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TESTING AND INFERENCE IN NONLINEAR COINTEGRATING VECTOR ERROR CORRECTION MODELS

Published online by Cambridge University Press:  06 August 2013

Dennis Kristensen  and
Anders Rahbek
Dennis Kristensen*
Affiliation:
University College London, and, Institute of Fiscal Studies
Anders Rahbek
Affiliation:
University of Copenhagen
*
*Address correspondence to Dennis Kristensen, University College London, Gower Street, London WC1E 6BT, United Kingdom; e-mail: d.kristensen@ucl.ac.uk.
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Abstract

We analyze estimators and tests for a general class of vector error correction models that allows for asymmetric and nonlinear error correction. For a given number of cointegration relationships, general hypothesis testing is considered, where testing for linearity is of particular interest. Under the null of linearity, parameters of nonlinear components vanish, leading to a nonstandard testing problem. We apply so-called sup-tests to resolve this issue, which requires development of new(uniform) functional central limit theory and results for convergence of stochastic integrals. We provide a full asymptotic theory for estimators and test statistics. The derived asymptotic results prove to be nonstandard compared to results found elsewhere in the literature due to the impact of the estimated cointegration relations. This complicates implementation of tests motivating the introduction of bootstrap versions that are simple to compute. A simulation study shows that the finite-sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes.

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ARTICLES
Information
Econometric Theory , Volume 29 , Issue 6 , December 2013 , pp. 1238 - 1288
Copyright
Copyright © Cambridge University Press 2013 

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Footnotes

We thank the co-editor Michael Jansson and editor Peter C.B. Phillips and the anonymous referees whose comments and suggestions much improved the paper. We also thank Juan Carlos Escanciano and Myung Hwan Seo for very helpful discussions and suggestions. Both authors are affiliated with CREATES, funded by the DanishNational Research Foundation. The Velux Foundation funded a longer research visit for Kristensen at the University of Copenhagen, where part of this research was conducted. Part of the research was also conducted while Kristensen visited Princeton University, whose hospitality is gratefully acknowledged. Kristensen received research support from the National Science Foundation (grant SES-0961596). Rahbek gratefully acknowledges funding from the Danish Council for Independent Research, Social Sciences (grant 10-079774). We also thank participants at the 18th Annual Symposium of the Society for Nonlinear Dynamics and Econometrics in Novara, Italy, and at the Montreal Econometrics Seminar and Oxbridge Time Series Group Workshop 2010, Cambridge.

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