PMCMC for Term Structure of Interest Rates under Markov Regime Switching and Jumps

A parameter estimation method,called PMCMC in this paper,is proposed to estimate a continuous-time model of the term structure of interests under Markov regime switching and jumps.There is a closed form solution to term structure of interest rates under Markov regime.However,the model is extended to be a CKLS model with non-closed form solutions which is a typical nonlinear and non-Gaussian state-space model(SSM)in the case of adding jumps.Although the difficulty of parameter estimation greatly prevents from researching models,we prove that the nonlinear and non-Gaussian state-space model has better performances in studying volatility.The method proposed in this paper will be implemented in simulation and empirical study for SHIBOR.Empirical results illustrate that the PMCMC algorithm has powerful advantages in tackling the models.

非线性MS-DSGE模型的条件最优粒子滤波与贝叶斯估计

研究目标:提出线性与非线性MS-DSGE模型的条件最优粒子滤波(COPF)以及参数的贝叶斯估计方法。研究方法:利用MS-DSGE模型状态空间表示的条件线性特征来构造COPF,基于上述算法进一步提出粒子马尔科夫链蒙特卡洛(PMCMC)方法,实现参数的贝叶斯估计。最后构建可变货币政策规则的新凯恩斯理论模型,运用数值模拟方法检验了COPF与参数贝叶斯估计的效果,同时对中国实际数据进行了估计与分析。研究发现:在粒子滤波的低观测误差设定与小样本条件下,模型深度参数的贝叶斯估计结果表现精确,所有参数的真值都在其后验分布的[5%,95%]分位数区间内;实际应用结果显示,中国货币政策存在积极与被动这两种区制,且政策的区制转换会导致价格通胀波动幅度上升1%左右;2011年之后,中国货币政策区制表现的非常稳健,对通胀的响应程度较高。研究创新:提出了非线性MS-DSGE的COPF以及PMCMC方法,从而实现深度参数的贝叶斯估计。研究价值:所构建的粒子滤波与贝叶斯估计方法为一般的MS-DSGE模型提供了实证分析工具,对未来内生区制转换、系统性风险传染等问题的研究奠定了基础。