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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.

Discrete time periodically correlated Markov processes

Nematollahi A. R., Soltani A. R.

Probability and Mathematical Statistics

2000

Vol. 20, Fasc. 1

127--140

We consider a discrete time periodically correlated process {Xn} which is also Markov in the wide sense. We provide closed formulas for the covariance function R (n, m) = EXn, Xm, and for the spectral density f = [fj,k,] of such a process. Interestingly, we observe that the covariance function, and also the spectral density, is fully specified only by the values of {R(j,j), R(j, j+1), j = 0, 1, ..., T-l}, where T is the period of the process.