A Continuous Time Approximation to the Unstable First-Order Autoregressive Process: The Case without an Intercept
AbstractWe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Econometric Society in its journal Econometrica.
Volume (Year): 59 (1991)
Issue (Month): 1 (January)
Other versions of this item:
- Perron,P., 1988. "A Continuous Time Approximation To The Unstable First- Order Autoregressive Process: The Case Without An Intercept," Papers 337, Princeton, Department of Economics - Econometric Research Program.
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Mukhtar M. Ali, 1996. "Distribution of the Least Squares Estimator in a First-Order Autoregressive Model," Econometrics 9610004, EconWPA.
- 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.
- Hendrik P. van Dalen & Kene Henkens, 2000. "What makes a Scientific Article influential?," Tinbergen Institute Discussion Papers 00-032/1, Tinbergen Institute.
- Cosme Vodounou, 1998. "Inférence fondée sur les statistiques des rendements de long terme," CIRANO Working Papers 98s-20, CIRANO.
- Mukhtar Ali, 2002. "Distribution Of The Least Squares Estimator In A First-Order Autoregressive Model," Econometric Reviews, Taylor and Francis Journals, vol. 21(1), pages 89-119.
- Kurozumi, Eiji, 2002. "Testing for stationarity with a break," Journal of Econometrics, Elsevier, vol. 108(1), pages 63-99, May.
- repec:dgr:uvatin:2000033 is not listed on IDEAS
- PERRON, Pierre & VODOUNOU, Cosme, 1998.
"Asymptotic Approximations in the Near-Integrated Model with a Non-Zero Initial Condition,"
Cahiers de recherche
9815, Universite de Montreal, Departement de sciences economiques.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
If references are entirely missing, you can add them using this form.