## Annals of Statistics

### Bootstrapping Unstable First-Order Autoregressive Processes

#### 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

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