統計学輪講 第12回

In this study we consider the simulation-based Bayesian analysis of stochastic volatility in mean (SVM) models. Extending the highly efficient Markov chain Monte Carlo mixture sampler for the SV model proposed in [1] and [2], we develop an accurate approximation of the non-central chi-squared distribution as a mixture of thirty normal distributions. Under this mixture representation, we sample the parameters and latent volatilities in one block. We also detail a correction of the small approximation error by using additional Metropolis-Hastings steps. The proposed method is extended to the SVM model with leverage. The methodology and models are applied to excess holding yields in empirical studies, and the SVM model with leverage is shown to outperform competing volatility models based on marginal likelihoods.

This presentation is based on joint work with Professor Omori and Professor Chib.

[1] Kim, S., N. Shephard, and S. Chib (1998). Stochastic volatility: likelihood inference andcomparison with arch models. The review of economic studies 65 (3), 361–393.
[2] Omori, Y., S. Chib, N. Shephard, and J. Nakajima (2007). Stochastic volatility with leverage: Fast and efficient likelihood inference. Journal of Econometrics 140 (2), 425–449.