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September, 1987 Asymptotic Inference for Nearly Nonstationary AR(1) Processes
N. H. Chan, C. Z. Wei
Ann. Statist. 15(3): 1050-1063 (September, 1987). DOI: 10.1214/aos/1176350492

Abstract

A first-order autoregressive process, $Y_t = \beta Y_{t - 1} + \epsilon_t$, is said to be nearly nonstationary when $\beta$ is close to one. The limiting distribution of the least-squares estimate $b_n$ for $\beta$ is studied when $Y_t$ is nearly nonstationary. By reparameterizing $\beta$ to be $1 - \gamma/n, \gamma$ being a fixed constant, it is shown that the limiting distribution of $\tau_n = (\sum^n_{t = 1}Y^2_{t - 1})^{1/2}(b_n - \beta)$ converges to $\mathscr{L}(\gamma)$ which is a quotient of stochastic integrals of standard Brownian motion. This provides a reasonable alternative to the approximation of the distribution of $\tau_n$ proposed by Ahtola and Tiao (1984).

Citation

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N. H. Chan. C. Z. Wei. "Asymptotic Inference for Nearly Nonstationary AR(1) Processes." Ann. Statist. 15 (3) 1050 - 1063, September, 1987. https://doi.org/10.1214/aos/1176350492

Information

Published: September, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0638.62082
MathSciNet: MR902245
Digital Object Identifier: 10.1214/aos/1176350492

Subjects:
Primary: 62M10

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 3 • September, 1987
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