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Journal Article

Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation

P. C. B. Phillips
Econometrica
Vol. 45, No. 2 (Mar., 1977), pp. 463-485
Published by: The Econometric Society
DOI: 10.2307/1911222
Stable URL: http://www.jstor.org/stable/1911222
Page Count: 23
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Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation
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Abstract

Edgeworth series expansions are obtained of the finite sample distributions of the least squares estimator and the associated t ratio test statistic in the context of a first-order noncircular stochastic difference equation. General formulae are given for these expansions up to 0(T^-1) where T is the sample size and explicit representations of these in terms of the true parameters are derived up to 0(T^-1/2). Some numerical comparisons of the approximations and the exact distributions are made in the case of the least squares estimator.

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