We study a bootstrap method for stationary real-valued time series, which is based on the sieve of autoregressive processes. Given a sample [math] from a linear process [math] , we approximate the underlying process by an autoregressive model with order [math] , where [math] as the sample size [math] . Based on such a model, a bootstrap process [math] is constructed from which one can draw samples of any size.
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We show that, with high probability, such a sieve bootstrap process
satisfies a new type of mixing
condition. This implies that many results for stationary mixing
sequences carry over to the sieve bootstrap process. As an example
we derive a functional central limit theorem under a bracketing
condition.
Publié le : 1999-06-14
Classification:
AR(∞),
ARMA,
autoregressive approximation,
bracketing,
convex sets,
linear process,
MA(∞),
smooth bootstrap,
stationary process,
strong-mixing
@article{1172617198,
author = {Bickel, Peter J. and B\"uhlmann, Peter},
title = {A new mixing notion and functional central limit theorems for a sieve bootstrap in time series},
journal = {Bernoulli},
volume = {5},
number = {6},
year = {1999},
pages = { 413-446},
language = {en},
url = {http://dml.mathdoc.fr/item/1172617198}
}
Bickel, Peter J.; Bühlmann, Peter. A new mixing notion and functional central limit theorems for a sieve bootstrap in time series. Bernoulli, Tome 5 (1999) no. 6, pp. 413-446. http://gdmltest.u-ga.fr/item/1172617198/