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Parameterizing Unconditional Skewness in Models for Financial Time Series

  • 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)

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.qfrc.uts.edu.au/research/research_papers/rp169.pdf
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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 pages
Date of creation: 01 Oct 2005
Date of revision:
Publication status: Published as: He, C., Silvennoinen, A. and Teräsvirta, T., 2008, "Parameterizing Unconditional Skewness in Models for Financial Time Series", Journal of Financial Econometrics, 6(2), 208-230.
Handle: RePEc:uts:rpaper:169
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