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Testing for ARCH in the presence of nonlinearity of unknown form in the conditional mean

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  • Blake, Andrew P.
  • Kapetanios, George

Abstract

Tests of ARCH are a routine diagnostic in empirical econometric and financial analysis. However, it is well known that misspecification of the conditional mean may lead to spurious rejections of the null hypothesis of no ARCH. Nonlinearity is a prime example of this phenomenon. There is little work on the extent of the effect of neglected nonlinearity on the properties of ARCH tests. This paper provides some such evidence and also new ARCH testing procedures that are robust to the presence of neglected nonlinearity. Monte Carlo evidence shows that the problem is serious and that the new methods alleviate this problem to a very large extent.
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Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:137:y:2007:i:2:p:472-488
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    Cited by:

    1. 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.
    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. 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.
    4. Kanazawa, Nobuyuki, 2020. "Radial basis functions neural networks for nonlinear time series analysis and time-varying effects of supply shocks," Journal of Macroeconomics, Elsevier, vol. 64(C).
    5. Meher Manzur, 2018. "Exchange rate economics is always and everywhere controversial," Applied Economics, Taylor & Francis Journals, vol. 50(3), pages 216-232, January.
    6. 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.
    7. Wasel Shadat, 2011. "On the Nonparametric Tests of Univariate GARCH Regression Models," Economics Discussion Paper Series 1115, Economics, The University of Manchester.
    8. Erdenebat Bataa & Andrew Vivian & Mark Wohar, 2019. "Changes in the relationship between short‐term interest rate, inflation and growth: evidence from the UK, 1820–2014," Bulletin of Economic Research, Wiley Blackwell, vol. 71(4), pages 616-640, October.
    9. Martin Vance L. & Sarkar Saikat & Kanto Antti Jaakko, 2014. "Modelling nonlinearities in equity returns: the mean impact curve analysis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(1), pages 51-72, February.
    10. repec:lan:wpaper:2454 is not listed on IDEAS
    11. repec:lan:wpaper:2375 is not listed on IDEAS
    12. 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.
    13. Sitzia, Bruno & Iovino, Doriana, 2008. "Nonlinearities in Exchange rates: Double EGARCH Threshold Models for Forecasting Volatility," MPRA Paper 8661, University Library of Munich, Germany.
    14. Richard Ashley, 2012. "On the Origins of Conditional Heteroscedasticity in Time Series," Korean Economic Review, Korean Economic Association, vol. 28, pages 5-25.
    15. repec:lan:wpaper:2596 is not listed on IDEAS
    16. repec:lan:wpaper:2373 is not listed on IDEAS
    17. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "Some thoughts on accurate characterization of stock market indexes trends in conditions of nonlinear capital flows during electronic trading at stock exchanges in global capital markets," MPRA Paper 49921, University Library of Munich, Germany.
    18. Anatolyev, Stanislav & Tarasyuk, Irina, 2015. "Missing mean does no harm to volatility!," Economics Letters, Elsevier, vol. 134(C), pages 62-64.
    19. Daiki Maki & Yasushi Ota, 2019. "Testing for time-varying properties under misspecified conditional mean and variance," Papers 1907.12107, arXiv.org, revised Aug 2019.
    20. 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.
    21. Lee Jinu, 2019. "A Neural Network Method for Nonlinear Time Series Analysis," Journal of Time Series Econometrics, De Gruyter, vol. 11(1), pages 1-18, January.
    22. 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.
    23. Sadek Melhem & Mahmoud Melhem, 2012. "Comments on “Re-examining the source of Heteroskedasticity: The paradigm of noisy chaotic models”," Working Papers 12-13, LAMETA, Universtiy of Montpellier, revised Apr 2012.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics

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