Fast and Flexible Bayesian Inference in Time-varying Parameter Regression Models

In this article, we write the time-varying parameter (TVP) regression model involving <i>K</i> explanatory variables and <i>T</i> observations as a constant coefficient regression model with <i>KT</i> explanatory variables. In contrast with much of the existing literature which assumes coefficients to evolve according to a random walk, a hierarchical mixture model on the TVPs is introduced. The resulting model closely mimics a random coefficients specification which groups the TVPs into several regimes. These flexible mixtures allow for TVPs that feature a small, moderate or large number of structural breaks. We develop computationally efficient Bayesian econometric methods based on the singular value decomposition of the <i>KT</i> regressors. In artificial data, we find our methods to be accurate and much faster than standard approaches in terms of computation time. In an empirical exercise involving inflation forecasting using a large number of predictors, we find our models to forecast better than alternative approaches and document different patterns of parameter change than are found with approaches which assume random walk evolution of parameters.

本文将包含$K$个解释变量、$T$个观测值的时变参数（time-varying parameter, TVP）回归模型，重构为具有$KT$个解释变量的常系数回归模型。与多数假设系数服从随机游走演化的现有文献不同，本文引入了针对时变参数的分层混合模型。所得到的模型近似于将时变参数划分为若干机制的随机系数设定形式。这类灵活的混合模型可适配具有少量、中等数量或大量结构突变的时变参数。本文基于$KT$个回归元的奇异值分解（singular value decomposition），构建了计算高效的贝叶斯计量经济学方法。在人工数据集实验中，本文所提方法不仅精度可靠，且计算耗时远低于标准方法。在一项基于大量预测因子开展通胀预测的实证研究中，本文模型的预测性能优于其他备选方法，且所揭示的参数变化模式，与假设参数服从随机游走演化的方法所得结果存在显著差异。