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

Author

Listed:
  • Cuestas Juan Carlos

    (Department of Economics, University of Sheffield, 9 Mappin Street, Sheffield, S1 4DT, UK)

  • Gil-Alana Luis Alberiko

    (Faculty of Economics, University of Navarra, Edificio Amigos, Pamplona, E-31080, Spain)

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.

Suggested Citation

  • Cuestas Juan Carlos & Gil-Alana Luis Alberiko, 2016. "Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(1), pages 57-74, February.
    • Handle: RePEc:bpj:sndecm:v:20:y:2016:i:1:p:57-74:n:2
    DOI: 10.1515/snde-2014-0005
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    More about this item

    Keywords

    Chebyshev polynomials; fractional integration; long run dependence;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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