The moving Fourier transformation of locally stationary processes with application to bootstrap procedures

In applications, many time series can be described using the class of locally stationary processes (Dahlhaus (1997)). In this work existing Fourier-based bootstrap methods are extended to this setting using a moving Fourier transform, correctly mimicking the local structure of the process. Asymptotic properties of the corresponding Fourier transform are derived. Using these properties the covariance structure of the bootstrap sample is shown to be asymptotically correct.