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

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  • Jin-Guan Lin
  • Li-Xing Zhu
  • Chun-Zheng Cao
  • Yong Li

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.

Suggested Citation

  • Jin-Guan Lin & Li-Xing Zhu & Chun-Zheng Cao & Yong Li, 2011. "Tests of heteroscedasticity and correlation in multivariate t regression models with AR and ARMA errors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1509-1531, August.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:7:p:1509-1531
    DOI: 10.1080/02664763.2010.515301
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    1. Murray Aitkin, 1987. "Modelling Variance Heterogeneity in Normal Regression Using GLIM," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 332-339, November.
    2. Borjas, George J. & Freeman, Richard B. (ed.), 1992. "Immigration and the Work Force," National Bureau of Economic Research Books, University of Chicago Press, edition 1, number 9780226066332, September.
    3. Bo-Cheng Wei & Jian-Qing Shi & Wing-Kam Fung & Yue-Qing Hu, 1998. "Testing for Varying Dispersion in Exponential Family Nonlinear Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 277-294, June.
    4. Jin-Guan Lin & Bo-Cheng Wei & Nan-Song Zhang, 2004. "Varying Dispersion Diagnostics for Inverse Gaussian Regression Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(10), pages 1157-1170.
    5. Singh, Radhey S., 1988. "Estimation of error variance in linear regression models with errors having multivariate student-t distribution with unknown degrees of freedom," Economics Letters, Elsevier, vol. 27(1), pages 47-53.
    6. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    7. Jeffrey S. Simonoff & Chih‐Ling Tsai, 1994. "Use of Modified Profile Likelihood for Improved Tests of Constancy of Variance in Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(2), pages 357-370, June.
    8. Cysneiros, Francisco José A. & Paula, Gilberto A. & Galea, Manuel, 2007. "Heteroscedastic symmetrical linear models," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1084-1090, June.
    9. J. L. Hutton & P. J. Solomon, 1997. "Parameter Orthogonality in Mixed Regression Models for Survival Data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 125-136.
    10. Barroso, Lúcia P. & Cordeiro, Gauss M., 2005. "Bartlett corrections in heteroskedastic t regression models," Statistics & Probability Letters, Elsevier, vol. 75(2), pages 86-96, November.
    11. Godfrey, Leslie G, 1978. "Testing against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1293-1301, November.
    12. Epps, Thomas W & Epps, Mary Lee, 1977. "The Robustness of Some Standard Tests for Autocorrelation and Heteroskedasticity When Both Problems Are Present," Econometrica, Econometric Society, vol. 45(3), pages 745-753, April.
    13. Lin, Jin-Guan & Wei, Bo-cheng, 2006. "Approximate power of score test for variance heterogeneity under local alternatives in nonlinear models," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3179-3198, July.
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