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Estimation and Inference in ARCH Models in the Presence of Outliers

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  • Allan W. Gregory
  • Jonathan J. Reeves

Abstract

In this paper, we show the effects that outliers have on estimation and inference for autoregressive conditional heteroskedasticity (ARCH) models. We propose for a wide class of ARCH models commonly estimated, an empirically tractable solution to this problem by replacing outliers with their conditional expectations (optimal forecasts) in the likelihood function. This solution works well in both simulations and applications, as opposed to dummy variables which can lead to multimodality in the ARCH likelihood and invalid inference. We demonstrate the accuracy of our procedure for parameter estimation and forecasting. The empirical examples include U.S. interest rate, foreign exchange rate, and stock index data. In addition, we suggest a robust bootstrap test for outliers and evaluate this against the Andrews (2003) S test. Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

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  • Allan W. Gregory & Jonathan J. Reeves, 2010. "Estimation and Inference in ARCH Models in the Presence of Outliers," Journal of Financial Econometrics, Oxford University Press, vol. 8(4), pages 547-549, Fall.
    • Handle: RePEc:oup:jfinec:v:8:y:2010:i:4:p:547-549
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbq028
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    Cited by:

    1. Frédérick Demers & Annie De Champlain, 2005. "Forecasting Core Inflation in Canada: Should We Forecast the Aggregate or the Components?," Staff Working Papers 05-44, Bank of Canada.
    2. M. Angeles Carnero & Daniel Peña & Esther Ruiz, 2004. "Spurious And Hidden Volatility," Working Papers. Serie AD 2004-45, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    3. Piotr Fiszeder & Marta Ma³ecka, 2022. "Forecasting volatility during the outbreak of Russian invasion of Ukraine: application to commodities, stock indices, currencies, and cryptocurrencies," Equilibrium. Quarterly Journal of Economics and Economic Policy, Institute of Economic Research, vol. 17(4), pages 939-967, December.
    4. Escribano, Alvaro & Sucarrat, Genaro, 2018. "Equation-by-equation estimation of multivariate periodic electricity price volatility," Energy Economics, Elsevier, vol. 74(C), pages 287-298.
    5. Doan, Bao & Papageorgiou, Nicolas & Reeves, Jonathan J. & Sherris, Michael, 2018. "Portfolio management with targeted constant market volatility," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 134-147.
    6. Amado Peir, 2016. "Changes in the Unconditional Variance and Autoregressive Conditional Heteroscedasticity," International Journal of Economics and Financial Issues, Econjournals, vol. 6(4), pages 1338-1343.
    7. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723, September.
    8. Carnero, M. Angeles & Peña, Daniel & Ruiz, Esther, 2012. "Estimating GARCH volatility in the presence of outliers," Economics Letters, Elsevier, vol. 114(1), pages 86-90.

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