Gaussian Process Vector Autoregressions and Macroeconomic Uncertainty

We develop a nonparametric multivariate time series model that remains agnostic on the precise relationship between a (possibly) large set of macroeconomic time series and their lagged values. The main building block of our model is a Gaussian process prior on the functional relationship that determines the conditional mean of the model, hence, the name of Gaussian process vector autoregression (GP-VAR). A flexible stochastic volatility specification is used to provide additional flexibility and control for heteroscedasticity. Markov chain Monte Carlo (MCMC) estimation is carried out through an efficient and scalable algorithm which can handle large models. The GP-VAR is used to analyze the effects of macroeconomic uncertainty, with a particular emphasis on time variation and asymmetries in the transmission mechanisms.

本研究构建了一款非参数多变量时间序列模型，该模型不对数量可能庞大的宏观经济时间序列集合与其滞后项之间的精确关系做出预设。本模型的核心构建模块为：针对决定模型条件均值的函数关系设定高斯过程先验，本模型也因此得名高斯过程向量自回归（Gaussian Process Vector Autoregression，GP-VAR）。我们采用灵活的随机波动率设定形式，以进一步提升模型灵活性并实现对异方差性的管控。本研究通过高效且可扩展的算法实现马尔可夫链蒙特卡洛（Markov Chain Monte Carlo，MCMC）估计，该算法可适配大规模模型的处理需求。本研究利用GP-VAR模型分析宏观经济不确定性的影响，尤其聚焦于传导机制中的时变性与非对称性特征。