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Biometrika 1977 64(2):355-365; doi:10.1093/biomet/64.2.355
© 1977 by Biometrika Trust
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A canonical analysis of multiple time series

G. E. P. BOX and G. C. TIAO

Department of Statistics, University of Wisconsin Madison

This paper proposes a canonical transformation of a k-dimensional stationary autoregressive process. The components of the transformed process are ordered from least to most predictable. The least predictable components are often nearly white noise which can reflect stable contemporaneous relationships among the original variables. The most predictable can be nearly nonstationary representing the dynamic growth characteristic of the series. The method is illustrated with a series with five variables.

Key Words: Autoregressive process • Canonical variable • Eigenvalue • Eigenvector • Multiple time series • Variance component


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