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Parameterizing unconditional skewness in models for financial time series

Changli He, Annastiina Silvennoinen and Timo Teräsvirta ()

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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.

Keywords: Asymmetry; GARCH; Nonlinearity; Shock Impact Curve; Time series; Unconditional skewness (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ets
Date: 2008-01-28
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Journal Article: Parameterizing Unconditional Skewness in Models for Financial Time Series (2008) Downloads
Working Paper: Parameterizing Unconditional Skewness in Models for Financial Time Series (2005) Downloads
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