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THE RANK OF A SUBMATRIX OF COINTEGRATION

Published online by Cambridge University Press:  31 March 2005

Eiji Kurozumi
Eiji Kurozumi
Affiliation:
Hitotsubashi University and Boston University
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Abstract

This paper proposes a test of the rank of the submatrix of β, where β is a cointegrating matrix. In addition, the submatrix of β⊥, an orthogonal complement to β, is investigated. We construct the test statistic by using the eigenvalues of the quadratic form of the submatrix. We show that the test statistic has a limiting chi-square distribution when data are nontrending, whereas for trending data we have to consider a conservative test or other testing procedure that requires the pretest of the structure of the matrix. Finite sample simulations show that, although the simulation settings are limited, the proposed test works well for nontrending data, whereas we have to carefully use the test for trending data because it may become too conservative in some cases.I owe special thanks to two anonymous referees, the co-editor, Pierre Perron, and Taku Yamamoto. All errors are my responsibility. This research was supported by the Ministry of Education, Culture, Sports, Science and Technology under grants-in-aid 13730023 and 14203003.

Type
Research Article
Information
Econometric Theory , Volume 21 , Issue 2 , April 2005 , pp. 299 - 325
Copyright
© 2005 Cambridge University Press

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