Testing the Rank of the Hankel Matrix: A Statistical Approach

25 Pages Posted: 26 Feb 2003

Date Written: March 2001

Abstract

The rank of the Hankel matrix, corresponding to a system transfer function, is equal to the order of its minimal state space realization. The computation of the rank of the Hankel matrix is complicated by the fact that its block elements are rarely given exactly but are estimated instead. In this paper, we propose new statistical tests to determine the rank of the Hankel matrix. We also provide a Monte Carlo study on the reliability of these tests compared to existing procedures.

Keywords: Tests of Rank, Model Reduction, Hankel Operator, Monte Carlo

JEL Classification: C12, C15, C32

Suggested Citation

Camba-Mendez, Gonzalo and Kapetanios, George, Testing the Rank of the Hankel Matrix: A Statistical Approach (March 2001). Available at SSRN: https://ssrn.com/abstract=356006

Gonzalo Camba-Mendez (Contact Author)

European Central Bank (ECB) ( email )

Sonnemannstrasse 22
Frankfurt am Main, 60314
Germany
0049 69 13440 (Phone)
0044 69 1344 6000 (Fax)

George Kapetanios

King's College, London ( email )

30 Aldwych
London, WC2B 4BG
United Kingdom
+44 20 78484951 (Phone)

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