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A consistent estimator for spectral density matrix of a discrete time periodically correlated process

Azimmohseni M., Soltani A. R., Khalafi M., Ghalesary N. M.

Probability and Mathematical Statistics

2018

Vol. 38, Fasc. 1

225--242

In this article, we introduce a weighted periodogram in the class of smoothed periodograms as a consistent estimator for the spectra density matrix of a periodically correlated process. We derive its li miting distribution that appears to be a certain finite linear combination of Wishart distribution. We also provide numerical derivations for our smoothed period ogram and exhibit its asymptotic consistency using simulated data.