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A Continuous Time Approximation to the Stationary First-Order Autoregressive Model

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  • Perron, Pierre

Abstract

We consider the least-squares estimator in a strictly stationary first-order autoregression without an estimated intercept. We study its continuous time asymptotic distribution based on an asymptotic framework where the sampling interval converges to zero as the sample size increases. We derive a momentgenerating function which permits the calculation of percentage points and moments of this asymptotic distribution and assess the adequacy of the approximation to the finite sample distribution. In general, the approximation is excellent for values of the autoregressive parameter near one. We also consider the behavior of the power function of tests based on the normalized leastsquares estimator. Interesting nonmonotonic properties are uncovered. This analysis extends the study of Perron [15] and helps to provide explanations for the finite sample results established by Nankervis and Savin [13].

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  • Perron, Pierre, 1991. "A Continuous Time Approximation to the Stationary First-Order Autoregressive Model," Econometric Theory, Cambridge University Press, vol. 7(2), pages 236-252, June.
    • Handle: RePEc:cup:etheor:v:7:y:1991:i:02:p:236-252_00
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    Cited by:

    1. Cosme Vodounou, 1998. "Inférence fondée sur les statistiques des rendements de long terme," CIRANO Working Papers 98s-20, CIRANO.
    2. Perron, Pierre & Vodounou, Cosme, 2004. "Tests of return predictability: an analysis of their properties based on a continuous time asymptotic framework," Journal of Empirical Finance, Elsevier, vol. 11(2), pages 203-230, March.
    3. Pierre Perron & Cosme Vodounou, 2001. "Asymptotic approximations in the near-integrated model with a non-zero initial condition," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-42.
    4. Mukhtar Ali, 2002. "Distribution Of The Least Squares Estimator In A First-Order Autoregressive Model," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 89-119.
    5. Perron, Pierre, 1996. "The adequacy of asymptotic approximations in the near-integrated autoregressive model with dependent errors," Journal of Econometrics, Elsevier, vol. 70(2), pages 317-350, February.
    6. H. Peter Boswijk, 2001. "Block Local to Unity and Continuous Record Asymptotics," Tinbergen Institute Discussion Papers 01-078/4, Tinbergen Institute.
    7. Mukhtar M. Ali, 1996. "Distribution of the Least Squares Estimator in a First-Order Autoregressive Model," Econometrics 9610004, University Library of Munich, Germany.

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