Asymptotic Approximations in the Near-Integrated Model with a Non-Zero Initial Condition

Posted: 12 Sep 2001

See all articles by Pierre Perron

Pierre Perron

Boston University - Department of Economics

Cosme Vodounou

Institut National de la Statistique et de l'Analyse Economique (INSAE)

Abstract

This paper considers various asymptotic approximations in the near-integrated first-order autoregressive model with a non-zero initial condition. We first extend the work of Knight and Satchell (1993), who considered the random walk case with a zero initial condition, to derive the expansion of the relevant joint moment generating function in this more general framework. We also consider, as alternative approximations, the stochastic expansion of Phillips (1987c) and the continuous-time approximation of Perron (1991a). We assess, via a Monte Carlo simulation study, the extent to which these alternative methods provide adequate approximations to the finite sample distribution of the least-squares estimator in a first-order autoregressive model. The results show that, when the initial condition is non-zero, Perron's (1991a) continuous-time approximation performs very well while the others only offer improvements when the initial condition is zero.

Keywords: Edgeworth expansion, Continuous-time asymptotics, Stochastic expansion, Distribution function, Autoregressive model

Suggested Citation

Perron, Pierre and Vodounou, Cosme, Asymptotic Approximations in the Near-Integrated Model with a Non-Zero Initial Condition. Econometrics Journal, Vol. 4, pp. 143-169, 2001. Available at SSRN: https://ssrn.com/abstract=281963

Pierre Perron (Contact Author)

Boston University - Department of Economics ( email )

270 Bay State Road
Boston, MA 02215
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Cosme Vodounou

Institut National de la Statistique et de l'Analyse Economique (INSAE) ( email )

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Airport Road
Cotonou, West Africa 01
Benin

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