Time-varying parameter (TVP) regression models can involve a huge number of coefficients. Careful prior elicitation is required to yield sensible posterior and predictive inferences. In addition, the computational demands of Markov Chain Monte Carlo (MCMC) methods mean their use is limited to the case where the number of predictors is not too large. In light of these two concerns, this paper proposes a new dynamic shrinkage prior which reflects the empirical regularity that TVPs are typically sparse (i.e. time variation may occur only episodically and only for some of the coefficients). A scalable MCMC algorithm is developed which is capable of handling very high dimensional TVP regressions or TVP Vector Autoregressions. In an exercise using artificial data we demonstrate the accuracy and computational efficiency of our methods. In an application involving the term structure of interest rates in the eurozone, we find our dynamic shrinkage prior to effectively pick out small amounts of parameter change and our methods to forecast well.

翻译：时变参数回归模型可能涉及大量系数。为了获得合理的后验推断和预测，需要谨慎设置先验分布。此外，马尔可夫链蒙特卡洛方法的计算需求限制了其仅能应用于预测变量数量不太大的场景。针对这两个问题，本文提出了一种新的动态收缩先验，该先验反映了时变参数通常具有稀疏性这一经验规律（即参数的时间变化可能仅间歇性发生，且仅涉及部分系数）。我们开发了一种可扩展的MCMC算法，能够处理极高维度的时变参数回归或时变参数向量自回归模型。通过人工数据实验，我们验证了所提方法的准确性和计算效率。在欧元区利率期限结构的应用案例中，我们的动态收缩先验能有效捕捉到微小的参数变化，且所提方法具有良好的预测性能。