A consistent estimator for spectral density matrix of a discrete time periodically correlated process

• Autorzy: Azimmohseni M. , Soltani A. R. , Khalafi M. , Ghalesary N. M.

Identyfikatory

DOI

10.19195/0208-4147.38.1.12

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

periodically correlated processes; spectra density matrix; Kullback-Leibler distance; smoothed periodogram; Wishart distribution; limiting distribution

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2018
• Tom: Vol. 38, Fasc. 1
• Strony: 225--242
• Opis fizyczny: Bibliogr. 9 poz., wykr.

Twórcy

autor

Azimmohseni M.

• Department of Statistic, Faculty of Science, Golestan University, P.O. Box 155, Gorgan, Iran

autor

Soltani A. R.

• Department of Statistics and Operations Research, Faculty of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

autor

Khalafi M.

• Department of Statistic, Faculty of Science, Golestan University, P.O. Box 155, Gorgan, Iran

autor

Ghalesary N. M.

• Department of Statistic, Faculty of Science, Golestan University, P.O. Box 155, Gorgan, Iran

Bibliografia

• [1] P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, second edition, Springer, New York 1991.
• [2] E. G. Gladyshev, Periodically correlated random sequences, Soviet Math. Dokl. 2 (1961), pp. 385-388.
• [3] H. L. Hurd and A. G. Miamee, Periodically Correlated Random Sequences: Spectral Theory and Practice, Wiley, Hoboken, NJ, 2007.
• [4] Y. Kakizawa, R. H. Shumway, and M. Taniguchi, Discrimination and clustering for multivariate time series, J. Amer. Statist. Assoc. 93 (1998), pp. 328-340.
• [5] A. L. Khuri, T. Mathew, and D. G. Nel, A test to determine closeness of multivariate Satterthwaite’s approximation, J. Multivariate Anal. 51 (1) (1994), pp. 201-209.
• [6] A. R. Nematollahi and S. Rao, On the spectral density estimation of periodically correlated time series, Sankhya 67 (3) (2005), pp. 568-589.
• [7] A. R. Soltani and M. Azimmohseni, Periodograms asymptotic distributions in periodically correlated processes and multivariate stationary processes: An alternative approach, J. Statist. Plann. Inference 137 (2007), pp. 1236-1242.
• [8] A. R. Soltani and Z. Shishebor, Weakly periodic sequences of bounded linear transformation, Georgian Math. J. 6 (1) (1999), pp. 91-98.
• [9] W. Y. Tan and R. P. Gupta, On approximating a linear combination of central Wishart matrices with positive coefficients, Comm. Statist. Theory Methods 12 (22) (1983), pp. 2589-2600.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).