We propose a continuous-time Markov-switching generalized autoregressive conditional heteroskedasticity (COMS-GARCH) process for handling irregularly spaced time series (TS) with multiple volatilities states. We employ a Gibbs sampler in the Bayesian framework to estimate the COMS-GARCH model parameters, the latent state path and volatilities. To improve the inferential robustness and computational efficiency for obtaining the maximum a posteriori estimates for the state path and volatilities, we suggest a multi-path sampling scheme and incorporate the Bernoulli noise injection in the computational algorithm. We provide theoretical justifications for the improved stability and robustness with the Bernoulli noise injection through the concept of ensemble learning and the low sensitivity of the objective function to external perturbation in the TS. We apply the proposed COMS-GARCH process and the computational procedure to simulated TS, a real currency exchange rate TS, and a real blood volume amplitude TS. The empirical results demonstrate that the COMS-GARCH process and the computational procedure are able to predict volatility regimes and volatilities in a TS with satisfactory accuracy.
翻译:我们建议采用连续时间的Markov开关通用自动递减式、条件性、不定期间距时间序列(TS)程序,处理多挥发状态;在巴伊西亚框架中使用Gibs取样器,估计COMS-GaRCH模型参数、潜在状态路径和挥发性;为了提高获取国家路径和挥发性最高后继估计值的推断力和计算效率,我们建议采用多路采样办法,并将Bernoulli噪声注入纳入计算算法;我们从理论上说明如何通过共通性学习概念和客观功能对TS外部扰动敏感度低,改进Bernoulli噪声注入的稳定性和稳健性;我们采用拟议的COMS-GaRCH进程和计算程序对模拟TS、实际货币汇率TT和真实血量调 T. 实验结果显示,COMS-GaRCH进程具有令人满意的波动性和计算程序。