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Frequency: Continuous
ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

Asymptotic Properties of Spectral Estimates of Second-Order with Missed Observations

G. S. Mokaddis, M. A. Ghazal and A. E. El-Desokey

Abstract

Problem statement: As a complement of the periodogram study the asymptotic properties of the spectral density using data window for stationary stochastic process are investigated. Some statistical properties of covariance estimation function with missing observations are studied. Approach: The asymptotic normality was discussed. A numerical example was discussed by using computer programming. Results: The study of time series with missed observations and with the modified periodogram had the same results of the study of the classic time series. Conclusion: Modified periodogram with expanded finite Fourier transformation for time series with missed observation has improved the results of the classic time series.

Journal of Mathematics and Statistics
Volume 6 No. 1, 2010, 10-16

DOI: https://doi.org/10.3844/jmssp.2010.10.16

Submitted On: 16 October 2009 Published On: 31 March 2010

How to Cite: Mokaddis, G. S., Ghazal, M. A. & El-Desokey, A. E. (2010). Asymptotic Properties of Spectral Estimates of Second-Order with Missed Observations. Journal of Mathematics and Statistics, 6(1), 10-16. https://doi.org/10.3844/jmssp.2010.10.16

Open AccessCopyright: © 2010 G. S. Mokaddis, M. A. Ghazal and A. E. El-Desokey. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Continuous time series
  • modified periodogram
  • spectral density
  • spectral measure
  • autocovariance
  • data window and asymptotic normality