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The power log-GARCH model

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  • Genaro Sucarrat

    ()

  • Alvaro Escribano

Abstract

Exponential models of autoregressive conditional heteroscedasticity (ARCH) are attractive in empirical analysis because they guarantee the non-negativity of volatility, and because they enable richer autoregressive dynamics. However, the currently available models exhibit stability only for a limited number of conditional densities, and the available estimation and inference methods in the case where the conditional density is unknown hold only under very specific and restrictive assumptions. Here, we provide results and simple methods that readily enables consistent estimation and inference of univariate and multivariate power log-GARCH models under very general and non-restrictive assumptions when the power is fixed, via vector ARMA representations. Additionally, stability conditions are obtained under weak assumptions, and the power log-GARCH model can be viewed as nesting certain classes of stochastic volatility models, including the common ASV(1) specification. Finally, our simulations and empirical applications suggest the model class is very useful in practice.

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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we1013.

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Date of creation: Jun 2010
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Handle: RePEc:cte:werepe:we1013

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Keywords: Power ARCH; Exponential GARCH; Log-GARCH; Multivariate GARCH; Stochastic volatility;

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Citations

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Cited by:
  1. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2013. "Estimation and Inference in Univariate and Multivariate Log-GARCH-X Models When the Conditional Density is Unknown," MPRA Paper 49344, University Library of Munich, Germany.
  2. Francq, Christian & Wintenberger, Olivier & Zakoïan, Jean-Michel, 2013. "GARCH models without positivity constraints: Exponential or log GARCH?," Journal of Econometrics, Elsevier, Elsevier, vol. 177(1), pages 34-46.
  3. Alvaro Escribano & Genaro Sucarrat, 2011. "Automated model selection in finance: General-to-speci c modelling of the mean and volatility speci cations," Working Papers, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales 2011-09, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  4. Smith, Geoffrey Peter, 2012. "Google Internet search activity and volatility prediction in the market for foreign currency," Finance Research Letters, Elsevier, Elsevier, vol. 9(2), pages 103-110.
  5. Wintenberger, Olivier, 2013. "Continuous invertibility and stable QML estimation of the EGARCH(1,1) model," MPRA Paper 46027, University Library of Munich, Germany.

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