Inference on Periodograms of Infinite Dimensional Discrete Time Periodically Correlated Processes
In this work we shall consider two classes of periodically correlated processes with values in separable Hilbert spaces: weakly second order and strongly second order. It is proved that the sample Fourier transforms are asymptotically uncorrelated and the periodograms are asymptotically unbiased for corresponding spectral densities.
KeywordsSpectral Density Bounded Variation Separable Hilbert Space Cholesky Factor White Noise Process
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