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A non-linear approach with long range dependence based on chebyshev polynomials

Cuestas, J.C. and Gil-Alana, L.A. (2012) A non-linear approach with long range dependence based on chebyshev polynomials. Working Paper. Sheffield Economic Research Paper Series . Department of Economics, University of Sheffield ISSN 1749-8368

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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, we present a procedure that permits 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 an empirical application, using data of real exchange rates, is also carried out at the end of the article.

Item Type: Monograph (Working Paper)
Copyright, Publisher and Additional Information: The Sheffield Economics Research Paper (SERP) series offers a forum for the research output of the academic staff and research students of the Department of Economics, University of Sheffield. Papers are reviewed for quality and presentation by a departmental editor. However, the contents and opinions expressed remain the responsibility of the authors. All papers may be downloaded free on the understanding that the contents are preliminary and therefore permission from the author(s) should be sought before they are referenced.
Keywords: Chebyshev polynomials; long run dependence; fractional integration;
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Social Sciences (Sheffield) > Department of Economics (Sheffield) > Sheffield Economics Research Papers Series
Depositing User: Miss Anthea Tucker
Date Deposited: 04 May 2012 16:02
Last Modified: 08 Jun 2014 12:06
Published Version: http://www.shef.ac.uk/economics/research/serps/yea...
Status: Published
Publisher: Department of Economics, University of Sheffield
Identification Number: 2012013
URI: http://eprints.whiterose.ac.uk/id/eprint/43893

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