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The HESSIAN Method for Models with Leverage-like Effects


  • Barnabé Djegnéné
  • William J. McCausland


We propose a new method for simulation smoothing in state space models with univariate states and conditional dependence between the observation yt and the contemporaneous innovation of the state equation. Stochastic volatility models with the leverage effect are a leading example. Our method extends the HESSIAN method of McCausland (2012, Journal of Econometrics, 168, 189–206), which required conditional independence between yt and the state innovation. Our generic method is more numerically efficient than the model-specific methods of Omori et al. (2007, J. Fin. Econ., 140, 425–449)—for a stochastic volatility model with Gaussian innovations—and Nakajima and Omori (2009, Comput. Stat. Data Anal., 53, 2335–2353)—for a model with Student's t innovations.

Suggested Citation

  • Barnabé Djegnéné & William J. McCausland, 2015. "The HESSIAN Method for Models with Leverage-like Effects," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 13(3), pages 722-755.
  • Handle: RePEc:oup:jfinec:v:13:y:2015:i:3:p:722-755.

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    Cited by:

    1. Joshua C.C. Chan & Angelia L. Grant, 2014. "Issues in Comparing Stochastic Volatility Models Using the Deviance Information Criterion," CAMA Working Papers 2014-51, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    2. Joshua C. C. Chan & Eric Eisenstat, 2018. "Bayesian model comparison for time‐varying parameter VARs with stochastic volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(4), pages 509-532, June.
    3. Joshua C. C. Chan, 2017. "The Stochastic Volatility in Mean Model With Time-Varying Parameters: An Application to Inflation Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 17-28, January.
    4. Gong, Xiao-Li & Liu, Xi-Hua & Xiong, Xiong & Zhuang, Xin-Tian, 2018. "Modeling volatility dynamics using non-Gaussian stochastic volatility model based on band matrix routine," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 193-201.


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