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

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  • 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
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    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. Tillman, John A, 1975. "The Power of the Durbin-Watson Test," Econometrica, Econometric Society, vol. 43(5-6), pages 959-974, Sept.-Nov.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
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    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.

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