CANONICAL CORRELATION AND REDUCTION OF MULTIPLE TIME SERIES

MOHSEN POURAHMADI

Division of Statistics and Statistical Consulting Laboratory, Northern Illinois University, DeKalb, IL 60115-2854, U.S.A.

(Received February 22, 1993; revised November 4, 1993)

Abstract. 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 ρ, 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 ρ = 1 are outlined, the latter is related to testing the unit root hypothesis in ARMA models.

Key words and phrases: Rank of multiple time series, transformation, spectrum.