We develop an efficient sampling approach for handling complex missing data patterns and a large number of missing observations in conditionally Gaussian state space models. Two important examples are dynamic factor models with unbalanced datasets and large Bayesian VARs with variables in multiple frequencies. A key insight underlying the proposed approach is that the joint distribution of the missing data conditional on the observed data is Gaussian. Moreover, the inverse covariance or precision matrix of this conditional distribution is sparse, and this special structure can be exploited to substantially speed up computations. We illustrate the methodology using two empirical applications. The first application combines quarterly, monthly and weekly data using a large Bayesian VAR to produce weekly GDP estimates. In the second application, we extract latent factors from unbalanced datasets involving over a hundred monthly variables via a dynamic factor model with stochastic volatility.

翻译：本文针对条件高斯状态空间模型中复杂缺失数据模式及大量缺失观测值的问题，提出了一种高效采样方法。两个重要应用实例为：非平衡数据集下的动态因子模型，以及包含多频率变量的大规模贝叶斯向量自回归模型。该方法的理论基础在于：在给定观测数据的条件下，缺失数据的联合分布服从高斯分布。此外，该条件分布的逆协方差矩阵（即精度矩阵）具有稀疏特性，这一特殊结构可被利用以显著提升计算效率。我们通过两个实证应用验证该方法的有效性。第一个应用利用大规模贝叶斯向量自回归模型整合季度、月度与周度数据，生成周度GDP估计值。第二个应用则通过含随机波动的动态因子模型，从包含百余个月度变量的非平衡数据集中提取潜在因子。