Statistical inference for nonlinear dynamic model by Markov chain Monte Carlo method

在宏观经济数据的计量经济分析中，由于微观经济数据不易获得，个别特征或未观察到的变量的动态结构被忽略，这些随机效应也被认为在汇总微观经济数据后被抵消。然而，有人指出，忽略这些随机效应或未观察到的变量（潜变量）将导致模型参数估计的偏差。最近，微观经济数据已经开始公开，例如描述个人特征动态结构的面板数据。利用这些微观经济数据，我们能够模拟个人经济行为的真实结构。自20世纪99年代以来，人们提出了各种各样的计量经济学模型来处理潜变量的动态建模问题。当潜变量较多时，传统的极大似然估计需要对高维数值积分进行反复评估。我们需要使用 ...更多信息 使用超级计算机来进行这样的计算，或者我们必须以牺牲计算精度为代价来近似这种可能性。甚至在某些情况下，数值最大化步骤无法收敛到似然函数的最大值。虽然替代方法，如GEE或GMM方法已被提出来估计这些模型的基础上的方法是鲁棒的存在的潜在变量，这些估计方法是已知的是低效的，在这个项目中，我们采取贝叶斯方法，并提出有效的马尔可夫链蒙特卡罗（MCMC）估计方法的各种统计和计量经济学的非线性动态模型。为了获得模型参数的边际后验分布，已知MCMC估计方法使用模拟方法提供精确的多维积分。MCMC方法是计算机密集型的，但这些计算可以由PC完成（注意，我们不需要超级计算机）。当模型中存在潜变量或引入辅助变量时（对于数据扩充方法），MCMC样本收敛到目标分布（后验分布）在某些模型中甚至可以加速。我们考虑了各种非线性动态模型：商业周期依赖的持续期模型，具有杠杆效应的随机波动模型，马尔可夫转换和重尾误差（基于混合正态分布），以及外汇市场的随机波动模型。我们首先为这些模型提出了简单的采样方法（如一次采样一个参数的单移动采样器），并详细说明了多移动采样器（对一组参数进行采样），以提高收敛到目标后验分布的速度。少

In the econometric analysis of macroeconomic data, dynamic structures of individual characteristics or unobserved variables have been ignored since microeconomic data were not easily available and these random effects are also considered to be cancelled out after aggregating microeconomic data. However, it has been pointed out that ignoring these random effects or unobserved variables (latent variables) would lead to the bias in the estimation of model parameters. Recently, microeconomic data have started to become disclosed such as panel data which describes dynamic structure of individual characteristics. Using these microeconomic data, we are able to model true structure of individual economic behavior. Various econometric models are proposed to deal with dynamic modeling of latent variables since 1999's.When there are many latent variables, the conventional maximum likelihood estimation requires the repeated evaluations of highly multidimensional numerical integration. We need to u … More se supercomputers to conduct such computations or we have to approximate the likelihood at the expense of computational accuracies. There are even some cases in which the numerical maximization step fails to converge to the maximum of the likelihood functions. Although alternative approaches such as GEE or GMM methods have been proposed to estimate these models based on methods which are robust to the existence of latent variables, those estimation methods are known to be inefficient.In this project, we take Bayesian approach and proposed efficient Markov chain Monte Carlo (MCMC) estimation method for various statistical and econometric nonlinear dynamic models. To obtain marginal posterior distribution of model parameters, the MCMC estimation method is known to provide accurate multidimensional integration using simulation method. The MCMC method is computer intensive, but these computations can be done by PC's (note that we do not need supercomputers). When there exist latent variables in the models or we introduce auxiliary variables (for the data augmentation method), the convergence of MCMC samples to the target distribution (posterior distribution) may even be accelerated in some models.We considered various nonlinear dynamic models : duration models for business cycle dependence, stochastic volatility model with leverage effects, Markov switching and heavy-tailed errors (based on mixture of normal distributions), and stochastic volatility model for foreign exchange markets. We first proposed simple sampling methods (such as single-move sampler which samples one parameter at a time) for these models and elaborate the multi-move samplers (which samples a block of parameters) to improve the speed of the convergence to the target posterior distributions. Less