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

Juan Cuestas and Luis Gil-Alana ()

No 13-01, Working Papers from Asociación Española de Economía y Finanzas Internacionales

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, and an empirical application, using data of real exchange rates is also carried out at the end of the article.

Keywords: Chebyshev polynomials; long run dependence; fractional integration (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ets and nep-ore
Date: 2013-02
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Related works:
Working Paper: A non-linear approach with long range dependence based on Chebyshev polynomials (2012) Downloads
Working Paper: A Non-Linear Approach with Long Range Dependence Based on Chebyshev Polynomials (2012) Downloads
Working Paper: A Non-linear Approach with Long Range Dependence based on Chebyshev Polynomials (2012) Downloads
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