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A Continuous Time Approximation to the Unstable First-Order Autoregressive Process: The Case without an Intercept

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  • Perron, Pierre

Abstract

We consider a first-order autoregression with i.i.d. errors and a fixed initial condition. The asymptotic distribution of the normalized least-squares estimator as the sampling interval converges to zero is shown to be the same as the exact distribution of the continuous-time estimator in an Ornstein-Uhlenbeck process. This asymptotic distribution permits explicit consideration of the effect of the initial condition. The appropriate moment-generating function is derived and used to tabulate the limiting distribution and probability density functions, the moments and some power functions. The adequacy of this asymptotic approximation is found to be excellent for values of the autoregressive parameter near one and any fixed initial condition. Copyright 1991 by The Econometric Society.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 59 (1991)
Issue (Month): 1 (January)
Pages: 211-36

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Handle: RePEc:ecm:emetrp:v:59:y:1991:i:1:p:211-36

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Cited by:
  1. Hendrik P. van Dalen & Kene Henkens, 2000. "What makes a Scientific Article influential?," Tinbergen Institute Discussion Papers 00-032/1, Tinbergen Institute.
  2. Cosme Vodounou, 1998. "Inférence fondée sur les statistiques des rendements de long terme," CIRANO Working Papers 98s-20, CIRANO.
  3. John Hatgioannides & Spiros Mesomeris, 2005. "Mean Reversion in Equity Prices: the G-7 Evidence," Money Macro and Finance (MMF) Research Group Conference 2005 64, Money Macro and Finance Research Group.
  4. 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.
  5. 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 42.
  6. Kurozumi, Eiji, 2002. "Testing for stationarity with a break," Journal of Econometrics, Elsevier, vol. 108(1), pages 63-99, May.
  7. Paparoditis, Efstathios & Politis, Dimitris N, 2013. "The Asymptotic Size and Power of the Augmented Dickey-Fuller Test for a Unit Root," University of California at San Diego, Economics Working Paper Series qt0784p55m, Department of Economics, UC San Diego.
  8. repec:dgr:uvatin:2000033 is not listed on IDEAS
  9. 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.
  10. Mukhtar M. Ali, 1996. "Distribution of the Least Squares Estimator in a First-Order Autoregressive Model," Econometrics 9610004, EconWPA.

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