Abstract
We study a bootstrap method for stationary real-valued time series, which is based on the sieve of autoregressive processes. Given a sample from a linear process , we approximate the underlying process by an autoregressive model with order , where as the sample size . Based on such a model, a bootstrap process is constructed from which one can draw samples of any size.
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.
Citation
Peter J. Bickel. Peter Bühlmann. "A new mixing notion and functional central limit theorems for a sieve bootstrap in time series." Bernoulli 5 (3) 413 - 446, June 1999.
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