Annals of Statistics

Bootstrapping Unstable First-Order Autoregressive Processes

I. V. Basawa, A. K. Mallik, W. P. McCormick, J. H. Reeves, and R. L. Taylor

Full-text: Open access

Abstract

Consider a first-order autoregressive process $X_t = \beta X_{t - 1} + \varepsilon_t$, where $\{\varepsilon_t\}$ are independent and identically distributed random errors with mean 0 and variance 1. It is shown that when $\beta = 1$ the standard bootstrap least squares estimate of $\beta$ is asymptotically invalid, even if the error distribution is assumed to be normal. The conditional limit distribution of the bootstrap estimate at $\beta = 1$ is shown to converge to a random distribution.

Article information

Source
Ann. Statist., Volume 19, Number 2 (1991), 1098-1101.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348142

Digital Object Identifier
doi:10.1214/aos/1176348142

Mathematical Reviews number (MathSciNet)
MR1105866

Zentralblatt MATH identifier
0725.62076

JSTOR
links.jstor.org

Subjects
Primary: 62M07: Non-Markovian processes: hypothesis testing
Secondary: 62M09: Non-Markovian processes: estimation 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62E20: Asymptotic distribution theory

Keywords
Autoregressive processes bootstrapping least squares estimator bootstrap invalidity unstable process

Citation

Basawa, I. V.; Mallik, A. K.; McCormick, W. P.; Reeves, J. H.; Taylor, R. L. Bootstrapping Unstable First-Order Autoregressive Processes. Ann. Statist. 19 (1991), no. 2, 1098--1101. doi:10.1214/aos/1176348142. https://projecteuclid.org/euclid.aos/1176348142


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