Cuestas, J.C. and Gil-Alana, L.A. (2015) Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials. Studies in Nonlinear Dynamics and Econometrics, 20 (1). pp. 57-74.
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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2015, Luis Alberiko Gil-Alana et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. |
Keywords: | Chebyshev polynomials; long run dependence; fractional integration |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Social Sciences (Sheffield) > Department of Economics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 01 Jun 2015 15:12 |
Last Modified: | 26 Feb 2016 14:57 |
Published Version: | http://dx.doi.org/10.1515/snde-2014-0005 |
Status: | Published |
Publisher: | De Gruyter |
Refereed: | Yes |
Identification Number: | 10.1515/snde-2014-0005 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:86549 |