Department of Economics and Business Economics

Parameterizing unconditional skewness in models for financial time series

Research output: Working paperResearch

  • Changli He, South Western University of Finance and Economics, China
  • Annastiina Silvennoinen, University of Technology Sydney, Australia
  • Timo Teräsvirta
  • School of Economics and Management
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.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages22
Publication statusPublished - 2008

    Research areas

  • Asymmetry; GARCH; Nonlinearity; Shock Impact Curve; Time series; Unconditional

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