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

Published online by Cambridge University Press:  11 February 2009

Pierre Perron
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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].

Type
Research Article
Information
Econometric Theory , Volume 7 , Issue 2 , June 1991 , pp. 236 - 252
Copyright
Copyright © Cambridge University Press 1991

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References

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