A non-linear approach with long range dependence based on Chebyshev polynomials
AbstractThis 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, and an empirical application, using data of real exchange rates is also carried out at the end of the article.
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Bibliographic InfoPaper provided by Asociación Española de Economía y Finanzas Internacionales in its series Working Papers with number 13-01.
Length: 37 pages
Date of creation: Feb 2013
Date of revision:
Chebyshev polynomials; long run dependence; fractional integration;
Other versions of this item:
- Juan Carlos Cuestas & Luis A. Gil-Alana, 2012. "A Non-Linear Approach with Long Range Dependence Based on Chebyshev Polynomials," Working Papers 2012013, The University of Sheffield, Department of Economics.
- Luis A. Gil-Alana & Juan Carlos Cuestas, 2012. "A Non-linear Approach with Long Range Dependence based on Chebyshev Polynomials," Faculty Working Papers 14/12, School of Economics and Business Administration, University of Navarra.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-03-02 (All new papers)
- NEP-ETS-2013-03-02 (Econometric Time Series)
- NEP-ORE-2013-03-02 (Operations Research)
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