Dégerine, Serge Canonical partial autocorrelation function of a multivariate time series. (English) Zbl 0703.62095 Ann. Stat. 18, No. 2, 961-971 (1990). Summary: We propose a definition of the partial autocorrelation function \(\beta\) (\(\cdot)\) for multivariate stationary time series suggested by the canonical analysis of the forward and backward innovations. Here \(\beta\) (\(\cdot)\) satisfies \(\beta (-n)=\beta (n)'\), \(n=0,1,...\), where \(\beta\) (0) is nonnegative definite, \(\{\beta\) (n), \(n=1,2,...\}\) is a sequence of square matrices having singular values less than or equal to 1 and such that the order of \(\beta (n+1)\) is equal to the rank of \(I-\beta (n)\beta (n)'\), the order of \(\beta\) (1) being equal to the rank of \(\beta\) (0). We shown that there exists a one-to-one correspondence between the set of matrix autocovariance functions \(\Lambda\) (\(\cdot)\), with the positive definiteness property, and the set of canonical partial autocorrelation functions \(\beta\) (\(\cdot)\) as described above. Cited in 4 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62H20 Measures of association (correlation, canonical correlation, etc.) Keywords:canonical correlations; Levinson-Durbin algorithm; Gram-Schmidt process; principal components; multivariate stationary time series; canonical analysis; forward and backward innovations; matrix autocovariance functions; canonical partial autocorrelation functions × Cite Format Result Cite Review PDF Full Text: DOI