A Canonical Analysis of Multiple Time Series
George E. P. Box, George C. Tiao · Biometrika · 1977
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.