(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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