Sequential Monitoring for Changes from Stationarity to Mild Non-stationarity

55 Pages Posted: 16 Oct 2018 Last revised: 10 Jun 2019

See all articles by Lajos Horváth

Lajos Horváth

University of Utah - Department of Mathematics

Zhenya Liu

Renmin University of China; CERGAM, Aix-Marseille University

Gregory Rice

University of Waterloo - Department of Statistics and Actuarial Science

Shixuan Wang

University of Reading - Department of Economics

Date Written: June 7, 2019

Abstract

We develop and study sequential testing procedures á la Chu et al. (1996) for on-line detection of changes in a time series from stationarity to mild forms of non-stationarity. The proposed tests are based on sequential CUSUM and KPSS-type detector processes, and are shown to provide consistent detection under a wide range of change point models, including changes in the parameters of ARMA and GARCH series from values within the model's stationarity parameter region to values close (converging) to the stationarity boundary. Local asymptotic results are established giving precise descriptions of the time to detection under several of these models, which show that such procedures are powerful to detect a wide range of non-stationary characteristics, including changes in mean, volatility, and unit root behaviour. The proposed methods are investigated by means of a simulation study and in applications to monitoring for changes in trend and unit root behaviour in macroeconomic production series, and to detect changes in volatility of the S&P-500 stock market index.

Keywords: change point detection, stationarity testing, normal approximation, non-stationary ARMA time series, non-stationary GARCH time series

JEL Classification: C12, C22, C58

Suggested Citation

Horváth, Lajos and Liu, Zhenya and Rice, Gregory and Wang, Shixuan, Sequential Monitoring for Changes from Stationarity to Mild Non-stationarity (June 7, 2019). Available at SSRN: https://ssrn.com/abstract=3260824 or http://dx.doi.org/10.2139/ssrn.3260824

Lajos Horváth

University of Utah - Department of Mathematics ( email )

1645 E. Campus Center
Salt Lake City, UT 84112
United States
801 581-8159 (Phone)

Zhenya Liu (Contact Author)

Renmin University of China ( email )

School of Finance
Beijing, Beijing 100872
China

CERGAM, Aix-Marseille University ( email )

Aix-Marseille University
3 Avenue Robert Schuman,
Aix-en-Provence, 13628
France
0781668685 (Phone)

Gregory Rice

University of Waterloo - Department of Statistics and Actuarial Science ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Croatia

Shixuan Wang

University of Reading - Department of Economics ( email )

Reading, RG6 6AA
United Kingdom

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
56
Abstract Views
312
rank
386,505
PlumX Metrics