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ON THE COVARIANCE OF THE PERIODOGRAM
Author(s) -
Krogstad Harald E.
Publication year - 1982
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.1467-9892.1982.tb00342.x
Subject(s) - mathematics , pointwise , covariance , autocovariance , law of total covariance , stationary process , convolution (computer science) , covariance function , consistency (knowledge bases) , periodogram , matérn covariance function , statistics , mathematical analysis , covariance intersection , fourier transform , discrete mathematics , machine learning , artificial neural network , computer science
. The paper discusses the covariance of the periodogram from a zero mean fourth order stationary stochastic process. The fourth order cumulant term appearing in the covariance is shown to be a convolution between the fourth order cumulant spectrum and a bounded approximate identity, and this gives precise results about its asymptotic behaviour. The covariance is also studied both pointwise and as a measure of two variables. This leads to necessary and sufficient conditions for mean square consistency of estimates of the spectral moments and related parameters.