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Bayesian Inference of Stochastic Volatility Model by Hybrid Monte Carlo

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  • Tetsuya Takaishi

Abstract

The hybrid Monte Carlo (HMC) algorithm is applied for the Bayesian inference of the stochastic volatility (SV) model. We use the HMC algorithm for the Markov chain Monte Carlo updates of volatility variables of the SV model. First we compute parameters of the SV model by using the artificial financial data and compare the results from the HMC algorithm with those from the Metropolis algorithm. We find that the HMC algorithm decorrelates the volatility variables faster than the Metropolis algorithm. Second we make an empirical study for the time series of the Nikkei 225 stock index by the HMC algorithm. We find the similar correlation behavior for the sampled data to the results from the artificial financial data and obtain a $\phi$ value close to one ($\phi \approx 0.977$), which means that the time series has the strong persistency of the volatility shock.

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  • Tetsuya Takaishi, 2009. "Bayesian Inference of Stochastic Volatility Model by Hybrid Monte Carlo," Papers 1001.0024, arXiv.org.
    • Handle: RePEc:arx:papers:1001.0024
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    1. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    2. Stefan Bornholdt, 2001. "Expectation Bubbles In A Spin Model Of Markets: Intermittency From Frustration Across Scales," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(05), pages 667-674.
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    1. Takaishi, Tetsuya, 2018. "Bias correction in the realized stochastic volatility model for daily volatility on the Tokyo Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 139-154.
    2. Didit Nugroho & Takayuki Morimoto, 2015. "Estimation of realized stochastic volatility models using Hamiltonian Monte Carlo-Based methods," Computational Statistics, Springer, vol. 30(2), pages 491-516, June.
    3. Abanto-Valle, Carlos A. & Rodríguez, Gabriel & Garrafa-Aragón, Hernán B., 2021. "Stochastic Volatility in Mean: Empirical evidence from Latin-American stock markets using Hamiltonian Monte Carlo and Riemann Manifold HMC methods," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 272-286.

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