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Parameterizing Unconditional Skewness in Models for Financial Time Series

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  • Changli He
  • Annastiina Silvennoinen
  • Timo Teräsvirta

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 modeling 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. Copyright The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org., Oxford University Press.

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  • Changli He & Annastiina Silvennoinen & Timo Teräsvirta, 2008. "Parameterizing Unconditional Skewness in Models for Financial Time Series," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(2), pages 208-230, Spring.
  • Handle: RePEc:oup:jfinec:v:6:y:2008:i:2:p:208-230
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    2. Rombouts, Jeroen V.K. & Stentoft, Lars, 2014. "Bayesian option pricing using mixed normal heteroskedasticity models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 588-605.
    3. Constantin ANGHELACHE & Janusz GRABARA & Alexandru MANOLE, 2016. "Using the Dynamic Model ARMA to Forecast the Macroeconomic Evolution," Romanian Statistical Review Supplement, Romanian Statistical Review, vol. 64(1), pages 3-13, January.
    4. Christensen, Bent Jesper & Nielsen, Morten Ørregaard & Zhu, Jie, 2015. "The impact of financial crises on the risk–return tradeoff and the leverage effect," Economic Modelling, Elsevier, vol. 49(C), pages 407-418.
    5. Timo Terasvirta & Zhenfang Zhao, 2011. "Stylized facts of return series, robust estimates and three popular models of volatility," Applied Financial Economics, Taylor & Francis Journals, vol. 21(1-2), pages 67-94.
    6. Christensen, Bent Jesper & Nielsen, Morten Ørregaard & Zhu, Jie, 2010. "Long memory in stock market volatility and the volatility-in-mean effect: The FIEGARCH-M Model," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 460-470, June.
    7. Linton, Oliver & Wu, Jianbin, 2020. "A coupled component DCS-EGARCH model for intraday and overnight volatility," Journal of Econometrics, Elsevier, vol. 217(1), pages 176-201.
    8. Dahiru A. Balaa & Taro Takimotob, 2017. "Stock markets volatility spillovers during financial crises: A DCC-MGARCH with skewed-t density approach," Borsa Istanbul Review, Research and Business Development Department, Borsa Istanbul, vol. 17(1), pages 25-48, March.
    9. Wen-Jun Xue & Li-Wen Zhang, 2016. "Stock Return Autocorrelations and Predictability in the Chinese Stock Market: Evidence from Threshold Quantile Autoregressive Models," Working Papers 1605, Florida International University, Department of Economics.
    10. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Carnero M. Angeles & Pérez Ana, 2021. "Outliers and misleading leverage effect in asymmetric GARCH-type models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(1), pages 1-19, February.
    12. María José Rodríguez & Esther Ruiz, 2012. "Revisiting Several Popular GARCH Models with Leverage Effect: Differences and Similarities," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(4), pages 637-668, September.
    13. Haas Markus, 2010. "Skew-Normal Mixture and Markov-Switching GARCH Processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-56, September.
    14. Syriopoulos, Theodore & Makram, Beljid & Boubaker, Adel, 2015. "Stock market volatility spillovers and portfolio hedging: BRICS and the financial crisis," International Review of Financial Analysis, Elsevier, vol. 39(C), pages 7-18.
    15. Ruiz, Esther & Rodríguez, Mª José, 2009. "GARCH models with leverage effect : differences and similarities," DES - Working Papers. Statistics and Econometrics. WS ws090302, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Teräsvirta, Timo, 2006. "An introduction to univariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 646, Stockholm School of Economics.
    17. Ruiz, Esther & Nieto, María Rosa, 2008. "Measuring financial risk : comparison of alternative procedures to estimate VaR and ES," DES - Working Papers. Statistics and Econometrics. WS ws087326, Universidad Carlos III de Madrid. Departamento de Estadística.
    18. Carnero, M. Angeles & Pérez, Ana, 2019. "Leverage effect in energy futures revisited," Energy Economics, Elsevier, vol. 82(C), pages 237-252.
    19. Morema, Kgotso & Bonga-Bonga, Lumengo, 2018. "The impact of oil and gold price fluctuations on the South African equity market: volatility spillovers and implications for portfolio management," MPRA Paper 87637, University Library of Munich, Germany.
    20. José‐María Montero & Gema Fernández‐Avilés & María‐Carmen García, 2010. "Estimation of Asymmetric Stochastic Volatility Models: Application to Daily Average Prices of Energy Products," International Statistical Review, International Statistical Institute, vol. 78(3), pages 330-347, December.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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