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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.