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Estimation and Inference in ARCH Models in the Presence of Outliers


  • Allan W. Gregory
  • Jonathan J. Reeves


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:, Oxford University Press.

Suggested Citation

  • Allan W. Gregory & Jonathan J. Reeves, 2010. "Estimation and Inference in ARCH Models in the Presence of Outliers," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 8(4), pages 547-549, Fall.
  • Handle: RePEc:oup:jfinec:v:8:y:2010:i:4:p:547-549

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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. Amado Peiró, 2016. "Changes in the Unconditional Variance and Autoregressive Conditional Heteroscedasticity," International Journal of Economics and Financial Issues, Econjournals, vol. 6(4), pages 1338-1343.
    3. Carnero, María Ángeles & Peña, Daniel & Ruiz, Esther, 2004. "Spurious and hidden volatility," DES - Working Papers. Statistics and Econometrics. WS ws042007, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Escribano, Alvaro & Sucarrat, Genaro, 2016. "Equation-by-Equation Estimation of Multivariate Periodic Electricity Price Volatility," MPRA Paper 72736, University Library of Munich, Germany.
    5. 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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