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Contents of PMS, Vol. 20, Fasc. 1,
pages 127 - 140
 

DISCRETE TIME PERIODICALLY CORRELATED MARKOV PROCESSES

A. R. Nematollahi
A. R. Soltani

Abstract: We consider a discrete time periodically correlated process (X ) n which is also Markov in the wide sense. We provide closed formulas for the covariance function R(n,m) = EX X n m and for the spectral density f = [f ] jk 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 + l),j = 0,1,...,T -1), where T is the period of the process.

1991 AMS Mathematics Subject Classification: 60J05, 60G12, 60G15, 60G10.

Key words and phrases: periodically correlated processes, Markov processes, covariance characterization, spectral density characterization, second order processes.

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