Sankhya: The Indian Journal of Statistics

2005, Volume 67, Pt. 3, 568--589

On The Spectral Density Estimation of Periodically Correlated (Cyclostationary) Time Series

A.R. Nematollahi, Department of Statistics, Shiraz University, Shiraz, Iran
T. Subba Rao, School of Mathematics, The University of Manchester

SUMMARY. We consider the estimation of the spectral density matrix of a periodically correlated (PC) time series (also known as cyclostationary time series). We use the well known relation between the spectral density matrix of a periodically correlated time series and a stationary vector time series (Gladyshev, 1961). The spectral matrix of the stationary vector time series is estimated using the eigenvalue decomposition of block Toeplitz matrices. The method of estimation is illustrated with simulated and real time series.

AMS (1991) subject classification. 60G10, 62G07, 62M15, 15A18.

Key words and phrases. Periodically correlated (cyclostationary) processes, Capon's estimate, high resolution estimate, eigenvalue decomposition, block-Toeplitz matrix.

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