# On the extreme eigenvalues of the precision matrix of the nonstationary autoregressive process and its applications to outlier estimation of panel time series

@inproceedings{Yang2021OnTE, title={On the extreme eigenvalues of the precision matrix of the nonstationary autoregressive process and its applications to outlier estimation of panel time series}, author={Junho Yang}, year={2021} }

This paper investigates the structural change of the coefficients in the autoregressive process of order one by considering extreme eigenvalues of an inverse covariance matrix (precision matrix). More precisely, under mild assumptions, extreme eigenvalues are observed when the structural change has occurred. A consistent estimator of extreme eigenvalues is provided under the panel time series framework. The proposed estimation method is demonstrated with simulations.

## References

SHOWING 1-10 OF 33 REFERENCES

Approximations of the eigenvalues of the covariance matrix of a first-order autoregressive process

- Mathematics, Computer Science
- 1983

BANDING SAMPLE AUTOCOVARIANCE MATRICES OF STATIONARY PROCESSES

- Mathematics
- 2009

We consider estimation of covariance matrices of stationary processes. Under a short-range dependence condition for a wide class of nonlinear processes, it is shown that the banded covariance matrix…

Sequential Procedures for Detecting Parameter Changes in a Time-Series Model

- Mathematics
- 1977

Abstract Procedures are proposed for monitoring forecast errors in order to detect changes in a time-series model. These procedures are based on likelihood ratio statistics which consist of…

Estimation of time series parameters in the presence of outliers

- Computer Science
- 1988

An iterative procedure is proposed for detecting IO and AO in practice and for estimating the time series parameters in autoregressive-integrated-moving-average models in the presence of outliers.

Testing and estimating change-points in the covariance matrix of a high-dimensional time series

- Mathematics, Computer ScienceJ. Multivar. Anal.
- 2020

The Cusum Test for Parameter Change in Time Series Models

- Mathematics
- 2003

Abstract. In this paper, we consider the problem of testing for parameter changes in time series models based on a cusum test. Although the test procedure is well established for the mean and…

Testing for a Change in the Parameter Values and Order of an Autoregressive Model

- Mathematics
- 1995

The problem of testing whether or not a change has occurred in the parameter values and order of an autoregressive model is considered. It is shown that if the white noise in the AR model is weakly…

Bayesian Inference and Prediction for Mean and Variance Shifts in Autoregressive Time Series

- Mathematics, Computer Science
- 1993

The analysis of random mean- shift models to random variance-shift models is extended and a method for predicting when a shift is about to occur is considered, which involves adding to the autoregressive model a probit model for the probability that a shift occurs given a chosen set of explanatory variables.