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Parameterizing unconditional skewness in models for financial time series

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Author Info
Changli He
Annastiina Silvennoinen
Timo Teräsvirta () (School of Economics and Management, University of Aarhus, Denmark and CREATES)

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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.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-07.

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Length: 22
Date of creation: 28 Jan 2008
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Handle: RePEc:aah:create:2008-07

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Related research
Keywords: Asymmetry; GARCH; Nonlinearity; Shock Impact Curve; Time series; Unconditional skewness;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Jeroen Rombouts & Lars Peter Stentoft, 2009. "Bayesian Option Pricing Using Mixed Normal Heteroskedasticity Models," CIRANO Working Papers 2009s-19, CIRANO. [Downloadable!]
    Other versions:
  2. Teräsvirta, Timo, 2006. "An introduction to univariate GARCH models," Working Paper Series in Economics and Finance 646, Stockholm School of Economics. [Downloadable!]
  3. 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. [Downloadable!]
  4. 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. [Downloadable!]
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