Unit root tests for time series with outliers

Dong Wan Shin; Sahadeb Sarkar; Jong Hyup Lee

doi:10.1016/0167-7152(95)00218-9

Unit root tests for time series with outliers

Dong Wan Shin, Sahadeb Sarkar, Jong Hyup Lee

Department of Statistics

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

Effects of additive and innovational outliers on unit root tests in ARIMA(p, 1, q) models are investigated. The limiting distribution of the ordinary least-squares estimator of the unit root parameter in the AR(1) model is affected by additive outliers but is unaffected by innovational outliers. To test for a unit root in ARIMA(p, 1, q) models in the presence of outliers, a very simple, easy-to-compute procedure is given that detects additive outliers and adjusts the observations accordingly. The detection method performed well in our numerical experiment. Our unit root tests based on the adjusted data are shown to have very good empirical sizes and powers in AR(1), AR(2) and ARMA(1, 1) models.

Original language	English
Pages (from-to)	189-197
Number of pages	9
Journal	Statistics and Probability Letters
Volume	30
Issue number	3
DOIs	https://doi.org/10.1016/0167-7152(95)00218-9
State	Published - 30 Oct 1996

Bibliographical note

Funding Information:
The researcho f the first author was supportedb y a grant from Korea Sciencea nd EngineeringF oundation and the researcho f the seconda uthorwas supportedb y a Grant from the Arts and SciencesR esearchF und

Keywords

ARIMA model
Additive outlier
Innovational outlier
Outlier detection
Time series
Unit root

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10.1016/0167-7152(95)00218-9

Cite this

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title = "Unit root tests for time series with outliers",

abstract = "Effects of additive and innovational outliers on unit root tests in ARIMA(p, 1, q) models are investigated. The limiting distribution of the ordinary least-squares estimator of the unit root parameter in the AR(1) model is affected by additive outliers but is unaffected by innovational outliers. To test for a unit root in ARIMA(p, 1, q) models in the presence of outliers, a very simple, easy-to-compute procedure is given that detects additive outliers and adjusts the observations accordingly. The detection method performed well in our numerical experiment. Our unit root tests based on the adjusted data are shown to have very good empirical sizes and powers in AR(1), AR(2) and ARMA(1, 1) models.",

keywords = "ARIMA model, Additive outlier, Innovational outlier, Outlier detection, Time series, Unit root",

author = "Shin, {Dong Wan} and Sahadeb Sarkar and Lee, {Jong Hyup}",

note = "Funding Information: The researcho f the first author was supportedb y a grant from Korea Sciencea nd EngineeringF oundation and the researcho f the seconda uthorwas supportedb y a Grant from the Arts and SciencesR esearchF und",

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doi = "10.1016/0167-7152(95)00218-9",

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T1 - Unit root tests for time series with outliers

AU - Shin, Dong Wan

AU - Sarkar, Sahadeb

AU - Lee, Jong Hyup

N1 - Funding Information: The researcho f the first author was supportedb y a grant from Korea Sciencea nd EngineeringF oundation and the researcho f the seconda uthorwas supportedb y a Grant from the Arts and SciencesR esearchF und

PY - 1996/10/30

Y1 - 1996/10/30

N2 - Effects of additive and innovational outliers on unit root tests in ARIMA(p, 1, q) models are investigated. The limiting distribution of the ordinary least-squares estimator of the unit root parameter in the AR(1) model is affected by additive outliers but is unaffected by innovational outliers. To test for a unit root in ARIMA(p, 1, q) models in the presence of outliers, a very simple, easy-to-compute procedure is given that detects additive outliers and adjusts the observations accordingly. The detection method performed well in our numerical experiment. Our unit root tests based on the adjusted data are shown to have very good empirical sizes and powers in AR(1), AR(2) and ARMA(1, 1) models.

AB - Effects of additive and innovational outliers on unit root tests in ARIMA(p, 1, q) models are investigated. The limiting distribution of the ordinary least-squares estimator of the unit root parameter in the AR(1) model is affected by additive outliers but is unaffected by innovational outliers. To test for a unit root in ARIMA(p, 1, q) models in the presence of outliers, a very simple, easy-to-compute procedure is given that detects additive outliers and adjusts the observations accordingly. The detection method performed well in our numerical experiment. Our unit root tests based on the adjusted data are shown to have very good empirical sizes and powers in AR(1), AR(2) and ARMA(1, 1) models.

KW - ARIMA model

KW - Additive outlier

KW - Innovational outlier

KW - Outlier detection

KW - Time series

KW - Unit root

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U2 - 10.1016/0167-7152(95)00218-9

DO - 10.1016/0167-7152(95)00218-9

M3 - Article

AN - SCOPUS:0030607409

SN - 0167-7152

VL - 30

SP - 189

EP - 197

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 3

ER -

Unit root tests for time series with outliers

Abstract

Bibliographical note

Keywords

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