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NOTES AND PROBLEMS A GENERAL BOUND FOR THE LIMITING DISTRIBUTION OF BREITUNG'S STATISTIC

Published online by Cambridge University Press:  09 July 2008

James Davidson ,
Jan R. Magnus  and
Jan Wiegerinck
James Davidson
Affiliation:
University of Exeter
Jan R. Magnus*
Affiliation:
Tilburg University
Jan Wiegerinck
Affiliation:
University of Amsterdam
*
Address correspondence to Jan R. Magnus, Department of Econometrics and Operations Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands; e-mail: [email protected]
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Abstract

We consider the Breitung (2002, Journal of Econometrics 108, 343–363) statistic ξn, which provides a nonparametric test of the I(1) hypothesis. If ξ denotes the limit in distribution of ξn as n → ∞, we prove (Theorem 1) that 0 ≤ ξ ≤ 1/π2, a result that holds under any assumption on the underlying random variables. The result is a special case of a more general result (Theorem 3), which we prove using the so-called cotangent method associated with Cauchy's residue theorem.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 5 , October 2008 , pp. 1443 - 1455
Copyright
Copyright © Cambridge University Press 2008

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References

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