### Local moving Fourier based bootstrapping

Lindner, F *(Karlsruhe Institute of Technology)*

Thursday 16 January 2014, 15:30-15:50

Seminar Room 1, Newton Institute

#### Abstract

In applications, many time series while not being globally stationary are locally well approximated by stationary time series models such as autoregressive processes. Such time series can be well approximated by the class of locally stationary processes as introduced by Dahlhaus (1997) allowing for a rigorous asymptotic theory. In this work we extend existing Fourier based bootstrap methods to locally stationary time series. Using a local moving Fourier transform we can do this globally for the full locally stationary time series as opposed to only local bootstrap versions which can only pointwise mimic the local stationary approximation. This allows us to obtain locally stationary bootstrap processes in the time domain. We derive asymptotic properties of the corresponding Fourier transform based on which we can show that the bootstrap time series has asymptotically the same covariance structure as the original locally stationary time series. We will then illustrate the behaviour with some simulations.

#### Presentation

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