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Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials

Testing for long memory in the presence of non-linear deterministic trends with Chebyshev... Abstract This paper examines the interaction between non-linear deterministic trends and long run dependence by means of employing Chebyshev time polynomials and assuming that the detrended series displays long memory with the pole or singularity in the spectrum occurring at one or more possibly non-zero frequencies. The combination of the non-linear structure with the long memory framework produces a model which is linear in parameters and therefore it permits the estimation of the deterministic terms by standard OLS-GLS methods. Moreover, the orthogonality property of Chebyshev’s polynomials makes them especially attractive to approximate non-linear structures of data. We present a procedure which allows us to test (possibly fractional) orders of integration at various frequencies in the presence of the Chebyshev trends with no effect on the standard limit distribution of the method. Several Monte Carlo experiments are conducted and the results indicate that the method performs well. An empirical application, using data of real exchange rates is also carried out at the end of the article. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Studies in Nonlinear Dynamics & Econometrics de Gruyter

Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials

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Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
1081-1826
eISSN
1558-3708
DOI
10.1515/snde-2014-0005
Publisher site
See Article on Publisher Site

Abstract

Abstract This paper examines the interaction between non-linear deterministic trends and long run dependence by means of employing Chebyshev time polynomials and assuming that the detrended series displays long memory with the pole or singularity in the spectrum occurring at one or more possibly non-zero frequencies. The combination of the non-linear structure with the long memory framework produces a model which is linear in parameters and therefore it permits the estimation of the deterministic terms by standard OLS-GLS methods. Moreover, the orthogonality property of Chebyshev’s polynomials makes them especially attractive to approximate non-linear structures of data. We present a procedure which allows us to test (possibly fractional) orders of integration at various frequencies in the presence of the Chebyshev trends with no effect on the standard limit distribution of the method. Several Monte Carlo experiments are conducted and the results indicate that the method performs well. An empirical application, using data of real exchange rates is also carried out at the end of the article.

Journal

Studies in Nonlinear Dynamics & Econometricsde Gruyter

Published: Feb 1, 2016

References