IDEAS home Printed from https://ideas.repec.org/p/uts/rpaper/58.html
   My bibliography  Save this paper

Testing for Time Dependence in Parameters

Author

Listed:
  • 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.

Suggested Citation

  • Ralf Becker & Walter Enders & A. Stan Hurn, 2001. "Testing for Time Dependence in Parameters," Research Paper Series 58, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:58
    as

    Download full text from publisher

    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp58.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549.
    2. William A. Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan, 2004. "A Single-Blind Controlled Competition Among Tests for Nonlinearity and Chaos," Contributions to Economic Analysis, in: Functional Structure and Approximation in Econometrics, pages 581-615, Emerald Group Publishing Limited.
    3. repec:bla:jecsur:v:13:y:1999:i:5:p:551-76 is not listed on IDEAS
    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. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    6. 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.
    7. Timo Teräsvirta & Chien‐Fu Lin & Clive W. J. Granger, 1993. "Power Of The Neural Network Linearity Test," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(2), pages 209-220, March.
    8. Bruce Hansen, 1999. "Testing for Linearity," Journal of Economic Surveys, Wiley Blackwell, vol. 13(5), pages 551-576, December.
    9. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(3), pages 295-325, June.
    10. 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.
    11. Hansen,B.E., 1999. "Testing for linearity," Working papers 7, Wisconsin Madison - Social Systems.
    12. Ludlow, Jorge & Enders, Walter, 2000. "Estimating non-linear ARMA models using Fourier coefficients," International Journal of Forecasting, Elsevier, vol. 16(3), pages 333-347.
    13. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    14. Tan, Hui Boon & Ashley, Richard, 1999. "Detection And Modeling Of Regression Parameter Variation Across Frequencies," Macroeconomic Dynamics, Cambridge University Press, vol. 3(1), pages 69-83, March.
    15. 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.
    16. 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.
    17. 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.
    18. 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, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Stengos Thanasis & Yazgan M. Ege, 2014. "Persistence in real exchange rate convergence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(1), pages 73-88, February.
    3. Gallegati, Marco & Ramsey, James B., 2013. "Structural change and phase variation: A re-examination of the q-model using wavelet exploratory analysis," Structural Change and Economic Dynamics, Elsevier, vol. 25(C), pages 60-73.
    4. Jing Li & Henry Thompson, 2010. "A Note on the Oil Price Trend and GARCH Shocks," The Energy Journal, , vol. 31(3), pages 159-166, July.
    5. Stengos, Thanasis & Yazgan, M. Ege, 2014. "Persistence In Convergence," Macroeconomic Dynamics, Cambridge University Press, vol. 18(4), pages 753-782, June.
    6. Christopoulos Dimitris K & Leon-Ledesma Miguel A., 2011. "International Output Convergence, Breaks, and Asymmetric Adjustment," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(3), pages 1-33, May.
    7. Lee, Chia-Hao & Chou, Pei-I, 2013. "The behavior of real exchange rate: Nonlinearity and breaks," International Review of Economics & Finance, Elsevier, vol. 27(C), pages 125-133.
    8. Christopoulos, Dimitris K. & León-Ledesma, Miguel A., 2010. "Smooth breaks and non-linear mean reversion: Post-Bretton Woods real exchange rates," Journal of International Money and Finance, Elsevier, vol. 29(6), pages 1076-1093, October.
    9. 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.
    10. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Terasvirta, Timo, 2006. "Forecasting economic variables with nonlinear models," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 8, pages 413-457, Elsevier.
    2. Chihwa Kao & Yongmiao Hong, 2004. "Detecting Neglected Nonlinearity in Dynamic Panel Data with Time-Varying Conditional Heteroskedasticity," Econometric Society 2004 Far Eastern Meetings 753, Econometric Society.
    3. Pérez-Alonso Alicia & Di Sanzo Silvestro, 2010. "Unemployment and Hysteresis: A Nonlinear Unobserved Components Approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(1), pages 1-29, December.
    4. Jonathan B. Hill, 2004. "Consistent Model Specification Tests Against Smooth Transition Alternatives," Econometrics 0402004, University Library of Munich, Germany, revised 05 Aug 2005.
    5. Tarlok Singh, 2012. "Testing nonlinearities in economic growth in the OECD countries: an evidence from SETAR and STAR models," Applied Economics, Taylor & Francis Journals, vol. 44(30), pages 3887-3908, October.
    6. Jonathan B. Hill, 2004. "Consistent LM-Tests for Linearity Against Compound Smooth Transition Alternatives," Econometric Society 2004 North American Summer Meetings 42, Econometric Society.
    7. Henry, Olan T. & Shields, Kalvinder, 2004. "Is there a unit root in inflation?," Journal of Macroeconomics, Elsevier, vol. 26(3), pages 481-500, September.
    8. repec:wyi:journl:002062 is not listed on IDEAS
    9. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871.
    10. Gabriel Vasco J. & Alexandre Fernando & Bação Pedro, 2008. "The Consumption-Wealth Ratio under Asymmetric Adjustment," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(4), pages 1-32, December.
    11. Singh, Tarlok, 2014. "On the regime-switching and asymmetric dynamics of economic growth in the OECD countries," Research in Economics, Elsevier, vol. 68(2), pages 169-192.
    12. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2010. "Regime specific predictability in predictive regressions," Discussion Paper Series In Economics And Econometrics 0916, Economics Division, School of Social Sciences, University of Southampton.
    13. Philip Kostov & John Lingard, 2004. "Regime-switching Vector Error Correction Model (VECM) analysis of UK meat consumption," Econometrics 0409007, University Library of Munich, Germany.
    14. Hill Jonathan B., 2013. "Stochastically weighted average conditional moment tests of functional form," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(2), pages 121-139, April.
    15. Jesús Gonzalo & Jean-Yves Pitarakis, 2011. "Regime-Specific Predictability in Predictive Regressions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(2), pages 229-241, June.
    16. Dreger, Christian & Gerdesmeier, Dieter & Roffia, Barbara, 2020. "The impact of credit for house price overvaluations in the euro area: Evidence from threshold models," MPRA Paper 99523, University Library of Munich, Germany.
    17. Francq, Christian & Horvath, Lajos & Zakoian, Jean-Michel, 2008. "Sup-tests for linearity in a general nonlinear AR(1) model when the supremum is taken over the full parameter space," MPRA Paper 16669, University Library of Munich, Germany.
    18. Kirstin Hubrich & Timo Teräsvirta, 2013. "Thresholds and Smooth Transitions in Vector Autoregressive Models," CREATES Research Papers 2013-18, Department of Economics and Business Economics, Aarhus University.
    19. Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models — A Survey Of Recent Developments," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 1-47.
    20. Penelope Smith, 2006. "Bayesian Inference for a Threshold Autoregression with a Unit Root," Melbourne Institute Working Paper Series wp2006n20, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    21. repec:wsr:wpaper:y:2019:i:189 is not listed on IDEAS
    22. Jonathan B. Hill, 2004. "LM-Tests for Linearity Against Smooth Transition Alternatives: A Bootstrap Simulation Study," Econometrics 0401004, University Library of Munich, Germany, revised 05 Jul 2004.

    More about this item

    Keywords

    time varying parameters; fourier-series; nuisance parameters;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:uts:rpaper:58. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Duncan Ford (email available below). General contact details of provider: https://edirc.repec.org/data/qfutsau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.