High-Dimensional Conditionally Gaussian State Space Models with Missing Data

TL;DR

This paper introduces an efficient sampling method for complex missing data patterns in high-dimensional conditionally Gaussian state space models, leveraging sparsity in the precision matrix to improve computational speed.

Contribution

The paper presents a novel approach that exploits the Gaussian conditional distribution and sparsity in the precision matrix to handle missing data efficiently in high-dimensional models.

Findings

Successfully applied to large Bayesian VARs with mixed-frequency data.

Effectively extracted latent factors from unbalanced datasets.

Produced weekly GDP estimates from mixed-frequency data.

Abstract

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.