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A Continuous Time Approximation to theStationary First-Order AutoregressiveModel

Published online by Cambridge University Press:  11 February 2009

Pierre Perron
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Abstract

We consider the least-squares estimator in a strictlystationary first-order autoregression without anestimated intercept. We study its continuous timeasymptotic distribution based on an asymptoticframework where the sampling interval converges tozero as the sample size increases. We derive amomentgenerating function which permits thecalculation of percentage points and moments of thisasymptotic distribution and assess the adequacy ofthe approximation to the finite sample distribution.In general, the approximation is excellent forvalues of the autoregressive parameter near one. Wealso consider the behavior of the power function oftests based on the normalized leastsquaresestimator. Interesting nonmonotonic properties areuncovered. This analysis extends the study of Perron[15] and helps to provide explanations for thefinite sample results established by Nankervis andSavin [13].

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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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