Asymptotic approximations in the near-integrated model with a non-zero initial condition

Pierre Perron and Cosme Vodounou

Econometrics Journal, 2001, vol. 4, issue 1, 42

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 con-dition, 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, Perron¹s (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; Dis-tribution function; Autoregressive model. (search for similar items in EconPapers)
Date: 2001
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Working Paper: Asymptotic Approximations in the Near-Integrated Model with a Non-Zero Initial Condition (1998)
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