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Rational transfer function approximation (with discussion). (English) Zbl 0638.62091
The paper is devoted to the problem how to approximate a general n- dimensional stationary time series by an n-dimensional ARMA process. The author discusses general features of linear systems and their description by an infinite, block Hankel matrix. He considers criteria for choosing orders of the ARMA process, especially AIC and BIC, and describes their properties.
Some algorithms are also introduced. They concern mainly real time calculations of the estimates. The comments written by Bhansali, Brillinger, Dahlhaus, Rissanen, Shibata and Solo contain some additional information and reflect views of their authors on specific problems discussed in the paper.
Reviewer: J.Anděl

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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