A Kernel Based Bootstrap Method for Dependent Processes

A novel bootstrap method for stationary strong mixing processes is proposed in this article. The method consists in transforming the original data in an appropriate way using a kernel and applying standard m out of n bootstrap for independent and identically distributed observations. We investigate the first order asymptotic properties of the method in the case of the mean of the process and prove that the bootstrap distribution is consistent. Additionally, we show how the method can be applied to mean regression and quasi-maximum likelihood and demonstrate the first-order asymptotic validity of the bootstrap approximation in this context.

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