Tests of heteroscedasticity and correlation in multivariate t regression models with AR and ARMA errors

Jin Guan Lin; Lixing ZHU; Chun Zheng Cao; Yong Li

doi:10.1080/02664763.2010.515301

Tests of heteroscedasticity and correlation in multivariate t regression models with AR and ARMA errors

Jin Guan Lin^*, Lixing ZHU, Chun Zheng Cao, Yong Li

^*Corresponding author for this work

Department of Mathematics

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

Abstract

Heteroscedasticity checking in regression analysis plays an important role in modelling. It is of great interest when random errors are correlated, including autocorrelated and partial autocorrelated errors. In this paper, we consider multivariate t linear regression models, and construct the score test for the case of AR(1) errors, and ARMA(s,d) errors. The asymptotic properties, including asymptotic chi-square and approximate powers under local alternatives of the score tests, are studied. Based on modified profile likelihood, the adjusted score test is also developed. The finite sample performance of the tests is investigated through Monte Carlo simulations, and also the tests are illustrated with two real data sets.

Original language	English
Pages (from-to)	1509-1531
Number of pages	23
Journal	Journal of Applied Statistics
Volume	38
Issue number	7
DOIs	https://doi.org/10.1080/02664763.2010.515301
Publication status	Published - Jul 2011

Scopus Subject Areas

Statistics and Probability
Statistics, Probability and Uncertainty

User-Defined Keywords

Adjusted score test
Approximate local powers
Autocorrelation
Heteroscedasticity
Multivariate t regression models
Score test
Simulation studies

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10.1080/02664763.2010.515301

Cite this

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title = "Tests of heteroscedasticity and correlation in multivariate t regression models with AR and ARMA errors",

abstract = "Heteroscedasticity checking in regression analysis plays an important role in modelling. It is of great interest when random errors are correlated, including autocorrelated and partial autocorrelated errors. In this paper, we consider multivariate t linear regression models, and construct the score test for the case of AR(1) errors, and ARMA(s,d) errors. The asymptotic properties, including asymptotic chi-square and approximate powers under local alternatives of the score tests, are studied. Based on modified profile likelihood, the adjusted score test is also developed. The finite sample performance of the tests is investigated through Monte Carlo simulations, and also the tests are illustrated with two real data sets.",

keywords = "Adjusted score test, Approximate local powers, Autocorrelation, Heteroscedasticity, Multivariate t regression models, Score test, Simulation studies",

author = "Lin, {Jin Guan} and Lixing ZHU and Cao, {Chun Zheng} and Yong Li",

note = "Funding Information: This study is supported by NSFJS BK2008284 (Jiangsu, China) and a grant (HKBU2030/07P) from the Grant Council of Hong Kong (Hong Kong, China).",

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AU - Cao, Chun Zheng

AU - Li, Yong

N1 - Funding Information: This study is supported by NSFJS BK2008284 (Jiangsu, China) and a grant (HKBU2030/07P) from the Grant Council of Hong Kong (Hong Kong, China).

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Tests of heteroscedasticity and correlation in multivariate t regression models with AR and ARMA errors

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