Journal of Mathematics and Statistics

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

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

DOI : 10.3844/jmssp.2010.10.16

Journal of Mathematics and Statistics

Volume 6, Issue 1

Pages 10-16

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.

Copyright

© 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.
{"cc_re__cc_re__cc_by_4_0": ["Modified periodogram with expanded finite Fourier transformation for time series with missed observation has improved the results of the classic time series.\"/>    \n<meta name=\"dc.source\" content=\"Journal of Mathematics and Statistics 2010, Vol. 6, Page 10\"/>\n<meta name=\"dc.date\" content=\"2010/03/31\"/>    \n<meta name=\"dcterms.issued\" content=\"2010/03/31\"/>        \n<meta name=\"dc.identifier\" content=\"doi:10.3844/jmssp.2010.10.16\"/>    \n<meta name=\"dc.publisher\" content=\"Science Publications\"/>  \n<meta name=\"dc.rights\" content=\"http://creativecommons.org/licenses/by/4.0/\">\n<meta name=\"dc.format\" content=\"application/pdf\">    \n<meta name=\"dc.format\" content=\"text/html\">        \n<meta name=\"dc.language\" content=\"en\">\n<meta name=\"dc.subject\" content=\"Continuous time series\"/>\n<meta name=\"dc.subject\" content=\"modified periodogram\"/>\n<meta name=\"dc.subject\" content=\"spectral density\"/>\n<meta name=\"dc.subject\" content=\"spectral measure\"/>\n<meta name=\"dc.subject\" content=\"autocovariance\"/>\n<meta name=\"dc.subject\" content=\"data window and asymptotic normality\"/>\n    \n   ", "the modified periodogram had the same results of the study of the classic time series. <b>Conclusion:</b> Modified periodogram with expanded finite Fourier transformation for time series with missed observation has improved the results of the classic time series.</p>\n\n<h3 class=\"block-title sub-title\" style=\"text-align:justify\">\n<strong>Copyright</strong>\n</h3>\n<p>\n &copy; 2010 G. S. Mokaddis, M. A. Ghazal and A. E. El-Desokey. This is an open access article distributed under the terms of the \n <a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\">Creative Commons Attribution License</a>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.\n</p>\n</div>\n\n<br>\n<br>\n            \n            \n\n          </div>\n          \n          <!-- sidebar -->\n          \n          <div class=\"span4 sidebar sidebar-right\">\n            <div class=\"inner\">\n<div class=\"block\">\n  <table style=\"table-layout : fixed;\">\n    <tr>\n      <td rowspan=\"3\" style=\"width:150px\"><img src=\"http:"], "copyright__copyright__copyright": ["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.\n\nCopyright\n\n\u00a9 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.", "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.\n\nCopyright\n\n\u00a9 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."]}