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.
Citation
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. https://doi.org/10.1214/aos/1176348142
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