Time-varying parameter (TVP) models often assume that the TVPs evolve according to a random walk. This assumption, however, might be questionable since it implies that coefficients change smoothly and in an unbounded manner. This assumption is relaxed by proposing a flexible law of motion for the TVPs in large-scale vector autoregressions (VARs). Instead of imposing a restrictive random walk evolution of the latent states, hierarchical mixture priors on the coefficients in the state equation are carefully designed. These priors effectively allow for discriminating between periods in which coefficients evolve according to a random walk and times where the TVPs are better characterized by a stationary stochastic process. Moreover, this approach is capable of introducing dynamic sparsity by pushing small parameter changes towards zero if necessary. The merits of the model are illustrated by means of two applications. Using synthetic data these flexible modeling techniques yield precise parameter estimates. When applied to US data, the model reveals interesting patterns of low-frequency dynamics in coefficients and forecasts well relative to a wide range of competing models.

时变参数 (TVP) 模型通常假设 TVP 根据随机游走演化。然而，这个假设可能是有问题的，因为它意味着系数以无限制的方式平滑地变化。通过为大规模向量自回归 (VAR) 中的 TVP 提出灵活的运动定律，可以放宽这一假设。不是对潜在状态施加限制性随机游走演化，而是仔细设计状态方程中系数的分层混合先验。这些先验有效地允许区分系数根据随机游走演化的时期和 TVP 更好地由平稳随机过程表征的时期。此外，如果需要，这种方法能够通过将小的参数变化推向零来引入动态稀疏性。通过两个应用程序说明了该模型的优点。使用合成数据，这些灵活的建模技术产生精确的参数估计。当应用于美国数据时，该模型揭示了系数中低频动态的有趣模式，并且相对于广泛的竞争模型进行了很好的预测。