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Estimating the Rank of the Spectral Density Matrix
Author(s) -
CambaMendez Gonzalo,
Kapetanios George
Publication year - 2005
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.1467-9892.2005.00389.x
Subject(s) - mathematics , rank (graph theory) , hermitian matrix , matrix (chemical analysis) , covariance matrix , statistics , variety (cybernetics) , estimation of covariance matrices , positive definite matrix , combinatorics , pure mathematics , eigenvalues and eigenvectors , materials science , physics , quantum mechanics , composite material
. The rank of the spectral density matrix conveys relevant information in a variety of statistical modelling scenarios. This note shows how to estimate the rank of the spectral density matrix at any given frequency. The method presented is valid for any hermitian positive definite matrix estimate that has a normal asymptotic distribution with a covariance matrix the rank of which is known.