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ANOTHER NUMERICAL METHOD OF FINDING CRITICAL VALUES FOR THE ANDREWS STABILITY TEST

Published online by Cambridge University Press:  02 August 2011

Stanislav Anatolyev  and
Grigory Kosenok
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Abstract

We propose a method, alternative to that of Estrella (2003, Econometric Theory 19, 1128–1143), of obtaining exact asymptotic p-values and critical values for the popular Andrews (1993, Econometrica 61, 821–856) test for structural stability. The method is based on inverting an integral equation that determines the intensity of crossing a boundary by the asymptotic process underlying the test statistic. Further integration of the crossing intensity yields a p-value. The proposed method can potentially be applied to other stability tests that employ the supremum functional.

Type
Research Article
Information
Econometric Theory , Volume 28 , Issue 1 , February 2012 , pp. 239 - 246
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

We are grateful to two anonymous referees for very helpful comments and suggestions. We also thank Paolo Paruolo and Geert Dhaene for useful conversations.

References

REFERENCES

Andrews, D.W.K. (1993) Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821–856.CrossRefGoogle Scholar
Andrews, D.W.K. (2003) Tests for parameter instability and structural change with unknown change point: A corrigendum. Econometrica 71, 395–397.CrossRefGoogle Scholar
Bai, J. & Perron, P. (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66, 47–78.CrossRefGoogle Scholar
Brunner, H. (1974) Global solution of the generalized Abel integral equation by implicit interpolation. Mathematics of Computation 28, 61–67.CrossRefGoogle Scholar
Clenshaw, C.W. & Curtis, A.R. (1960) A method for numerical integration on an automatic computer. Numerische Mathematik 2, 197–205.CrossRefGoogle Scholar
DeLong, D.M. (1981) Crossing probabilities for a square root boundary by a Bessel process. Communications in Statistics—Theory and Methods A10, 2197–2213.10.1080/03610928108828182CrossRefGoogle Scholar
Durbin, J. (1971) Boundary-crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov–Smirnov test. Journal of Applied Probability 8, 431–453.CrossRefGoogle Scholar
Estrella, A. (2003) Critical values and p values of Bessel process distributions: Computation and an application to structural break tests. Econometric Theory 19, 1128–1143.CrossRefGoogle Scholar
Feller, W. (1936) Zur Theorie der stochastischen Prozesse. Mathematische Annalen 113, 113–160.CrossRefGoogle Scholar
Fortet, R. (1943) Les fonctions aléatoires du type de Markoff associées à certaines équations linéaires aux dé rivées partielles du type parabolique. Journal de Mathé matiques Pures et Appliquées 22, 177–243.Google Scholar
Hansen, B.E. (1999) Discussion of “Data mining reconsidered.” Econometrics Journal 2, 192–201.CrossRefGoogle Scholar
Judd, K. (1998) Numerical Methods in Economics. MIT Press.Google Scholar
Pötzelberger, K. & Wang, L. (2001) Boundary crossing probability for Brownian motion. Journal of Applied Probability 38, 152–164.10.1239/jap/996986650CrossRefGoogle Scholar
Weiss, R. (1972) Product integration for the generalized Abel equation. Mathematics of Computation 26, 177–190.CrossRefGoogle Scholar