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Parameterizing unconditional skewness in models for financial time series

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  • Changli He
  • Annastiina Silvennoinen
  • Timo Teräsvirta

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

In this paper we consider the third-moment structure of a class of time series models. It is often argued that the marginal distribution of financial time series such as returns is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate unconditional skewness. We consider modelling the unconditional mean and variance using models that respond nonlinearly or asymmetrically to shocks. We investigate the implications of these models on the third-moment structure of the marginal distribution as well as conditions under which the unconditional distribution exhibits skewness and nonzero third-order autocovariance structure. In this respect, an asymmetric or nonlinear specification of the conditional mean is found to be of greater importance than the properties of the conditional variance. Several examples are discussed and, whenever possible, explicit analytical expressions provided for all third-order moments and cross-moments. Finally, we introduce a new tool, the shock impact curve, for investigating the impact of shocks on the conditional mean squared error of return series.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-07.

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Length: 22
Date of creation: 28 Jan 2008
Date of revision:
Handle: RePEc:aah:create:2008-07

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Asymmetry; GARCH; Nonlinearity; Shock Impact Curve; Time series; Unconditional skewness;

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References

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Citations

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Cited by:
  1. Christensen, Bent Jesper & Nielsen, Morten Ørregaard & Zhu, Jie, 2010. "Long memory in stock market volatility and the volatility-in-mean effect: The FIEGARCH-M Model," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 460-470, June.
  2. Jeroen V.K. Rombouts & Lars Stentoft, 2009. "Bayesian Option Pricing Using Mixed Normal Heteroskedasticity Models," Cahiers de recherche 0926, CIRPEE.
  3. Bent Jesper Christensen & Morten Ørregaard Nielsen & Jie Zhu, 2012. "The impact of financial crises on the risk-return tradeoff and the leverage effect," Working Papers 1295, Queen's University, Department of Economics.
  4. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," CORE Discussion Papers 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. María José Rodríguez & Esther Ruiz, 2009. "GARCH models with leverage effect : differences and similarities," Statistics and Econometrics Working Papers ws090302, Universidad Carlos III, Departamento de Estadística y Econometría.
  6. Teräsvirta, Timo, 2006. "An introduction to univariate GARCH models," Working Paper Series in Economics and Finance 646, Stockholm School of Economics.
  7. Maria Rosa Nieto & Esther Ruiz, 2008. "Measuring financial risk : comparison of alternative procedures to estimate VaR and ES," Statistics and Econometrics Working Papers ws087326, Universidad Carlos III, Departamento de Estadística y Econometría.

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