IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1907.12752.html
   My bibliography  Save this paper

Robust tests for ARCH in the presence of the misspecified conditional mean: A comparison of nonparametric approches

Author

Listed:
  • Daiki Maki
  • Yasushi Ota

Abstract

This study compares statistical properties of ARCH tests that are robust to the presence of the misspecified conditional mean. The approaches employed in this study are based on two nonparametric regressions for the conditional mean. First is the ARCH test using Nadayara-Watson kernel regression. Second is the ARCH test using the polynomial approximation regression. The two approaches do not require specification of the conditional mean and can adapt to various nonlinear models, which are unknown a priori. Accordingly, they are robust to misspecified conditional mean models. Simulation results show that ARCH tests based on the polynomial approximation regression approach have better statistical properties than ARCH tests using Nadayara-Watson kernel regression approach for various nonlinear models.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1907.12752
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1907.12752
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Péguin-Feissolle, Anne & Strikholm, Birgit & Teräsvirta, Timo, 2007. "Testing the Granger noncausality hypothesis in stationary nonlinear models of unknown functional form," SSE/EFI Working Paper Series in Economics and Finance 672, Stockholm School of Economics, revised 18 Jan 2012.
    2. 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.
    3. 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.
    4. Exterkate, Peter & Groenen, Patrick J.F. & Heij, Christiaan & van Dijk, Dick, 2016. "Nonlinear forecasting with many predictors using kernel ridge regression," International Journal of Forecasting, Elsevier, vol. 32(3), pages 736-753.
    5. Lee, John H. H., 1991. "A Lagrange multiplier test for GARCH models," Economics Letters, Elsevier, vol. 37(3), pages 265-271, November.
    6. 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.
    7. Shimizu, Kenichi, 2014. "Bootstrapping the nonparametric ARCH regression model," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 61-69.
    8. 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.
    9. 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.
    10. McMillan, David G., 2001. "Nonlinear predictability of stock market returns: Evidence from nonparametric and threshold models," International Review of Economics & Finance, Elsevier, vol. 10(4), pages 353-368, December.
    11. 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.
    12. Pavlidis, Efthymios G. & Paya, Ivan & Peel, David A., 2015. "Testing for linear and nonlinear Granger causality in the real exchange rate–consumption relation," Economics Letters, Elsevier, vol. 132(C), pages 13-17.
    13. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.
    14. 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.
    15. 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.
    16. 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)

    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, 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.
    2. Daiki Maki & Yasushi Ota, 2019. "Testing for time-varying properties under misspecified conditional mean and variance," Papers 1907.12107, arXiv.org, revised Aug 2019.
    3. Wasel Shadat, 2011. "On the Nonparametric Tests of Univariate GARCH Regression Models," Economics Discussion Paper Series 1115, Economics, The University of Manchester.
    4. E. Ruiz & M.A. Carnero & D. Pereira, 2004. "Effects of Level Outliers on the Identification and Estimation of GARCH Models," Econometric Society 2004 Australasian Meetings 21, Econometric Society.
    5. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911, November.
    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, January.
    8. Anatolyev, Stanislav & Tarasyuk, Irina, 2015. "Missing mean does no harm to volatility!," Economics Letters, Elsevier, vol. 134(C), pages 62-64.
    9. 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.
    10. Franses, Ph.H.B.F. & van Dijk, D.J.C., 1997. "Do We Often Find ARCH Because Of Neglected Outliers?," Econometric Institute Research Papers EI 9706-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Kyrtsou, Catherine, 2008. "Re-examining the sources of heteroskedasticity: The paradigm of noisy chaotic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6785-6789.
    12. Maki, Daiki, 2015. "Wild bootstrap testing for cointegration in an ESTAR error correction model," Economic Modelling, Elsevier, vol. 47(C), pages 292-298.
    13. Carnero, María Ángeles, 2001. "Outliers and conditional autoregressive heteroscedasticity in time series," DES - Working Papers. Statistics and Econometrics. WS ws010704, Universidad Carlos III de Madrid. Departamento de Estadística.
    14. 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.
    15. Grossi, Luigi & Laurini, Fabrizio, 2009. "A robust forward weighted Lagrange multiplier test for conditional heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2251-2263, April.
    16. Carlos Escanciano, J., 2008. "Joint and marginal specification tests for conditional mean and variance models," Journal of Econometrics, Elsevier, vol. 143(1), pages 74-87, March.
    17. Arouri, Mohamed El Hedi & Hammoudeh, Shawkat & Lahiani, Amine & Nguyen, Duc Khuong, 2013. "On the short- and long-run efficiency of energy and precious metal markets," Energy Economics, Elsevier, vol. 40(C), pages 832-844.
    18. Philip Hans Franses & Dick van Dijk & Andre Lucas, 2004. "Short patches of outliers, ARCH and volatility modelling," Applied Financial Economics, Taylor & Francis Journals, vol. 14(4), pages 221-231.
    19. Duchesne, Pierre, 2004. "On robust testing for conditional heteroscedasticity in time series models," Computational Statistics & Data Analysis, Elsevier, vol. 46(2), pages 227-256, June.
    20. 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.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1907.12752. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.