Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 94746, 17 pages
doi:10.1155/JAMSA/2006/94746

On covariance generating functions and spectral densities of periodically correlated autoregressive processes

Z. Shishebor,1 A. R. Nematollahi,1 and A. R. Soltani1,2

1Department of Statistics, College of Science, Shiraz University, Shiraz 71454, Iran
2Department of Statistics and Operations Research, College of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Received 11 May 2005; Revised 22 November 2005; Accepted 23 November 2005

Copyright © 2006 Z. Shishebor et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Periodically correlated autoregressive nonstationary processes of finite order are considered. The corresponding Yule-Walker equations are applied to derive the generating functions of the covariance functions, what are called here the periodic covariance generating functions. We also provide closed formulas for the spectral densities by using the periodic covariance generating functions, which is a new technique in the spectral theory of periodically correlated processes.