IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v57y2021i4d10.1007_s10614-020-10014-4.html
   My bibliography  Save this article

Testing for Time-Varying Properties Under Misspecified Conditional Mean and Variance

Author

Listed:
  • Daiki Maki

    (Doshisha University)

  • Yasushi Ota

    (Okayama University of Science)

Abstract

This study examines statistical performance of tests for time-varying properties under misspecified conditional mean and variance. When time-varying properties of the conditional mean are tested in the case in which data have no time-varying mean but have time-varying variance, asymptotic tests have size distortions. The distortions are minimized by the use of a bootstrap method. Similarly, when time-varying properties of the conditional variance are tested in the case in which data have time-varying mean but no time-varying variance, asymptotic tests have large size distortions. The distortions are not improved even by the use of bootstrap methods. We show that tests for time-varying properties of the conditional mean by the bootstrap are robust regardless of the time-varying variance model, whereas tests for time-varying properties of the conditional variance do not perform well in the presence of misspecified time-varying mean.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:compec:v:57:y:2021:i:4:d:10.1007_s10614-020-10014-4
    DOI: 10.1007/s10614-020-10014-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-020-10014-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-020-10014-4?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 search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Zhou Zhou, 2013. "Heteroscedasticity and Autocorrelation Robust Structural Change Detection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 726-740, June.
    3. Lumsdaine, Robin L. & Ng, Serena, 1999. "Testing for ARCH in the presence of a possibly misspecified conditional mean," Journal of Econometrics, Elsevier, vol. 93(2), pages 257-279, December.
    4. Boldea, Otilia & Cornea-Madeira, Adriana & Hall, Alastair R., 2019. "Bootstrapping structural change tests," Journal of Econometrics, Elsevier, vol. 213(2), pages 359-397.
    5. Pierre Perron & Yohei Yamamoto, 2019. "Pitfalls of Two-Step Testing for Changes in the Error Variance and Coefficients of a Linear Regression Model," Econometrics, MDPI, vol. 7(2), pages 1-11, May.
    6. Jean-Yves Pitarakis, 2004. "Least squares estimation and tests of breaks in mean and variance under misspecification," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 32-54, June.
    7. Amado, Cristina & Teräsvirta, Timo, 2013. "Modelling volatility by variance decomposition," Journal of Econometrics, Elsevier, vol. 175(2), pages 142-153.
    8. van Dijk, Dick & Franses, Philip Hans & Lucas, Andre, 1999. "Testing for ARCH in the Presence of Additive Outliers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 539-562, Sept.-Oct.
    9. Lundbergh, Stefan & Terasvirta, Timo & van Dijk, Dick, 2003. "Time-Varying Smooth Transition Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 104-121, January.
    10. Van Dijk, Dick & Franses, Philip Hans & Lucas, Andre, 1999. "Testing for Smooth Transition Nonlinearity in the Presence of Outliers," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(2), pages 217-235, April.
    11. 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.
    12. Matthew T. Holt & Joseph V. Balagtas, 2009. "Estimating Structural Change with Smooth Transition Regressions: An Application to Meat Demand," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(5), pages 1424-1431.
    13. Catani, P.S. & Ahlgren, N.J.C., 2017. "Combined Lagrange multiplier test for ARCH in vector autoregressive models," Econometrics and Statistics, Elsevier, vol. 1(C), pages 62-84.
    14. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    15. Stan Hurn & Ralf Becker, 2009. "Testing for Nonlinearity in Mean in the Presence of Heteroskedasticity," Economic Analysis and Policy, Elsevier, vol. 39(2), pages 311-326, September.
    16. 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.
    17. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    18. 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.
    19. 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.
    20. Kim, Kun Ho & Kim, Taejin, 2016. "Capital asset pricing model: A time-varying volatility approach," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 268-281.
    21. Donald W. K. Andrews & Moshe Buchinsky, 2000. "A Three-Step Method for Choosing the Number of Bootstrap Repetitions," Econometrica, Econometric Society, vol. 68(1), pages 23-52, January.
    22. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, vol. 62(2), pages 211-228, June.
    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. Yanglin Li, 2024. "New Unit Root Tests in the Nonlinear ESTAR Framework: The Movement and Volatility Characteristics of Crude oil and Copper Prices," Computational Economics, Springer;Society for Computational Economics, vol. 63(5), pages 1757-1776, May.

    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. Daiki Maki & Yasushi Ota, 2019. "Testing for time-varying properties under misspecified conditional mean and variance," Papers 1907.12107, arXiv.org, revised Aug 2019.
    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. Maki, Daiki, 2015. "Wild bootstrap testing for cointegration in an ESTAR error correction model," Economic Modelling, Elsevier, vol. 47(C), pages 292-298.
    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. Wasel Shadat, 2011. "On the Nonparametric Tests of Univariate GARCH Regression Models," Economics Discussion Paper Series 1115, Economics, The University of Manchester.
    6. 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.
    7. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, September.
    8. Cavaliere, Giuseppe & Nielsen, Morten Ørregaard & Taylor, A.M. Robert, 2015. "Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets," Journal of Econometrics, Elsevier, vol. 187(2), pages 557-579.
    9. Pierre Perron & Yohei Yamamoto, 2022. "Structural change tests under heteroskedasticity: Joint estimation versus two‐steps methods," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 389-411, May.
    10. Michael Funke & Marc Gronwald, 2008. "The Undisclosed Renminbi Basket: Are the Markets Telling Us Something about Where the Renminbi–US Dollar Exchange Rate is Going?," The World Economy, Wiley Blackwell, vol. 31(12), pages 1581-1598, December.
    11. Emmanuel Flachaire, 2000. "Les méthodes du bootstrap dans les modèles de régression," Économie et Prévision, Programme National Persée, vol. 142(1), pages 183-194.
    12. 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.
    13. Joseph V. Balagtas & Matthew T. Holt, 2009. "The Commodity Terms of Trade, Unit Roots, and Nonlinear Alternatives: A Smooth Transition Approach," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(1), pages 87-105.
    14. Balagtas, Joseph Valdes & Holt, Matthew T., 2006. "Unit Roots, TV-STARs, and the Commodity Terms of Trade: A Further Assessment of the Prebisch-Singer Hypothesis," 2006 Annual meeting, July 23-26, Long Beach, CA 21405, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    15. Sandberg, Rickard, 2016. "Trends, unit roots, structural changes, and time-varying asymmetries in U.S. macroeconomic data: the Stock and Watson data re-examined," Economic Modelling, Elsevier, vol. 52(PB), pages 699-713.
    16. Giordani, Paolo & Kohn, Robert & van Dijk, Dick, 2007. "A unified approach to nonlinearity, structural change, and outliers," Journal of Econometrics, Elsevier, vol. 137(1), pages 112-133, March.
    17. Emmanuel Flachaire, 2005. "More Efficient Tests Robust to Heteroskedasticity of Unknown Form," Econometric Reviews, Taylor & Francis Journals, vol. 24(2), pages 219-241.
    18. MacKinnon, James G. & Nielsen, Morten Ørregaard & Webb, Matthew D., 2023. "Cluster-robust inference: A guide to empirical practice," Journal of Econometrics, Elsevier, vol. 232(2), pages 272-299.
    19. 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.
    20. 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.

    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:kap:compec:v:57:y:2021:i:4:d:10.1007_s10614-020-10014-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.