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Efficient Bayesian estimation for GARCH-type models via Sequential Monte Carlo

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  • Dan Li
  • Adam Clements
  • Christopher Drovandi

Abstract

The advantages of sequential Monte Carlo (SMC) are exploited to develop parameter estimation and model selection methods for GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) style models. It provides an alternative method for quantifying estimation uncertainty relative to classical inference. Even with long time series, it is demonstrated that the posterior distribution of model parameters are non-normal, highlighting the need for a Bayesian approach and an efficient posterior sampling method. Efficient approaches for both constructing the sequence of distributions in SMC, and leave-one-out cross-validation, for long time series data are also proposed. Finally, an unbiased estimator of the likelihood is developed for the Bad Environment-Good Environment model, a complex GARCH-type model, which permits exact Bayesian inference not previously available in the literature.

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  • Dan Li & Adam Clements & Christopher Drovandi, 2019. "Efficient Bayesian estimation for GARCH-type models via Sequential Monte Carlo," Papers 1906.03828, arXiv.org, revised Mar 2020.
    • Handle: RePEc:arx:papers:1906.03828
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    1. T. -N. Nguyen & M. -N. Tran & R. Kohn, 2020. "Recurrent Conditional Heteroskedasticity," Papers 2010.13061, arXiv.org, revised Jan 2022.
    2. Chen, Cathy W.S. & Watanabe, Toshiaki & Lin, Edward M.H., 2023. "Bayesian estimation of realized GARCH-type models with application to financial tail risk management," Econometrics and Statistics, Elsevier, vol. 28(C), pages 30-46.
    3. Amendola, Alessandra & Candila, Vincenzo & Gallo, Giampiero M., 2021. "Choosing the frequency of volatility components within the Double Asymmetric GARCH–MIDAS–X model," Econometrics and Statistics, Elsevier, vol. 20(C), pages 12-28.
    4. Li, Dan & Clements, Adam & Drovandi, Christopher, 2023. "A Bayesian approach for more reliable tail risk forecasts," Journal of Financial Stability, Elsevier, vol. 64(C).
    5. Trong‐Nghia Nguyen & Minh‐Ngoc Tran & Robert Kohn, 2022. "Recurrent conditional heteroskedasticity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 1031-1054, August.
    6. Chen Liu & Chao Wang & Minh-Ngoc Tran & Robert Kohn, 2023. "Deep Learning Enhanced Realized GARCH," Papers 2302.08002, arXiv.org, revised Oct 2023.

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