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Estimating ARCH Models when the Coefficients are Allowed to be Equal to Zero

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  • Christian Francq

    (Crest)

  • Jean-Michel Zakoïan

    (Crest)

Abstract

In order to be consistent with volatility processes, the autoregressiveconditional heteroskedastic (ARCH) models are constrained to havenon-negative coefficients. The estimators incorporating these constraints possessnon standard asymptotic distributions when the true parameter has zerocoefficients. This situation, where the parameter is on the boundary of theparameter space, must be considered to derive the critical values of tests thatone or several ARCH coefficients are equal to zero. In this paper we comparethe asymptotic theoretical properties, as well as the finite sample behavior, ofthe main estimation methods in this framework.

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  • Christian Francq & Jean-Michel Zakoïan, 2008. "Estimating ARCH Models when the Coefficients are Allowed to be Equal to Zero," Working Papers 2008-07, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2008-07
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    References listed on IDEAS

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    1. Søren Tolver Jensen & Anders Rahbek, 2004. "Asymptotic Normality of the QMLE Estimator of ARCH in the Nonstationary Case," Econometrica, Econometric Society, vol. 72(2), pages 641-646, March.
    2. Arup Bose & Kanchan Mukherjee, 2003. "Estimating The Arch Parameters By Solving Linear Equations," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 127-136, March.
    3. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    4. Francq, Christian & Zakoian, Jean-Michel, 2007. "Quasi-maximum likelihood estimation in GARCH processes when some coefficients are equal to zero," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1265-1284, September.
    5. Iglesias, Emma M. & Linton, Oliver B., 2007. "Higher Order Asymptotic Theory When A Parameter Is On A Boundary With An Application To Garch Models," Econometric Theory, Cambridge University Press, vol. 23(6), pages 1136-1161, December.
    6. 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.
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    Cited by:

    1. Lionel Truquet, 2017. "Parameter stability and semiparametric inference in time varying auto-regressive conditional heteroscedasticity models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1391-1414, November.

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