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Finite Sample Distributions of t and F Statistics in an AR(1) Model with Anexogenous Variable

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  • Nankervis, J.C.
  • Savin, N.E.

Abstract

The distributions of the test statistics are investigated in the context of an AR(1) model where the root is unity or near unity and where the exogenous process is a stable process, a random walk or a time trend. The finite sample distributions are estimated by Monte Carlo methods assuming normal disturbances. The sensitivity of the distributions to both the values of the parameters of the AR(1) model and the process generating the exogenous time series is examined. The Monte Carlo results motivate several theorems which describe the exact sampling behavior of the test statistics. The analytical and empirical results present a mixed picture with respect to the accuracy of the relevant asymptotic approximations.

Suggested Citation

  • Nankervis, J.C. & Savin, N.E., 1987. "Finite Sample Distributions of t and F Statistics in an AR(1) Model with Anexogenous Variable," Econometric Theory, Cambridge University Press, vol. 3(3), pages 387-408, June.
    • Handle: RePEc:cup:etheor:v:3:y:1987:i:03:p:387-408_01
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    Cited by:

    1. Neil Kellard & Denise Osborn & Jerry Coakley & Nathan E. (Gene) Savin, 2015. "Papers with John," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 663-671, September.
    2. Kiviet, Jan F. & Dufour, Jean-Marie, 1997. "Exact tests in single equation autoregressive distributed lag models," Journal of Econometrics, Elsevier, vol. 80(2), pages 325-353, October.
    3. Haldrup, Niels, 1996. "Mirror image distributions and the Dickey-Fuller regression with a maintained trend," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 301-312.
    4. Atukorala, Ranjani & Sriananthakumar, Sivagowry, 2015. "A comparison of the accuracy of asymptotic approximations in the dynamic regression model using Kullback-Leibler information," Economic Modelling, Elsevier, vol. 45(C), pages 169-174.
    5. Tena, Juan de Dios & Tremayne, A.R., 2009. "Modelling monetary transmission in UK manufacturing industry," Economic Modelling, Elsevier, vol. 26(5), pages 1053-1066, September.
    6. Kiviet, Jan F., 1995. "On bias, inconsistency, and efficiency of various estimators in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 68(1), pages 53-78, July.
    7. Lee, Boon L. & Wilson, Clevo & Simshauser, Paul & Majiwa, Eucabeth, 2021. "Deregulation, efficiency and policy determination: An analysis of Australia's electricity distribution sector," Energy Economics, Elsevier, vol. 98(C).
    8. Dufour, Jean-Marie & Kiviet, Jan F., 1996. "Exact tests for structural change in first-order dynamic models," Journal of Econometrics, Elsevier, vol. 70(1), pages 39-68, January.
    9. José Angel Roldán Casas & Rafaela Dios-Palomares, 2004. "A Strategy for Testing the Unit Root in AR(1) Model with Intercept. A Monte Carlo Experiment," Economic Working Papers at Centro de Estudios Andaluces E2004/37, Centro de Estudios Andaluces.
    10. repec:ebl:ecbull:v:3:y:2004:i:12:p:1-7 is not listed on IDEAS
    11. Hellstrom, Jorgen, 2001. "Unit root testing in integer-valued AR(1) models," Economics Letters, Elsevier, vol. 70(1), pages 9-14, January.

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