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.
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Shishebor, Z., Soltani, A.R., Zamani, A. (2008). Inference on Periodograms of Infinite Dimensional Discrete Time Periodically Correlated Processes. In: Functional and Operatorial Statistics. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2062-1_44
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DOI: https://doi.org/10.1007/978-3-7908-2062-1_44
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