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Discrete Fourier transform methods in the analysis of nonstationary time series

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The Discrete Fourier Transform (DFT) is often used to analysis time series, usually under the assumption of (second order) stationarity of the time series. One of the main reasons for using this transformation is that the DFT tends to uncorrelate the original time series. Thus the DFT can be treated as an almost uncorrelated complex random variable, and standard methods for independent data can be applied to the DFT . It can be shown that this useful uncorrelation property does not hold for nonstationary time series. This would suggest that the DFT is no longer a helpful tool for nonstationary time series analysis. However, the purpose of this talk is to demonstrate that correlations between the DFTs contain useful information about the nonstationary nature of the underlying time series. We will exploit the starkly contrasting correlation properties between stationarity and nonstationarity DFTs to construct a test for second order stationarity and, if time permits, to construct an estimator of the time-varying spectral density.

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