Asymptotics of tests for a unit root in autoregression

Kenji Sakiyama, Masanobu Taniguchi, Madan L. Puri

Research output: Contribution to journalArticle

Abstract

Testing for stationarity is an important issue in time series analysis. One approach for this is the unit root test in autoregression. For autoregressive models, a lot of statistics based on the least-squares estimator (LSE) of the coefficient have been used for the testing problem of unit root. In this paper, we develop an approach for this problem based on a generalized LSE (GLSE), which includes many important estimators as special cases. Then the asymptotics of some test statistics constructed by the GLSE is elucidated. Concretely, we derive their limiting distribution under both null and alternative hypotheses. Based on this result we evaluate their local power, and discuss their asymptotic optimality. Numerical studies for them are given.

Original languageEnglish
Pages (from-to)351-364
Number of pages14
JournalJournal of Statistical Planning and Inference
Volume108
Issue number1-2
DOIs
Publication statusPublished - 2002 Nov 1
Externally publishedYes

Fingerprint

Autoregression
Unit Root
Statistics
Generalized Least Squares Estimator
Local Power
Unit Root Tests
Asymptotic Optimality
Testing
Time series analysis
Least Squares Estimator
Time Series Analysis
Stationarity
Autoregressive Model
Limiting Distribution
Test Statistic
Null
Numerical Study
Estimator
Evaluate
Alternatives

Keywords

  • Autoregressive model
  • Generalized LSE
  • Local asymptotic normality
  • Local asymptotic optimality
  • Near integrated process
  • Tests for unit root

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Statistics and Probability

Cite this

Asymptotics of tests for a unit root in autoregression. / Sakiyama, Kenji; Taniguchi, Masanobu; Puri, Madan L.

In: Journal of Statistical Planning and Inference, Vol. 108, No. 1-2, 01.11.2002, p. 351-364.

Research output: Contribution to journalArticle

Sakiyama, Kenji ; Taniguchi, Masanobu ; Puri, Madan L. / Asymptotics of tests for a unit root in autoregression. In: Journal of Statistical Planning and Inference. 2002 ; Vol. 108, No. 1-2. pp. 351-364.
@article{9f728451b35d45158ed73d287c865639,
title = "Asymptotics of tests for a unit root in autoregression",
abstract = "Testing for stationarity is an important issue in time series analysis. One approach for this is the unit root test in autoregression. For autoregressive models, a lot of statistics based on the least-squares estimator (LSE) of the coefficient have been used for the testing problem of unit root. In this paper, we develop an approach for this problem based on a generalized LSE (GLSE), which includes many important estimators as special cases. Then the asymptotics of some test statistics constructed by the GLSE is elucidated. Concretely, we derive their limiting distribution under both null and alternative hypotheses. Based on this result we evaluate their local power, and discuss their asymptotic optimality. Numerical studies for them are given.",
keywords = "Autoregressive model, Generalized LSE, Local asymptotic normality, Local asymptotic optimality, Near integrated process, Tests for unit root",
author = "Kenji Sakiyama and Masanobu Taniguchi and Puri, {Madan L.}",
year = "2002",
month = "11",
day = "1",
doi = "10.1016/S0378-3758(02)00317-8",
language = "English",
volume = "108",
pages = "351--364",
journal = "Journal of Statistical Planning and Inference",
issn = "0378-3758",
publisher = "Elsevier",
number = "1-2",

}

TY - JOUR

T1 - Asymptotics of tests for a unit root in autoregression

AU - Sakiyama, Kenji

AU - Taniguchi, Masanobu

AU - Puri, Madan L.

PY - 2002/11/1

Y1 - 2002/11/1

N2 - Testing for stationarity is an important issue in time series analysis. One approach for this is the unit root test in autoregression. For autoregressive models, a lot of statistics based on the least-squares estimator (LSE) of the coefficient have been used for the testing problem of unit root. In this paper, we develop an approach for this problem based on a generalized LSE (GLSE), which includes many important estimators as special cases. Then the asymptotics of some test statistics constructed by the GLSE is elucidated. Concretely, we derive their limiting distribution under both null and alternative hypotheses. Based on this result we evaluate their local power, and discuss their asymptotic optimality. Numerical studies for them are given.

AB - Testing for stationarity is an important issue in time series analysis. One approach for this is the unit root test in autoregression. For autoregressive models, a lot of statistics based on the least-squares estimator (LSE) of the coefficient have been used for the testing problem of unit root. In this paper, we develop an approach for this problem based on a generalized LSE (GLSE), which includes many important estimators as special cases. Then the asymptotics of some test statistics constructed by the GLSE is elucidated. Concretely, we derive their limiting distribution under both null and alternative hypotheses. Based on this result we evaluate their local power, and discuss their asymptotic optimality. Numerical studies for them are given.

KW - Autoregressive model

KW - Generalized LSE

KW - Local asymptotic normality

KW - Local asymptotic optimality

KW - Near integrated process

KW - Tests for unit root

UR - http://www.scopus.com/inward/record.url?scp=0036840974&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036840974&partnerID=8YFLogxK

U2 - 10.1016/S0378-3758(02)00317-8

DO - 10.1016/S0378-3758(02)00317-8

M3 - Article

VL - 108

SP - 351

EP - 364

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 1-2

ER -