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Simulated likelihood inference for stochastic volatility models using continuous particle filtering

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  • Michael Pitt
  • Sheheryar Malik
  • Arnaud Doucet

Abstract

Discrete-time stochastic volatility (SV) models have generated a considerable literature in financial econometrics. However, carrying out inference for these models is a difficult task and often relies on carefully customized Markov chain Monte Carlo techniques. Our contribution here is twofold. First, we propose a new SV model, namely SV–GARCH, which bridges the gap between SV and GARCH models: it has the attractive feature of inheriting unconditional properties similar to the standard GARCH model but being conditionally heavier tailed. Second, we propose a likelihood-based inference technique for a large class of SV models relying on the recently introduced continuous particle filter. The approach is robust and simple to implement. The technique is applied to daily returns data for S&P 500 and Dow Jones stock price indices for various spans. Copyright The Institute of Statistical Mathematics, Tokyo 2014

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  • Michael Pitt & Sheheryar Malik & Arnaud Doucet, 2014. "Simulated likelihood inference for stochastic volatility models using continuous particle filtering," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 527-552, June.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:3:p:527-552
    DOI: 10.1007/s10463-014-0456-y
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    References listed on IDEAS

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    4. Benedikt Rotermann & Bernd Wilfling, 2015. "Estimating rational stock-market bubbles with sequential Monte Carlo methods," CQE Working Papers 4015, Center for Quantitative Economics (CQE), University of Muenster.
    5. Lux, Thomas, 2017. "Estimation of agent-based models using sequential Monte Carlo methods," Economics Working Papers 2017-07, Christian-Albrechts-University of Kiel, Department of Economics.
    6. Ilze Kalnina & Dacheng Xiu, 2017. "Nonparametric Estimation of the Leverage Effect: A Trade-Off Between Robustness and Efficiency," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 384-396, January.
    7. Mao, Xiuping & Czellar, Veronika & Ruiz, Esther & Veiga, Helena, 2020. "Asymmetric stochastic volatility models: Properties and particle filter-based simulated maximum likelihood estimation," Econometrics and Statistics, Elsevier, vol. 13(C), pages 84-105.
    8. Lux, Thomas, 2018. "Estimation of agent-based models using sequential Monte Carlo methods," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 391-408.
    9. Haroon Mumtaz, 2018. "A generalised stochastic volatility in mean VAR," Working Papers 855, Queen Mary University of London, School of Economics and Finance.
    10. Song, Zhaogang & Xiu, Dacheng, 2016. "A tale of two option markets: Pricing kernels and volatility risk," Journal of Econometrics, Elsevier, vol. 190(1), pages 176-196.
    11. Zhang, Xing & Yan, Zhibin & Chen, Yunqi & Yuan, Yanhua, 2022. "A novel particle filter for extended target tracking with random hypersurface model," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    12. Robert Stok & Paul Bilokon, 2023. "From Deep Filtering to Deep Econometrics," Papers 2311.06256, arXiv.org.
    13. Awijen, Haithem & Ben Zaied, Younes & Nguyen, Duc Khuong & Sensoy, Ahmet, 2020. "Endogenous Financial Uncertainty and Macroeconomic Volatility: Evidence from the United States," MPRA Paper 101276, University Library of Munich, Germany, revised Jun 2020.
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    15. Mumtaz, Haroon, 2018. "A generalised stochastic volatility in mean VAR," Economics Letters, Elsevier, vol. 173(C), pages 10-14.

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