Parameterizing Unconditional Skewness in Models for Financial Time Series

Changli He, Annastiina Silvennoinen and Timo Teräsvirta
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Changli He: Department of Economic Statistics, Stokholm School of Economic

No 169, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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.

Keywords: asymmetry; GARCH; nonlinearity; stock impact curve; time series; unconditional skewness (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2005-10-01
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (6)

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.

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https://www.uts.edu.au/sites/default/files/qfr-archive-02/QFR-rp169.pdf (application/pdf)

Related works:
Journal Article: Parameterizing Unconditional Skewness in Models for Financial Time Series (2008)
Working Paper: Parameterizing unconditional skewness in models for financial time series (2008)
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