Covariance Matrices Characterization by a Set of Scalar Partial Autocorrelation Coefficients

Abstract

It has been shown that the autocovariance matrices of a stationary multivariate time series can be uniquely characterized by a sequence of the normalized partial autocorrelation matrices having singular values less than one. In this note, we show that the same autocovariance matrices can be also uniquely characterized by a set of sequences of scalar partial autocorrelation coefficients whose magnitudes are all less than one.