[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/bpj/sndecm/v14y2010i3n3.html
   My bibliography  Save this article

Specifying Smooth Transition Regression Models in the Presence of Conditional Heteroskedasticity of Unknown Form

Author

Listed:
  • Pavlidis Efthymios G

    (Lancaster University Management School)

  • Paya Ivan

    (Lancaster University Management School)

  • Peel David A

    (Lancaster University Management School)

Abstract
The specification of Smooth Transition Regression models consists of a sequence of tests, which are typically based on the assumption of i.i.d. errors. In this paper we examine the impact of conditional heteroskedasticity and investigate the performance of several heteroskedasticity robust versions. Simulation evidence indicates that conventional tests can frequently result in finding spurious nonlinearity. Conversely, when the true process is nonlinear in mean, the tests appear to have low size adjusted power and can lead to the selection of misspecified models. The above deficiencies also hold for tests based on Heteroskedasticity Consistent Covariance Matrix Estimators but not for the Fixed Design Wild Bootstrap. We highlight the importance of robust inference through empirical applications.

Suggested Citation

  • Pavlidis Efthymios G & Paya Ivan & Peel David A, 2010. "Specifying Smooth Transition Regression Models in the Presence of Conditional Heteroskedasticity of Unknown Form," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(3), pages 1-40, May.
    • Handle: RePEc:bpj:sndecm:v:14:y:2010:i:3:n:3
    DOI: 10.2202/1558-3708.1702
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1558-3708.1702
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1558-3708.1702?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. James R. Lothian & Mark P. Taylor, 2008. "Real Exchange Rates Over the Past Two Centuries: How Important is the Harrod‐Balassa‐Samuelson Effect?," Economic Journal, Royal Economic Society, vol. 118(532), pages 1742-1763, October.
    2. Taylor, Nick & Dijk, Dick van & Franses, Philip Hans & Lucas, Andre, 2000. "SETS, arbitrage activity, and stock price dynamics," Journal of Banking & Finance, Elsevier, vol. 24(8), pages 1289-1306, August.
    3. James G. MacKinnon, 2002. "Bootstrap inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 35(4), pages 615-645, November.
    4. Michael, Panos & Nobay, A Robert & Peel, David A, 1997. "Transactions Costs and Nonlinear Adjustment in Real Exchange Rates: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 862-879, August.
    5. 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.
    6. Engel, Charles & Kim, Chang-Jin, 1999. "The Long-Run U.S./U.K. Real Exchange Rate," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 31(3), pages 335-356, August.
    7. Kilian, Lutz & Taylor, Mark P., 2003. "Why is it so difficult to beat the random walk forecast of exchange rates?," Journal of International Economics, Elsevier, vol. 60(1), pages 85-107, May.
    8. Lundbergh, Stefan & Terasvirta, Timo, 2006. "A time series model for an exchange rate in a target zone with applications," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 579-609.
    9. Ivan Paya & Ioannis A. Venetis & David A. Peel, 2003. "Further Evidence on PPP Adjustment Speeds: the Case of Effective Real Exchange Rates and the EMS," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(4), pages 421-437, September.
    10. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    11. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    12. Ivan Paya & David A. Peel, 2005. "A New Analysis Of The Determinants Of The Real Dollar-Sterling Exchange Rate: 1871-1994," Working Papers. Serie AD 2005-16, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    13. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    14. Dwyer, Gerald P, Jr & Locke, Peter R & Yu, Wei, 1996. "Index Arbitrage and Nonlinear Dynamics between the S&P 500 Futures and Cash," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 301-332.
    15. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    16. Skalin, Joakim & Terasvirta, Timo, 1999. "Another Look at Swedish Business Cycles, 1861-1988," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(4), pages 359-378, July-Aug..
    17. Taylor, Mark P & Peel, David A & Sarno, Lucio, 2001. "Nonlinear Mean-Reversion in Real Exchange Rates: Toward a Solution to the Purchasing Power Parity Puzzles," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(4), pages 1015-1042, November.
    18. Lothian, James R & Taylor, Mark P, 1996. "Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 488-509, June.
    19. Blake, Andrew P. & Kapetanios, George, 2007. "Testing for ARCH in the presence of nonlinearity of unknown form in the conditional mean," Journal of Econometrics, Elsevier, vol. 137(2), pages 472-488, April.
    20. Richard T. Baillie & Tim Bollerslev, 1991. "Intra-Day and Inter-Market Volatility in Foreign Exchange Rates," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 565-585.
    21. Eitrheim, Oyvind & Terasvirta, Timo, 1996. "Testing the adequacy of smooth transition autoregressive models," Journal of Econometrics, Elsevier, vol. 74(1), pages 59-75, September.
    22. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    23. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(3), pages 361-376, June.
    24. Godfrey, L.G. & Tremayne, A.R., 2005. "The wild bootstrap and heteroskedasticity-robust tests for serial correlation in dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 377-395, April.
    25. Andrés González & Timo Teräsvirta, 2006. "Simulation‐based Finite Sample Linearity Test against Smooth Transition Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 797-812, December.
    26. Sarno,Lucio & Taylor,Mark P., 2003. "The Economics of Exchange Rates," Cambridge Books, Cambridge University Press, number 9780521485845, September.
    27. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    28. Dumas, Bernard, 1992. "Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World," The Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 153-180.
    29. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    30. Engle, Robert F, 1990. "Stock Volatility and the Crash of '87: Discussion," The Review of Financial Studies, Society for Financial Studies, vol. 3(1), pages 103-106.
    31. Flachaire, Emmanuel, 2005. "Bootstrapping heteroskedastic regression models: wild bootstrap vs. pairs bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 361-376, April.
    32. Blake, Andrew P. & Kapetanios, George, 2007. "Testing for ARCH in the presence of nonlinearity of unknown form in the conditional mean," Journal of Econometrics, Elsevier, vol. 137(2), pages 472-488, April.
    33. Bera, Anil K & Higgins, Matthew L, 1997. "ARCH and Bilinearity as Competing Models for Nonlinear Dependence," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 43-50, January.
    34. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    35. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207.
    36. 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.
    37. Baillie, Richard T & Bollerslev, Tim, 2002. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 60-68, January.
    38. Bera, Anil K & Higgins, Matthew L, 1993. "ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-366, December.
    39. Hsieh, David A., 1992. "A nonlinear stochastic rational expectations model of exchange rates," Journal of International Money and Finance, Elsevier, vol. 11(3), pages 235-250, June.
    40. repec:bla:obuest:v:64:y:2002:i:4:p:315-39 is not listed on IDEAS
    41. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    42. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 669-682.
    43. Robert Engle, 2001. "GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 157-168, Fall.
    44. Philippe J. Deschamps, 2008. "Comparing smooth transition and Markov switching autoregressive models of US unemployment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(4), pages 435-462.
    45. Mussa, Michael, 1986. "Nominal exchange rate regimes and the behavior of real exchange rates: Evidence and implications," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 25(1), pages 117-214, January.
    46. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    47. Clive Granger & Tae-Hwy Lee, 1999. "The effect of aggregation on nonlinearity," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 259-269.
    48. Pradeep K. Yadav & Peter F. Pope & Krishna Paudyal, 1994. "Threshold Autoregressive Modeling In Finance: The Price Differences Of Equivalent Assets1," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 205-221, April.
    49. Marianne Sensier & Denise R. Osborn & Nadir Öcal, 2002. "Asymmetric Interest Rate Effects for the UK Real Economy," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 64(4), pages 315-339, September.
    50. Felix Chan & Michael McAleer, 2002. "Maximum likelihood estimation of STAR and STAR-GARCH models: theory and Monte Carlo evidence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 509-534.
    51. Philippe J. Deschamps, 2008. "Comparing smooth transition and Markov switching autoregressive models of US unemployment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(4), pages 435-462.
    52. Gallagher, Liam A & Taylor, Mark P, 2001. "Risky Arbitrage, Limits of Arbitrage, and Nonlinear Adjustment in the Dividend-Price Ratio," Economic Inquiry, Western Economic Association International, vol. 39(4), pages 524-536, October.
    53. Berka, Martin, 2005. "General Equilibrium Model of Arbitrage Trade and Real Exchange Rate Persistence," MPRA Paper 234, University Library of Munich, Germany.
    54. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    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. Maki, Daiki, 2015. "Wild bootstrap testing for cointegration in an ESTAR error correction model," Economic Modelling, Elsevier, vol. 47(C), pages 292-298.
    2. Daiki Maki & Yasushi Ota, 2019. "Robust tests for ARCH in the presence of the misspecified conditional mean: A comparison of nonparametric approches," Papers 1907.12752, arXiv.org, revised Sep 2019.
    3. Mohamed CHIKHI & Claude DIEBOLT, 2022. "Testing the weak form efficiency of the French ETF market with the LSTAR-ANLSTGARCH approach using a semiparametric estimation," Eastern Journal of European Studies, Centre for European Studies, Alexandru Ioan Cuza University, vol. 13, pages 228-253, June.
    4. Daiki Maki, 2015. "Wild bootstrap tests for unit root in ESTAR models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 475-490, September.
    5. Gabriel Zsurkis & JoÃo Nicolau & Paulo M. M. Rodrigues, 2021. "A Re‐Examination of Inflation Persistence Dynamics in OECD Countries: A New Approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(4), pages 935-959, August.
    6. Daiki Maki & Yasushi Ota, 2019. "Testing for time-varying properties under misspecified conditional mean and variance," Papers 1907.12107, arXiv.org, revised Aug 2019.
    7. Afsin Sahin, 2013. "Estimating Money Demand Function by a Smooth Transition Regression Model: An Evidence for Turkey," Working Papers 791, Economic Research Forum, revised Nov 2013.
    8. Pavlidis Efthymios G. & Paya Ivan & Peel David A., 2013. "Nonlinear causality tests and multivariate conditional heteroskedasticity: a simulation study," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(3), pages 297-312, May.
    9. Mohamed Chikhi & Claude Diebolt, 2019. "Testing Nonlinearity through a Logistic Smooth Transition AR Model with Logistic Smooth Transition GARCH Errors," Working Papers of BETA 2019-06, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    10. Rico Belda, Paz, 2013. "No linealidad y asimetría en el proceso generador del Índice Ibex35/Nonlinearity and Asymmetry in the Generator Process of Ibex35 Index," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 31, pages 555-576, Septiembr.
    11. Efthymios Pavlidis & Ivan Paya & David Peel, 2010. "Further empirical evidence on the consumption-real exchange rate anomaly," Working Papers 447022, Lancaster University Management School, Economics Department.
    12. Daiki Maki & Yasushi Ota, 2021. "Testing for Time-Varying Properties Under Misspecified Conditional Mean and Variance," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1167-1182, April.

    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. repec:lan:wpaper:2454 is not listed on IDEAS
    2. repec:lan:wpaper:2375 is not listed on IDEAS
    3. repec:lan:wpaper:2596 is not listed on IDEAS
    4. repec:lan:wpaper:2373 is not listed on IDEAS
    5. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654.
    6. I Paya & D Peel, 2005. "A new analysis of the determinants of the real dollar-sterling exchange rate: 1871-1994," Working Papers 565953, Lancaster University Management School, Economics Department.
    7. David A. Peel & Ivan Paya, 2006. "Temporal aggregation of an ESTAR process: some implications for purchasing power parity adjustment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 655-668.
    8. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    9. Efthymios Pavlidis & Ivan Paya & David Peel, 2010. "Further empirical evidence on the consumption-real exchange rate anomaly," Working Papers 447022, Lancaster University Management School, Economics Department.
    10. JamesR. Lothian & MarkP. Taylor, 2008. "Real Exchange Rates Over the Past Two Centuries: How Important is the Harrod-Balassa-Samuelson Effect?," Economic Journal, Royal Economic Society, vol. 118(532), pages 1742-1763, October.
    11. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    12. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.
    13. Fredj Jawadi, 2009. "Essay in dividend modelling and forecasting: does nonlinearity help?," Applied Financial Economics, Taylor & Francis Journals, vol. 19(16), pages 1329-1343.
    14. repec:bla:econom:v:72:y:2005:i:3:p:413-430 is not listed on IDEAS
    15. I Paya & D Peel, 2005. "Temporal aggregation of an ESTAR process," Working Papers 565938, Lancaster University Management School, Economics Department.
    16. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    17. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    18. Pavlidis, Efthymios G. & Paya, Ivan & Peel, David A., 2011. "Real exchange rates and time-varying trade costs," Journal of International Money and Finance, Elsevier, vol. 30(6), pages 1157-1179, October.
    19. repec:lan:wpaper:2400 is not listed on IDEAS
    20. Ivan Paya & David Peel, 2005. "The process followed by PPP data. On the properties of linearity tests," Applied Economics, Taylor & Francis Journals, vol. 37(21), pages 2515-2522.
    21. Geoffrey F. Loudon & Wing H. Watt & Pradeep K. Yadav, 2000. "An empirical analysis of alternative parametric ARCH models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 117-136.
    22. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.
    23. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    24. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    25. Wali, Muammer & Chan, Felix & Manzur, Meher, 2017. "Nonlinear dependence in exchange rate returns: How do emerging Asian currencies compare with major currencies?," Journal of Asian Economics, Elsevier, vol. 50(C), pages 62-72.
    26. repec:lan:wpaper:2623 is not listed on IDEAS
    27. repec:lan:wpaper:2402 is not listed on IDEAS
    28. Paya, Ivan & Peel, David A., 2006. "On the speed of adjustment in ESTAR models when allowance is made for bias in estimation," Economics Letters, Elsevier, vol. 90(2), pages 272-277, February.

    More about this item

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    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:bpj:sndecm:v:14:y:2010:i:3:n:3. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.