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.
Publié le : 1991-06-14
Classification:
Autoregressive processes,
bootstrapping least squares estimator,
bootstrap invalidity,
unstable process,
62M07,
62M09,
62M10,
62E20
@article{1176348142,
author = {Basawa, I. V. and Mallik, A. K. and McCormick, W. P. and Reeves, J. H. and Taylor, R. L.},
title = {Bootstrapping Unstable First-Order Autoregressive Processes},
journal = {Ann. Statist.},
volume = {19},
number = {1},
year = {1991},
pages = { 1098-1101},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348142}
}
Basawa, I. V.; Mallik, A. K.; McCormick, W. P.; Reeves, J. H.; Taylor, R. L. Bootstrapping Unstable First-Order Autoregressive Processes. Ann. Statist., Tome 19 (1991) no. 1, pp. 1098-1101. http://gdmltest.u-ga.fr/item/1176348142/