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June, 1991 Bootstrapping Unstable First-Order Autoregressive Processes
I. V. Basawa, A. K. Mallik, W. P. McCormick, J. H. Reeves, R. L. Taylor
Ann. Statist. 19(2): 1098-1101 (June, 1991). DOI: 10.1214/aos/1176348142


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.


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I. V. Basawa. A. K. Mallik. W. P. McCormick. J. H. Reeves. R. L. Taylor. "Bootstrapping Unstable First-Order Autoregressive Processes." Ann. Statist. 19 (2) 1098 - 1101, June, 1991.


Published: June, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0725.62076
MathSciNet: MR1105866
Digital Object Identifier: 10.1214/aos/1176348142

Primary: 62M07
Secondary: 62E20 , 62M09 , 62M10

Keywords: autoregressive processes , bootstrap invalidity , bootstrapping least squares estimator , unstable process

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 2 • June, 1991
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