Canonical Correlations of Past and Future for Time Series: Definitions and Theory

Abstract

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.