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Studies in Nonlinear Dynamics & Econometrics

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Volume 19, Issue 3


Testing for co-nonlinearity

Håvard Hungnes
Published Online: 2014-11-04 | DOI: https://doi.org/10.1515/snde-2013-0092


This article introduces the concept of co-nonlinearity. Co-nonlinearity is an example of a common feature in time series [Engle, Robert F., and Sharon Kozicki. 1993. “Testing for Common Features.” Journal of Business & Economic Statistics 11 (4): 369–380] and an extension of the concept of common nonlinear components [Anderson, Heather M., and Farshid Vahid. 1998. “Testing Multiple Equation Systems for Common Nonlinear Components.” Journal of Econometrics 84 (1): 1–36]. If some time series follow a nonlinear process but where a linear relationship between the levels of these series removes the nonlinearity, such a relationship is defined as co-nonlinear. In this article I show how to determine the number of such co-nonlinear relationships. Furthermore, I show how to formulate hypothesis tests on the co-nonlinear relationships in a full maximum likelihood framework. The framework for identifying co-nonlinear relationships is illustrated in a system of Norwegian interest rates.

This article offers supplementary material which is provided at the end of the article.

Keywords: common features; nonlinearity; reduced-rank regression

JEL classification: C32; E43


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About the article

Corresponding author: Håvard Hungnes, Research Department, Statistics Norway, P.O.B. 8131 Dep, N-0033 Oslo, Norway, e-mail: . Websites: http://people.ssb.no/hhu and http://www.hungnes.net

Published Online: 2014-11-04

Published in Print: 2015-06-01

Citation Information: Studies in Nonlinear Dynamics & Econometrics, Volume 19, Issue 3, Pages 339–353, ISSN (Online) 1558-3708, ISSN (Print) 1081-1826, DOI: https://doi.org/10.1515/snde-2013-0092.

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