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Modelling good and bad volatility


  • Matteo Pelagatti


The returns of many financial assets show significant skewness, but in the literature this issue is only marginally dealt with. Our conjecture is that this distributional asymmetry may be due to two different dynamics in positive and negative returns. In this paper we propose a process that allows the simultaneous modelling of skewed conditional returns and different dynamics in their conditional second moments. The main stochastic properties of the model are analyzed and necessary and sufficient conditions for weak and strict stationarity are derived. An application to the daily returns on the principal index of the London Stock Exchange supports our model when compared to other frequently used GARCH-type models, which are nested into ours.

Suggested Citation

  • Matteo Pelagatti, 2007. "Modelling good and bad volatility," Working Papers 20071101, Università degli Studi di Milano-Bicocca, Dipartimento di Statistica.
  • Handle: RePEc:mis:wpaper:20071101

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    References listed on IDEAS

    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Pentti Saikkonen & Markku Lanne, 2004. "A Skewed GARCH-in-Mean Model: An Application to U.S. Stock Returns," Econometric Society 2004 North American Summer Meetings 469, Econometric Society.
    3. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December.
    4. Stelios Arvanitis & Antonis Demos, 2004. "Time Dependence and Moments of a Family of Time-Varying Parameter Garch in Mean Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 1-25, January.
    5. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    6. Luc Bauwens & Sébastien Laurent, 2002. "A New Class of Multivariate skew Densities, with Application to GARCH Models," Computing in Economics and Finance 2002 5, Society for Computational Economics.
    7. Francesco Lisi, 2007. "Testing asymmetry in financial time series," Quantitative Finance, Taylor & Francis Journals, vol. 7(6), pages 687-696.
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    Cited by:

    1. 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.
    2. Tseng, Jie-Jun & Li, Sai-Ping, 2011. "Asset returns and volatility clustering in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(7), pages 1300-1314.
    3. Tseng, Jie-Jun & Li, Sai-Ping, 2012. "Quantifying volatility clustering in financial time series," International Review of Financial Analysis, Elsevier, vol. 23(C), pages 11-19.
    4. Geon Ho Choe & Kyungsub Lee, 2013. "Conditional correlation in asset return and GARCH intensity model," Papers 1311.4977,
    5. Geon Choe & Kyungsub Lee, 2014. "Conditional correlation in asset return and GARCH intensity model," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 197-224, July.

    More about this item


    Volatility; Skewness; GARCH; Asymmetric Dynamics; Stationarity;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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