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Bootstrap in Time Series We study a bootstrap method for stationary real-valued time series, which is based on the method of sieves. We restrict ourselves to autoregressive sieve bootstraps. Given a sample X_1,...,X_n from a linear process (X_t(t in Z), we approximate the underlying process by an autoregressive model with order p=p(n), where p(n) tends to infinity, p(n)=o(n) as the sample size n tends to infinity. Based on such a model a bootstrap process (X_t^*)t in Z) is constructed from which one can draw samples of any size. We give a novel result which says that with high probability, such a sieve bootstrap process (X_t^*(t in Z) 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.

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