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Biometrika 1986 73(2):447-453; doi:10.1093/biomet/73.2.447
© 1986 by Biometrika Trust
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A decomposition of some serially-structured variance matrices

C. A. GLASBEY

AFRC Unit of Statistics, University of Edinburgh Edinburgh, EH9 3JZ U.K.

Serially-structured variance matrices which can be decomposed into lower-triangular band matrices are defined. These may be thought of as the variance matrices of finite realizations of generalized autoregressive-moving average processes. A large number of serially-generated stochastic processes are shown to be of this type.

Key Words: Cholesky decomposition • Generalized autoregressive-moving average process • Linear stochastic difference equation • Lower-triangular band matrix • Serially-structured variance matrix • Stochastic compartment model


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