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The Usage of Markov Chain Monte Carlo (MCMC) Methods in Time-varying Volatility Models

Author

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  • Garefalakis Emmanouil
  • Giakoumatos Stefanos
  • Rezitis Antonios

Abstract

Markov Chain Monte Carlo (MCMC) techniques, in the context of Bayesian inference, constitute a practical and effective tool to produce samples from an arbitrary distribution. These algorithms are applied to calculate parameter values of predictive models of the phenomenon of varying volatility in data time series. For this purpose, 3 such research models of time-varying volatility are simulated in STAN a probabilistic programming language for statistical inference. The accuracy of these models’ predictive function is confirmed by applying in data time series with known prior values. Moreover, Stan models’ performance is illustrated by the real stock prices of two shares in the stock market of New York. Finally, an Information Criterion of the results is applied to each model as well, to evaluate their predictive ability, comparing and selecting the most effective one.

Suggested Citation

  • Garefalakis Emmanouil & Giakoumatos Stefanos & Rezitis Antonios, 2023. "The Usage of Markov Chain Monte Carlo (MCMC) Methods in Time-varying Volatility Models," Journal of Risk & Control, SCIENPRESS Ltd, vol. 10(1), pages 1-1.
    • Handle: RePEc:spt:rmkjrc:v:10:y:2023:i:1:f:10_1_1
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    References listed on IDEAS

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    1. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204, April.
    4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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