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Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes

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  • Griffin, J.E.
  • Steel, M.F.J.

Abstract

Continuous superpositions of Ornstein-Uhlenbeck processes are proposed as a model for asset return volatility. An interesting class of continuous superpositions is defined by a Gamma mixing distribution which can define long memory processes. In contrast, previously studied discrete superpositions cannot generate this behaviour. Efficient Markov chain Monte Carlo methods for Bayesian inference are developed which allow the estimation of such models with leverage effects. The continuous superposition model is applied to both stock index and exchange rate data. The continuous superposition model is compared with a two-component superposition on the daily Standard and Poor's 500 index from 1980 to 2000.

Suggested Citation

  • Griffin, J.E. & Steel, M.F.J., 2010. "Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2594-2608, November.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:11:p:2594-2608
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    Cited by:

    1. Zhongxian Men & Tony S. Wirjanto & Adam W. Kolkiewicz, 2021. "Multiscale Stochastic Volatility Model with Heavy Tails and Leverage Effects," JRFM, MDPI, vol. 14(5), pages 1-28, May.
    2. Taufer, Emanuele & Leonenko, Nikolai & Bee, Marco, 2011. "Characteristic function estimation of Ornstein-Uhlenbeck-based stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2525-2539, August.
    3. Raknerud, Arvid & Skare, Øivind, 2012. "Indirect inference methods for stochastic volatility models based on non-Gaussian Ornstein–Uhlenbeck processes," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3260-3275.
    4. Szczepocki Piotr, 2020. "Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process," Statistics in Transition New Series, Statistics Poland, vol. 21(2), pages 173-187, June.
    5. Behme, Anita & Chong, Carsten & Klüppelberg, Claudia, 2015. "Superposition of COGARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1426-1469.
    6. Zhongxian Men & Tony S. Wirjanto & Adam W. Kolkiewicz, 2016. "A Multiscale Stochastic Conditional Duration Model," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 1-28, December.
    7. Anzarut, Michelle & Mena, Ramsés H., 2019. "A Harris process to model stochastic volatility," Econometrics and Statistics, Elsevier, vol. 10(C), pages 151-169.
    8. Piotr Szczepocki, 2020. "Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 173-187, June.

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    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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