CANONICAL CORRELATION AND REDUCTION OF MULTIPLE TIME-SERIES

It is shown that a degenerate rank d-variate stationary time series can be reduced to a full rank time series of lower dimension via an orthogonal transformation T provided that rho, the canonical correlation between past and future of the time series is strictly less than one. Procedures for estimation of rank of the multiple time series, T and testing rho = 1 are outlined, the latter is related to testing the unit root hypothesis in ARMA models.