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A Non-Linear Approach with Long Range Dependence Based on Chebyshev Polynomials

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  • Juan Carlos Cuestas

    ()
    (Department of Economics, The University of Sheffield)

  • Luis A. Gil-Alana

    ()
    (Department of Economics, Universidad de Navarra)

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.

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File URL: http://www.shef.ac.uk/economics/research/serps/articles/2012_013.html
File Function: First version, 2012
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Bibliographic Info

Paper provided by The University of Sheffield, Department of Economics in its series Working Papers with number 2012013.

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Length: 29 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:shf:wpaper:2012013

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Keywords: Chebyshev polynomials; long run dependence; fractional integration;

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References

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  1. David O. Cushman, 2008. "Real exchange rates may have nonlinear trends," International Journal of Finance & Economics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 13(2), pages 158-173.
  2. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers, Princeton, Department of Economics - Econometric Research Program 338, Princeton, Department of Economics - Econometric Research Program.
  3. Robin L. Lumsdaine & David H. Papell, 1997. "Multiple Trend Breaks And The Unit-Root Hypothesis," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 212-218, May.
  4. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, Elsevier, vol. 105(1), pages 131-159, November.
  5. L. A. Gil-Alana & P. M. Robinson, 2001. "Testing of seasonal fractional integration in UK and Japanese consumption and income," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 16(2), pages 95-114.
  6. L. A. Gil-Alaña & Peter M. Robinson, 2001. "Testing of seasonal fractional integration in UK and Japanese consumption and income," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 298, London School of Economics and Political Science, LSE Library.
  7. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, Elsevier, vol. 14(2), pages 227-238, October.
  8. Dalla, Violetta & Hidalgo, Javier, 2005. "A parametric bootstrap test for cycles," Journal of Econometrics, Elsevier, Elsevier, vol. 129(1-2), pages 219-261.
  9. Sowell, Fallaw, 1992. "Modeling long-run behavior with the fractional ARIMA model," Journal of Monetary Economics, Elsevier, Elsevier, vol. 29(2), pages 277-302, April.
  10. Ferrara, Laurent & Guegan, Dominique, 2001. "Forecasting with k-Factor Gegenbauer Processes: Theory and Applications," Journal of Forecasting, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 20(8), pages 581-601, December.
  11. Papell, David H. & Prodan, Ruxandra, 2006. "Additional Evidence of Long-Run Purchasing Power Parity with Restricted Structural Change," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 38(5), pages 1329-1349, August.
  12. Diebold, Francis X. & Rudebusch, Glenn D., 1989. "Long memory and persistence in aggregate output," Journal of Monetary Economics, Elsevier, Elsevier, vol. 24(2), pages 189-209, September.
  13. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(1), pages 25-44, January.
  14. Lothian, James R. & Taylor, Mark P., 2000. "Purchasing power parity over two centuries: strengthening the case for real exchange rate stability: A reply to Cuddington and Liang," Journal of International Money and Finance, Elsevier, Elsevier, vol. 19(5), pages 759-764, October.
  15. Ray, Bonnie K., 1993. "Long-range forecasting of IBM product revenues using a seasonal fractionally differenced ARMA model," International Journal of Forecasting, Elsevier, Elsevier, vol. 9(2), pages 255-269, August.
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Cited by:
  1. Cuestas, Juan Carlos & Regis, Paulo José, 2013. "Purchasing power parity in OECD countries: Nonlinear unit root tests revisited," Economic Modelling, Elsevier, Elsevier, vol. 32(C), pages 343-346.

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