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A LIMITING PROPERTY OF SAMPLE AUTOCOVARIANCES OF PERIODICALLY CORRELATED PROCESSES WITH APPLICATION TO PERIOD DETERMINATION
Author(s) -
Tian C. J.
Publication year - 1988
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1988.tb00480.x
Subject(s) - autocovariance , mathematics , limiting , property (philosophy) , sample (material) , limit (mathematics) , convergence (economics) , lag , statistics , econometrics , mathematical analysis , thermodynamics , computer science , mechanical engineering , computer network , philosophy , physics , epistemology , fourier transform , engineering , economics , economic growth
. It is shown that the sample autocovariance of a periodically correlated process converges to a limit which reveals the same periodicity as the process. A theorem is proved relating to the rate of almost sure convergence, which is uniform in the lag up to some orders of observation length. Based on the limiting property, a strongly consistent estimate of hidden period is proposed.