# 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}
}
• Published 8 March 2014
• Mathematics, Computer Science
• arXiv: Methodology
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…
40 Citations

## Figures and Tables from this paper

Change-Point Detection in Autoregressive Processes via the Cross-Entropy Method
• Computer Science
Algorithms
• 2020
A flexible method to estimate the unknown number and the locations of change-points in autoregressive time series and a Cross-Entropy algorithm for the combinatorial optimization problem is developed.
ACF estimation via difference schemes for a semiparametric model with $m$-dependent errors
• Mathematics
• 2019
In this manuscript, we discuss a class of difference-based estimators of the autocovariance structure in a semiparametric regression model where the signal is discontinuous and the errors are
Robust multiscale estimation of time-average variance for time series segmentation
• Mathematics
• 2022
There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods,
Estimation and inference of time-varying auto-covariance under complex trend: A diﬀerence-based approach
• Mathematics
• 2021
: We propose a diﬀerence-based nonparametric methodology for the estimation and inference of the time-varying auto-covariance functions of a locally stationary time series when it is contaminated by
Estimation and inference of time-varying auto-covariance under complex trend: A difference-based approach
• Mathematics
Electronic Journal of Statistics
• 2021
We propose a difference-based nonparametric methodology for the estimation and inference of the time-varying auto-covariance functions of a locally stationary time series when it is contaminated by a
Non-homogeneous Poisson and linear regression models as approaches to study time series with change-points
• Mathematics, Computer Science
Communications in Statistics: Case Studies, Data Analysis and Applications
• 2022
Some stochastic models and a Bayesian approach to analyze count time series data in the presence of one or more change-points to consider non-homogeneous Poisson processes (NHPP) models with a suitable rate function.
A robust method for shift detection in time series
• Mathematics
• 2015
We present a robust test for change-points in time series which is based on the two-sample Hodges-Lehmann estimator. We develop new limit theory for a class of statistics based on the two-sample
Robust Algorithms for Change-Point Regressions Using the t-Distribution
• Computer Science
Mathematics
• 2021
A modified version of the proposed EMT and FCT, which fits the t change-point regression model to the data after moderately pruning high leverage points, is introduced, and the preference of the t-based approach over normal-based methods for better robustness and computational efficiency is demonstrated.
A factor model approach for the joint segmentation with between‐series correlation
• Computer Science
Scandinavian Journal of Statistics
• 2018
It is shown that such a dependence structure can be encoded in a factor model and the inference of the breakpoints can be achieved via dynamic programming, which remains one the most efficient algorithms.
A breakpoint detection in the mean model with heterogeneous variance on fixed time intervals
• Mathematics
Stat. Comput.
• 2020
A new segmentation model is proposed that is a breakpoint detection in the mean model of a Gaussian process with heterogeneous variance on known time intervals that can be applied to homogenization of global navigation satellite system-derived integrated water vapour series.

## 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
• M. Lavielle
• Mathematics, Computer Science
Signal 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