Markov Chain Monte Carlo Methods for Parameter Estimation in Multidimensional Continuous Time Markov Switching Models
针对多维连续时间模型，其中漂移和波动率由共同状态过程驱动，开发了精确连续时间和近似离散时间的MCMC采样器，用于估计状态和速率矩阵，模拟显示MCMC在高速率等困难情形下优于最大似然估计，并应用于四国股指识别出四个状态。
We consider a multidimensional, continuous-time model where the observation process is a diffusion with drift and volatility coefficients being modeled as continuous-time, finite-state Markov chains with a common state process. For the econometric estimation of the states for drift and volatility and the rate matrix of the underlying Markov chain, we develop both an exact continuous time and an approximate discrete-time Markov chain Monte Carlo (MCMC) sampler and compare these approaches with maximum likelihood (ML) estimation. For simulated data, MCMC outperforms ML estimation for difficult cases like high rates. Finally, for daily stock index quotes from Argentina, Brazil, Mexico, and the USA we identify four states differing not only in the volatility of the various assets but also in their correlation.