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 InfoPaper provided by Princeton, Department of Economics - Econometric Research Program in its series Papers with number 337.
Length: 43 pages
Date of creation: 1988
Date of revision:
maximum likelihood ; sampling ; mathematical analysis;
Other versions of this item:
- Perron, Pierre, 1991. "A Continuous Time Approximation to the Unstable First-Order Autoregressive Process: The Case without an Intercept," Econometrica, Econometric Society, vol. 59(1), pages 211-36, January.
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