Inference on Periodograms of Infinite Dimensional Discrete Time Periodically Correlated Processes
Z. Shishebor, A. R. Soltani, Ahmad Zamani · Contributions to statistics · 2008
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.