Econometrica: Mar 1977, Volume 45, Issue 2

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

https://doi.org/0012-9682(197703)45:2<463:ATSFSD>2.0.CO;2-O
p. 463-486

P. C. B. Phillips

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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