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Parameterizing Unconditional Skewness in Models for Financial Time Series

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Author Info

  • Changli He

    (Department of Economic Statistics, Stokholm School of Economic)

  • Annastiina Silvennoinen

    (School of Economics and Finance, Queensland University of Technology)

  • Timo Teräsvirta

    (Department of Economic Statistics, Stokholm School of Economic)

Abstract

In this paper we consider the third-moment structure of a class of nonlinear time series models. Empirically it is often found that the marginal distribution of financial time series is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate for unconditional skewness. We consider modelling the unconditional mean and variance using models which respond nonlinearly or asymmetrically to shocks. We investigate the implications these models have on the third moment structure of the marginal distribution and different conditions under which the unconditional distribution exhibits skewness as well as nonzero third-order autocovariance structure. With this respect, the 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 are provided for all third order moments and cross-moments. Finally, we introduce a new tool, shock impact curve, that can be used to investigate the impact of shocks on the conditional mean squared error of the return.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp169.pdf
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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 169.

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Length: 22
Date of creation: 01 Oct 2005
Date of revision:
Handle: RePEc:uts:rpaper:169

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Keywords: asymmetry; GARCH; nonlinearity; stock impact curve; time series; unconditional skewness;

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  1. He, Changli & Ter svirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(06), pages 824-846, December.
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Citations

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Cited by:
  1. Teräsvirta, Timo, 2006. "An introduction to univariate GARCH models," Working Paper Series in Economics and Finance 646, Stockholm School of Economics.
  2. Jeroen Rombouts & Lars Peter Stentoft, 2009. "Bayesian Option Pricing Using Mixed Normal Heteroskedasticity Models," CIRANO Working Papers 2009s-19, CIRANO.
  3. Bent Jesper Christensen & Morten Ørregaard Nielsen & Jie Zhu, 2012. "The impact of financial crises on the risk-return tradeoff and the leverage effect," CREATES Research Papers 2012-19, School of Economics and Management, University of Aarhus.
  4. 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.
  5. 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.
  6. 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.
  7. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," CORE Discussion Papers 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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