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Testing for Time Dependence in Parameters

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Author Info

  • Ralf Becker
  • Walter Enders
  • A. Stan Hurn

Abstract

This paper proposes a new test based on a Fourier series expansion to approximate the unknown functional form of a nonlinear time-series model. The test specifically allows for structural breaks, seasonal parameters and time-varying parameters. The test is shown to have evry good size and power properties. However, it is not especially good in detecting nonlinearity in variables. As such, the test can help determine whether an observed rejection of the joint null hypothesis of linearity and time invariant parameters is due to time-varying coefficients of a nonliearity in variables.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp58.pdf
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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 58.

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Date of creation: 01 Jun 2001
Date of revision:
Handle: RePEc:uts:rpaper:58

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Related research

Keywords: time varying parameters; fourier-series; nuisance parameters;

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References

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  1. William A. Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan & Mark J. Jensen, 1996. "A Single-Blind Controlled Competition among Tests for Nonlinearity and Chaos," Econometrics 9602005, EconWPA, revised 20 Sep 1996.
  2. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, vol. 56(3), pages 269-290, April.
  3. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549.
  4. Gallant, A. Ronald & Souza, Geraldo, 1991. "On the asymptotic normality of Fourier flexible form estimates," Journal of Econometrics, Elsevier, vol. 50(3), pages 329-353, December.
  5. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
  6. Ludlow, Jorge & Enders, Walter, 2000. "Estimating non-linear ARMA models using Fourier coefficients," International Journal of Forecasting, Elsevier, vol. 16(3), pages 333-347.
  7. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March.
  8. Lutkepohl, Helmut & Herwartz, Helmut, 1996. "Specification of varying coefficient time series models via generalized flexible least squares," Journal of Econometrics, Elsevier, vol. 70(1), pages 261-290, January.
  9. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
  10. Michael P. Clements & David F. Hendry, 2001. "Forecasting Non-Stationary Economic Time Series," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262531895.
  11. Hansen, Bruce E, 1999. " Testing for Linearity," Journal of Economic Surveys, Wiley Blackwell, vol. 13(5), pages 551-76, December.
  12. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  13. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
  14. Engle, Robert F, 1974. "Band Spectrum Regression," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 1-11, February.
  15. Tan, Hui Boon & Ashley, Richard, 1999. "Detection And Modeling Of Regression Parameter Variation Across Frequencies," Macroeconomic Dynamics, Cambridge University Press, vol. 3(01), pages 69-83, March.
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Citations

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Cited by:
  1. Dimitris, Chrsitopoulos & Miguel, Leon-Ledesma, 2009. "International Output Convergence, Breaks, and Asymmetric Adjustment," MPRA Paper 14566, University Library of Munich, Germany.
  2. Paulo M.M. Rodrigues & A. M. Robert Taylor, 2009. "The Flexible Fourier Form and Local GLS De-trended Unit Root Tests," Working Papers w200919, Banco de Portugal, Economics and Research Department.
  3. Thanasis Stengos & M. Ege Yazgan, 2011. "Persistence in Convergence," Working Paper Series 34_11, The Rimini Centre for Economic Analysis.
  4. Thanasis Stengos & M. Ege Yazgan, 2012. "Persistence in Real Exchange Rate Convergence," Working Papers 1207, University of Guelph, Department of Economics and Finance.
  5. Dimitris, Christopoulos & Miguel, Leon-Ledesma, 2009. "Smooth Breaks and Nonlinear Mean Reversion: Post-Bretton Woods Real Exchange Rates," MPRA Paper 22553, University Library of Munich, Germany.
  6. Enders, Walter & Holt, Matthew T., 2011. "Breaks, bubbles, booms, and busts: the evolution of primary commodity price fundamentals," MPRA Paper 31461, University Library of Munich, Germany.
  7. Razvan Pascalau, 2010. "Unit root tests with smooth breaks: an application to the Nelson-Plosser data set," Applied Economics Letters, Taylor & Francis Journals, vol. 17(6), pages 565-570.
  8. Jing, Li & Thompson, Henry, 2010. "A Note on the Oil Price Trend and GARCH Shocks," MPRA Paper 20654, University Library of Munich, Germany.

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