統計学輪講 第21回

A Stochastic volatility (SV) model describes the dynamics of unobserved volatility in financial time series. It is known that the simple MCMC sampling of latent variables is inefficient in a SV model, and to improve this problem, Kim and Shephard et.al (1998)[1], Omori and Watanabe (2007)[2], Watanabe and Omori (1997 )[3] proposed methods such as a mixture sampler and a multi-move sampler. In this study, we explain that efficient MCMC sampling is possible by applying the same methods to a stochastic volatility in mean (SVM) model, which is an extension of the SV model. Empirical studies suggest that the SVM model is a good fit for some financial time series data.
This is a joint work with Prof. Yasuhiro Omori.

[1] Kim, S., Shephard, N., Chib, S.: Stochastic volatility: likelihood inference and comparison with ARCH models. Rev. Econ. Stud. 65, 361-393 (1998)
[2] Omori, Y., Chib, S., Shephard, N., Nakajima, J.: Stochastic volatility with leverage: fast and efficient likelihood inference. J. Econometrics 140(2), 425-449 (2007). https://doi.org/10.1016/j.jeconom.2006.07.008
[3] Watanabe, T., Omori, Y.: A multi-move sampler for estimating non-gaussian time series models: comments on Shephard & Pitt (1997). Biometrika 91(1), 246-248 (2004)