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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- Diebold, Francis X. & Rudebusch, Glenn D., 1989.
"Long memory and persistence in aggregate output,"
Journal of Monetary Economics,
Elsevier, vol. 24(2), pages 189-209, September.
- 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, vol. 38(5), pages 1329-1349, August.
- Tom Doan, . "RATS programs to replicate Papell and Prodan one and two break unit root tests," Statistical Software Components RTZ00130, Boston College Department of Economics.
- Ferrara, Laurent & Guegan, Dominique, 2001. "Forecasting with k-Factor Gegenbauer Processes: Theory and Applications," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(8), pages 581-601, December.
- 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.
- Tom Doan, . "LPUNIT: RATS procedure to implement Lumsdaine-Papell unit root test with structural breaks," Statistical Software Components RTS00110, Boston College Department of Economics.
- Francis X. Diebold & Atsushi Inoue, 2000.
"Long Memory and Regime Switching,"
NBER Technical Working Papers
0264, National Bureau of Economic Research, Inc.
- 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, vol. 20(1), pages 25-44, January.
- Zivot, Eric & Andrews, Donald W K, 1992. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 251-70, July.
- Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation for Research in Economics, Yale University.
- Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
- 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., vol. 16(2), pages 95-114.
- L A Gil-Alaña & Peter M Robinson, 2000. "Testing of Seasonal Fractional Integration in UK and Japanese Consumption and Income," STICERD - Econometrics Paper Series /2000/402, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Gil-Alana, L. & Robinson, P.M., 1998. "Testing of Seasonal Fractional Integration in U.K. and Japanese Consumption and Income," Economics Working Papers eco98/20, European University Institute.
- Ray, Bonnie K., 1993. "Long-range forecasting of IBM product revenues using a seasonal fractionally differenced ARMA model," International Journal of Forecasting, Elsevier, vol. 9(2), pages 255-269, August.
- Dalla, Violetta & Hidalgo, Javier, 2005.
"A parametric bootstrap test for cycles,"
Journal of Econometrics,
Elsevier, vol. 129(1-2), pages 219-261.
- Perron, Pierre, 1989.
"The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis,"
Econometric Society, vol. 57(6), pages 1361-1401, November.
- Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
- Sowell, Fallaw, 1992. "Modeling long-run behavior with the fractional ARIMA model," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 277-302, April.
- 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, vol. 19(5), pages 759-764, October.
- David O. Cushman, 2008. "Real exchange rates may have nonlinear trends," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 13(2), pages 158-173.
- Cuestas, Juan Carlos & Regis, Paulo José, 2013.
"Purchasing power parity in OECD countries: Nonlinear unit root tests revisited,"
Elsevier, vol. 32(C), pages 343-346.
- Juan Carlos Cuestas & Paulo José Regis, 2010. "Purchasing power parity in OECD countries: nonlinear unit root tests revisited," Working Papers 2010/3, Nottingham Trent University, Nottingham Business School, Economics Division.
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