IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v118y2013icp77-101.html
   My bibliography  Save this article

Further results on the h-test of Durbin for stable autoregressive processes

Author

Listed:
  • Proïa, Frédéric

Abstract

The purpose of this paper is to investigate the asymptotic behavior of the Durbin–Watson statistic for the stable p-order autoregressive process when the driven noise is given by a first-order autoregressive process. It is an extension of the previous work of Bercu and Proïa devoted to the particular case p=1. We establish the almost sure convergence and the asymptotic normality for both the least squares estimator of the unknown vector parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise. In addition, the almost sure rates of convergence of our estimates are also provided. Then, we prove the almost sure convergence and the asymptotic normality for the Durbin–Watson statistic and we derive a two-sided statistical procedure for testing the presence of a significant first-order residual autocorrelation that appears to simplify and to improve the well-known h-test suggested by Durbin. Finally, we briefly summarize our observations on simulated samples.

Suggested Citation

  • Proïa, Frédéric, 2013. "Further results on the h-test of Durbin for stable autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 77-101.
  • Handle: RePEc:eee:jmvana:v:118:y:2013:i:c:p:77-101
    DOI: 10.1016/j.jmva.2013.03.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13000365
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmva.2013.03.009?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Breusch, T S, 1978. "Testing for Autocorrelation in Dynamic Linear Models," Australian Economic Papers, Wiley Blackwell, vol. 17(31), pages 334-355, December.
    2. Toni Stocker, 2007. "On the asymptotic bias of OLS in dynamic regression models with autocorrelated errors," Statistical Papers, Springer, vol. 48(1), pages 81-93, January.
    3. Inder, Brett, 1986. "An Approximation to the Null Distribution of the Durbin-Watson Statistic in Models Containing Lagged Dependent Variables," Econometric Theory, Cambridge University Press, vol. 2(3), pages 413-428, December.
    4. Bercu, B., 2004. "On the convergence of moments in the almost sure central limit theorem for martingales with statistical applications," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 157-173, May.
    5. King, Maxwell L. & Wu, Ping X., 1991. "Small-disturbance asymptotics and the Durbin-Watson and related tests in the dynamic regression model," Journal of Econometrics, Elsevier, vol. 47(1), pages 145-152, January.
    6. Maddala, G S & Rao, A S, 1973. "Tests for Serial Correlation in Regression Models with Lagged Dependent Variables and Serially Correlated Errors," Econometrica, Econometric Society, vol. 41(4), pages 761-774, July.
    7. Tillman, John A, 1975. "The Power of the Durbin-Watson Test," Econometrica, Econometric Society, vol. 43(5-6), pages 959-974, Sept.-Nov.
    8. Durbin, J, 1970. "Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables," Econometrica, Econometric Society, vol. 38(3), pages 410-421, May.
    9. Inder, B. A., 1984. "Finite-sample power of tests for autocorrelation in models containing lagged dependent variables," Economics Letters, Elsevier, vol. 14(2-3), pages 179-185.
    10. 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.
    11. Lai, T. L. & Wei, C. Z., 1983. "Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 1-23, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bercu, Bernard & Proïa, Frédéric & Savy, Nicolas, 2014. "On Ornstein–Uhlenbeck driven by Ornstein–Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 36-44.

    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. Erum Toor & Tanweer Ul Islam, 2019. "Power Comparison of Autocorrelation Tests in Dynamic Models," International Econometric Review (IER), Econometric Research Association, vol. 11(2), pages 58-69, September.
    2. Sriananthakumar, Sivagowry, 2015. "Approximate Non-Similar critical values based tests vs Maximized Monte Carlo tests," Economic Modelling, Elsevier, vol. 49(C), pages 387-394.
    3. repec:wyi:journl:002087 is not listed on IDEAS
    4. 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.
    5. Belsley, David A, 1997. "A Small-Sample Correction for Testing for gth-Order Serial Correlation with Artificial Regressions," Computational Economics, Springer;Society for Computational Economics, vol. 10(3), pages 197-229, August.
    6. Adrian C. Darnell, 1994. "A Dictionary Of Econometrics," Books, Edward Elgar Publishing, number 118.
    7. Desiraju, Ramarao & Nair, Harikesh S. & Chintagunta, Pradeep, 2004. "Diffusion of New Pharmaceutical Drugs in Developing and Developed Nations," Research Papers 1950, Stanford University, Graduate School of Business.
    8. Mahmood, Talat, 1990. "Die Dynamik der Rentabilität als stochastischer Prozess: eine empirische Zeitreihenanalyse von ausgewählten deutschen und amerikanischen Unternehmen. Vom Fachbereich 20 Informatik der Technischen Univ," EconStor Books, ZBW - Leibniz Information Centre for Economics, number 112236.
    9. Leslie G. Godfrey, 2005. "Controlling the Overall Significance Level of a Battery of Least Squares Diagnostic Tests," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(2), pages 263-279, April.
    10. Wadud, Zia, 2015. "Imperfect reversibility of air transport demand: Effects of air fare, fuel prices and price transmission," Transportation Research Part A: Policy and Practice, Elsevier, vol. 72(C), pages 16-26.
    11. Yongmiao Hong, 2013. "Serial Correlation and Serial Dependence," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    12. Godfrey, L.G., 2007. "Alternative approaches to implementing Lagrange multiplier tests for serial correlation in dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3282-3295, April.
    13. Gabriele Fiorentini & Enrique Sentana, 2019. "Dynamic specification tests for dynamic factor models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 325-346, April.
    14. Vittorio Grilli, 1989. "Managing Exchange Rate Crises: Evidence from the 1890's," NBER Working Papers 3068, National Bureau of Economic Research, Inc.
    15. Jan F. Kiviet, 1986. "On the Rigour of Some Misspecification Tests for Modelling Dynamic Relationships," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 241-261.
    16. Kaboudan, M. A., 2001. "Genetically evolved models and normality of their fitted residuals," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1719-1749, November.
    17. Mizon, Grayham E., 1995. "A simple message for autocorrelation correctors: Don't," Journal of Econometrics, Elsevier, vol. 69(1), pages 267-288, September.
    18. Haluk Erlat, 1991. "An Ex Post Statistical Assessment of the Central Bank Quarterly Econometric Model of Turkey," Discussion Papers 9108, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
    19. Benin, Samuel, 2016. "Returns to agricultural public spending in Ghana: Cocoa versus noncocoa subsector:," IFPRI discussion papers 1503, International Food Policy Research Institute (IFPRI).
    20. Benjamin Auer & Frank Schuhmacher, 2013. "RETRACTED ARTICLE: Investor sentiment, stock market valuation and merger activity," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 60(2), pages 245-245, June.
    21. Wadud, Zia, 2014. "The asymmetric effects of income and fuel price on air transport demand," Transportation Research Part A: Policy and Practice, Elsevier, vol. 65(C), pages 92-102.

    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:eee:jmvana:v:118:y:2013:i:c:p:77-101. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.