}, year={2014} }

We consider the problem of change-points estimation in the mean of an AR(p) process. Taking into account the dependence structure does not allow us to use the approach of the independent case. Especially, the dynamic programming algorithm giving the optimal solution in the independent case cannot be used anymore. We propose a two-step method, based on the preliminary robust (to the change-points) estimation of the autoregression parameters. Then, we propose to follow the classical approach, by…

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## References

SHOWING 1-10 OF 57 REFERENCES

Multiple Change-Point Estimation With a Total Variation Penalty

- Computer Science, Mathematics
- 2010

An improved practical version of this method is provided by combining it with a reduced version of the dynamic programming algorithm and it is proved that, in an appropriate asymptotic framework, this method provides consistent estimators of the change points with an almost optimal rate.

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

- Mathematics
- 2010

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($\infty$),…

Structural Break Estimation for Nonstationary Time Series Models

- Computer Science
- 2006

This article considers the problem of modeling a class of nonstationary time series using piecewise autoregressive (AR) processes, and the minimum description length principle is applied to compare various segmented AR fits to the data.

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

- Mathematics
- 2012

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(∞),…

Using penalized contrasts for the change-point problem

- Mathematics, Computer ScienceSignal Process.
- 2005

Computation and Analysis of Multiple Structural-Change Models

- Mathematics
- 1998

In a recent paper, Bai and Perron (1998) considered theoretical issues related to the limiting distribution of estimators and test statistics in the linear model with multiple structural changes. In…

Robust estimation of the scale and of the autocovariance function of Gaussian short‐ and long‐range dependent processes

- Mathematics
- 2009

A desirable property of an autocovariance estimator is to be robust to the presence of additive outliers. It is well known that the sample autocovariance, being based on moments, does not have this…

Multiscale change point inference

- Mathematics, Computer Science
- 2013

A new estimator, the simultaneous multiscale change point estimator SMUCE, is introduced, which achieves the optimal detection rate of vanishing signals as n→∞, even for an unbounded number of change points.

Least‐squares Estimation of an Unknown Number of Shifts in a Time Series

- Mathematics
- 2000

In this contribution, general results on the off‐line least‐squares estimate of changes in the mean of a random process are presented. First, a generalisation of the Hajek‐Renyi inequality, dealing…

Detecting multiple change-points in the mean of Gaussian process by model selection

- Computer ScienceSignal Process.
- 2005