Econometric Theory

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A SIEVE BOOTSTRAP TEST FOR COINTEGRATION IN A CONDITIONAL ERROR CORRECTION MODEL

Franz C. Palma1 c1, Stephan Smeekesa1 and Jean-Pierre Urbaina1

a1 Maastricht University

Abstract

In this paper we propose a bootstrap version of the Wald test for cointegration in a single-equation conditional error correction model. The multivariate sieve bootstrap is used to deal with dependence in the series. We show that the introduced bootstrap test is asymptotically valid. We also analyze the small sample properties of our test by simulation and compare it with the asymptotic test and several alternative bootstrap tests. The bootstrap test offers significant improvements in terms of size properties over the asymptotic test, while having similar power properties. The sensitivity of the bootstrap test to the allowance for deterministic components is also investigated. Simulation results show that the tests with sufficient deterministic components included are insensitive to the true value of the trends in the model and retain correct size.

Correspondence

c1 Address correspondence to Franz C. Palm, Department of Quantitative Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands; e-mail: f.palm@maastrichtuniversity.nl.

Footnotes

Previous versions of this paper have been presented at the Econometric Society European Meeting in Milan, August 2008; at the International Workshop on Recent Advances in Time Series Analysis in Cyprus, June 2008; at the Workshop on Bootstrap and Time Series in Kaiserslautern, June 2008; at the conference entitled Inference and Tests in Econometrics, A Tribute to Russell Davidson in Marseille, April 2008; at an Ente Luigi Einaudi Seminar in Econometrics in Rome, November 2007; and at the first workshop of the Methods in International Finance Network in Maastricht, September 2007. We gratefully acknowledge the comments by participants at these seminars and by Anders Swensen, Pentti Saikkonen, and three anonymous referees. We thank NWO and the Royal Netherlands Academy of Arts and Sciences for financial support.

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