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Biometrika 1986 73(1):105-118; doi:10.1093/biomet/73.1.105
© 1986 by Biometrika Trust
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Reduced rank models for multiple time series

RAJA P. VELU, GREGORY C. REINSEL and DEAN W. WICHERN

Department of Marketing, University of Wisconsin Whitewater, Wisconsin 53190, U.S.A.
Department of Statistics, University of Wisconsin Madison, Wisconsin 53706, U.S.A.
Department of Business Analysis, Texas A&M University College Station, Texas 77843, U.S.A.

This paper is concerned with the investigation of reduced rank coefficient models for multiple time series. In particular, autoregressive processes which have a structure to their coefficient matrices similar to that of classical multivariate reduced rank regression are studied in detail. The estimation of parameters and associated asymptotic theory are derived. The exact correspondence between the reduced rank regression procedure for multiple autoregressive processes and the canonical analysis of Box & Tiao (1977) is briefly indicated. To illustrate the methods, U.S. hog data are considered.

Key Words: Canonical analysis • Canonical correlation • Multiple time series • Reduced rank regression


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