The concepts of canonical correlations and canonical components are familiar ideas in multivariate statistics. In this paper we extend these notions to stationary time series with a view to determining the most predictable aspect of the future of a time series. We relate properties of the canonical description of a time series to well known structural properties of the series such as (i) rational spectra (i.e., ARMA series), (ii) strong mixing, (iii) absolute regularity, etc.
"Canonical Correlations of Past and Future for Time Series: Definitions and Theory." Ann. Statist. 11 (3) 837 - 847, September, 1983. https://doi.org/10.1214/aos/1176346250