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Biometrika 1983 70(1):145-156; doi:10.1093/biomet/70.1.145
© 1983 by Biometrika Trust
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Some results on multivariate autoregressive index models

GREGORY REINSEL

Department of Statistics, University of Wisconsin Madison, Wisconsin, U.S.A.

We discuss methods for modelling multivariate autoregressive time series in terms of a smaller number of index series which are chosen to provide as complete a summary as possible of the past information contained in the original series necessary for prediction purposes. The maximum likelihood method of estimation and asymptotic properties of estimators of the coefficients which determine the index variables, a well as the corresponding autoregressive coefficients, are discussed. A numerical example is presented to illustrate the use of the autoregressive index models.

Key Words: Index series • Maximum likelihood estimation • Model dimension reduction • Model selection • Multiple autoregressive index model


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