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.
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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.
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- 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.
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