Inference on periodograms of infinite dimensional discrete time periodically correlated processes

Journal of Multivariate Analysis

Volumn 101, Issue 2, 2010, Pages 368-373

  Soltani, A R ^a,b   Shishebor, Z ^b   Zamani, A ^b  

^a KUWAIT UNIVERSITY   (Kuwait)

^b SHIRAZ UNIVERSITY   (Iran)

Author keywords

60G12; 60G57; Finite Fourier transforms; Hilbert space valued second order processes; Periodically correlated processes; Periodogram; primary

Indexed keywords

EID: 70449553573     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2009.01.004     Document Type: Article

References (13)

1. Rozanov Yu.~A. Some approximation problems in the theory of stationary processes. J. Multivariate Anal. 2 (1972) 135-144
2. Salehi H., and Soltani A.R. On regularity of homogeneous random fields. Prediction Theory and Harmonic Analysis (1983), North-Holland Publ. Co., Amsterdam 309-328
3. Gihman I.I., and Skorohod A.V. The Theory of Stochastic Processes (1974), Springer-Verlag, Berlin
4. Bosq D. Linear Processes in Function Spaces. Theory and Applications. Lecture Notes in Statistics vol. 149 (2000), Springer, Berlin
5. Chen X., and White H. Central limit and functional central limit theorems for Hilbert-valued dependent heterogeneous arrays with applications. Econometric Theory 14 (1998) 260-284
6. Soltani A.R., and Shishebor Z. On infinite dimensional discrete time dependent periodically correlated processes. Rocky Mountain. J. Math. 37 (2007) 1043-1058
7. Soltani A.R., and Azimmohseni M. Periodograms asymptotic distributions in periodically correlated processes and multivariate stationary processes: An alternative approach. J. Statist. Plann. Inference 137 (2007) 1236-1242
8. Hurd H.L. Representation of strongly harmonizable periodically correlated processes and their covariance. J. Multivariate Anal. 29 (1989) 53-67
9. Pourahmadi M., and Salehi H. On subordination and linear transformation of harmonizable and periodically correlated processes. Probability Theory on Vector Spaces III (1983), Springer-Verlag, Berlin 195-213
10. Gladyshev E.G. Periodically correlated random sequences. Soviet Math. Dokl. 2 (1961) 385-388
11. Rudin W. Functional Analysis (1976), McGraw-Hill, New York
12. Makagon A., Miamee A.G., Salehi H., and Soltani A.R. On spectral domain of periodically correlated processes. Theory Probab. Appl. 52 (2007) 1-12
13. Soltani A.R., and Shishebor Z. A spectral representation for weakly periodic sequences of bounded linear transformations. Acta Math. Hungar. 80 (1998) 265-270