IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v38y2011i7p1509-1531.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2010.515301
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2010.515301?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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, March.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jin-Guan Lin & Li-Xing Zhu & Feng-Chang Xie, 2009. "Heteroscedasticity diagnostics for t linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 59-77, June.
    2. Chun-Zheng Cao & Jin-Guan Lin & Li-Xing Zhu, 2010. "Heteroscedasticity and/or autocorrelation diagnostics in nonlinear models with AR(1) and symmetrical errors," Statistical Papers, Springer, vol. 51(4), pages 813-836, December.
    3. Feng-Chang Xie & Jin-Guan Lin & Bo-Cheng Wei, 2010. "Testing for varying zero-inflation and dispersion in generalized Poisson regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1509-1522.
    4. Xie, Feng-Chang & Lin, Jin-Guan & Wei, Bo-Cheng, 2009. "Diagnostics for skew-normal nonlinear regression models with AR(1) errors," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4403-4416, October.
    5. Xie, Feng-Chang & Wei, Bo-Cheng & Lin, Jin-Guan, 2009. "Homogeneity diagnostics for skew-normal nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 821-827, March.
    6. Ansgar Belke & Robert Czudaj, 2010. "Is Euro Area Money Demand (Still) Stable? Cointegrated VAR Versus Single Equation Techniques," Applied Economics Quarterly (formerly: Konjunkturpolitik), Duncker & Humblot, Berlin, vol. 56(4), pages 285-315.
    7. David F. Hendry, 2013. "Econometric Modelling: The ‘Consumption Function’ In Retrospect," Scottish Journal of Political Economy, Scottish Economic Society, vol. 60(5), pages 495-522, November.
    8. Ericsson, Neil R & Hendry, David F & Mizon, Grayham E, 1998. "Exogeneity, Cointegration, and Economic Policy Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 370-387, October.
    9. David F. Hendry & Hans-Martin Krolzig, 2005. "The Properties of Automatic "GETS" Modelling," Economic Journal, Royal Economic Society, vol. 115(502), pages 32-61, March.
    10. Amir Kia, 2006. "Economic policies and demand for money: evidence from Canada," Applied Economics, Taylor & Francis Journals, vol. 38(12), pages 1389-1407.
    11. Amir Kia, 2006. "Deficits, Debt Financing, Monetary Policy and Inflation in Developing Countries: Internal or External Factors? Evidence from Iran," Carleton Economic Papers 06-03, Carleton University, Department of Economics, revised Nov 2006.
    12. de Meulemeester, Jean-Luc & Rochat, Denis, 1995. "A causality analysis of the link between higher education and economic development," Economics of Education Review, Elsevier, vol. 14(4), pages 351-361, December.
    13. Cheng, Tsung-Chi, 2012. "On simultaneously identifying outliers and heteroscedasticity without specific form," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2258-2272.
    14. Søren Johansen & Bent Nielsen, 2014. "Optimal hedging with the cointegrated vector autoregressive model," Discussion Papers 14-23, University of Copenhagen. Department of Economics.
    15. Russell Davidson & Victoria Zinde‐Walsh, 2017. "Advances in specification testing," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 50(5), pages 1595-1631, December.
    16. Carlsson, M., 2000. "Measures of Technology and the Short-Run Responses to Technology Shocks - Is the RBC-Model Consistent with Swedish Manufacturing Data?," Papers 2000-20, Uppsala - Working Paper Series.
    17. Ericsson, Neil R., 1992. "Parameter constancy, mean square forecast errors, and measuring forecast performance: An exposition, extensions, and illustration," Journal of Policy Modeling, Elsevier, vol. 14(4), pages 465-495, August.
    18. Shamim Ahmed & M. Golam Mortaza, 2010. "Inflation and Economic Growth in Bangladesh: 1981-2005," Working Papers id:3033, eSocialSciences.
    19. Dragos Stefan Oprea & Elena Valentina Tilica, 2014. "Day-of-the-Week Effect in Post-Communist East European Stock Markets," International Journal of Academic Research in Accounting, Finance and Management Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Accounting, Finance and Management Sciences, vol. 4(3), pages 119-129, July.
    20. Klaus Grobys, 2015. "Size distortions of the wild bootstrapped HCCME-based LM test for serial correlation in the presence of asymmetric conditional heteroskedasticity," Empirical Economics, Springer, vol. 48(3), pages 1189-1202, May.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:japsta:v:38:y:2011:i:7:p:1509-1531. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.