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The intersection of past and future for multivariate stationary processes

Authors: Akihiko Inoue, Yukio Kasahara and Mohsen Pourahmadi
Journal: Proc. Amer. Math. Soc. 144 (2016), 1779-1786
MSC (2010): Primary 60G10; Secondary 62M10, 60G25
Published electronically: September 9, 2015
MathSciNet review: 3451253
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Abstract: We consider an intersection of past and future property of multivariate stationary processes which is the key to deriving various representation theorems for their linear predictor coefficient matrices. We extend useful spectral characterizations for this property from univariate processes to multivariate processes.

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Additional Information

Akihiko Inoue
Affiliation: Department of Mathematics, Hiroshima University, Higashi-Hiroshima 739-8526, Japan

Yukio Kasahara
Affiliation: Department of Mathematics, Hokkaido University, Sapporo 060-0811, Japan

Mohsen Pourahmadi
Affiliation: Department of Statistics, Texas A&M University, College Station, Texas 77843

Received by editor(s): December 31, 2014
Received by editor(s) in revised form: April 17, 2015
Published electronically: September 9, 2015
Additional Notes: The third author was supported by NFS grant DMS-1309586.
Communicated by: Mark M. Meerschaert
Article copyright: © Copyright 2015 American Mathematical Society

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