Inference for Time Series with Mixed Spectrum
The old and important problem of estimating the discontinuous (mixed) spectrum of a series containing periodic components was considered in this paper. Most nonparametric spectral estimation procedures were developed for estimating smooth spectra and did not provide satisfactory results in estimating mixed spectra. A nonparametric estimation procedure was proposed for estimating discontinuous spectra. The procedure first finds a robust filter, which is insensitive to the presence of periodic components, to prewhiten the noise series and then uses a feature preserving smoother on the residual periodograms to estimate the discontinuous spectrum of the filtered series. The procedure was applied to some simulated data, and the results were compared with the classical kernel estimates and the autoregressive spectral estimates. The proposed procedure performs much better than the classical methods in estimating mixed spectra. The proposed procedure was also applied to three real data sets, including the famous Canadian lynx data. The proposed procedure was extended to estimate high-dimensional spectra. The problem of testing the significance of periodic components was discussed, and a testing procedure was also suggested.
Citable link to this pagehttps://hdl.handle.net/1911/101619
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