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ON VECTOR AUTOCORRELATIONS AND GENERALIZED SECOND‐ORDER FUNCTIONS FOR TIME SERIES
Author(s) -
Paparoditis Efstathios
Publication year - 1994
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.1467-9892.1994.tb00197.x
Subject(s) - autocovariance , mathematics , autocorrelation , scalar (mathematics) , series (stratigraphy) , vector valued function , function (biology) , mathematical analysis , statistics , fourier transform , paleontology , geometry , biology , evolutionary biology
. Some structural properties of certain vector generalizations of second‐order functions of a stationary stochastic process based on determinantial functions of autocovariances are discussed. In particular, a generalized autocovariance function which retains all properties of the ordinary autocovariance function is considered and the linear dependence structure of certain scalar stochastic processes associated with this function is investigated. Properties of the normalized function are discussed and a duality property is found, according to which this function also generalizes in a natural way the ordinary partial autocorrelation function of stochastic processes.