M. Azimmohseni, A. Soltani, M. Khalafi, Naeemeh Akbari Ghalesary
{"title":"离散时间周期相关过程谱密度矩阵的一致估计","authors":"M. Azimmohseni, A. Soltani, M. Khalafi, Naeemeh Akbari Ghalesary","doi":"10.19195/0208-4147.38.1.12","DOIUrl":null,"url":null,"abstract":"In this article, we introduce a weighted periodogram in the class of smoothed periodograms as a consistent estimator for the spectral density matrix of a periodically correlated process. We derive its limiting distribution that appears to be a certain finite linear combination of Wishart distribution. We also provide numerical derivations for our smoothed periodogram and exhibit its asymptotic consistency using simulated data.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A consistent estimator for spectral density matrix of a discrete time periodically correlated process\",\"authors\":\"M. Azimmohseni, A. Soltani, M. Khalafi, Naeemeh Akbari Ghalesary\",\"doi\":\"10.19195/0208-4147.38.1.12\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we introduce a weighted periodogram in the class of smoothed periodograms as a consistent estimator for the spectral density matrix of a periodically correlated process. We derive its limiting distribution that appears to be a certain finite linear combination of Wishart distribution. We also provide numerical derivations for our smoothed periodogram and exhibit its asymptotic consistency using simulated data.\",\"PeriodicalId\":48996,\"journal\":{\"name\":\"Probability and Mathematical Statistics-Poland\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2018-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability and Mathematical Statistics-Poland\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.19195/0208-4147.38.1.12\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability and Mathematical Statistics-Poland","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.19195/0208-4147.38.1.12","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
A consistent estimator for spectral density matrix of a discrete time periodically correlated process
In this article, we introduce a weighted periodogram in the class of smoothed periodograms as a consistent estimator for the spectral density matrix of a periodically correlated process. We derive its limiting distribution that appears to be a certain finite linear combination of Wishart distribution. We also provide numerical derivations for our smoothed periodogram and exhibit its asymptotic consistency using simulated data.
期刊介绍：
PROBABILITY AND MATHEMATICAL STATISTICS is published by the Kazimierz Urbanik Center for Probability and Mathematical Statistics, and is sponsored jointly by the Faculty of Mathematics and Computer Science of University of Wrocław and the Faculty of Pure and Applied Mathematics of Wrocław University of Science and Technology. The purpose of the journal is to publish original contributions to the theory of probability and mathematical statistics.
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