Statistical Tests and Estimators of the Rank of a Matrix and their Applications in Econometric Modelling

41 Pages Posted: 27 Jan 2008

Date Written: January 2008

Abstract

Testing and estimating the rank of a matrix of estimated parameters is key in a large variety of econometric modelling scenarios. This paper describes general methods to test for and estimate the rank of a matrix, and provides details on a variety of modelling scenarios in the econometrics literature where such methods are required. Four different methods to test the true rank of a general matrix are described, as well as one method that can handle the case of a matrix subject to parameter constraints associated with defineteness structures. The technical requirements for the implementation of the tests of rank of a general matrix differ and hence there are merits to all of them that justify their use in applied work. Nonetheless, we review available evidence of their small sample properties in the context of different modelling scenarios where all, or some, are applicable.

Keywords: multiple time series, model specification, tests of rank

JEL Classification: C12, C15, C32

Suggested Citation

Camba-Mendez, Gonzalo and Kapetanios, George, Statistical Tests and Estimators of the Rank of a Matrix and their Applications in Econometric Modelling (January 2008). ECB Working Paper No. 850, Available at SSRN: https://ssrn.com/abstract=1077766

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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