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 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.

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

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