  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.
In this paper, we relax this assumption 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, we carefully design
hierarchical mixture priors on the coefficients in the state equation. These
priors effectively allow for discriminating between periods where 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 we show that our approach yields 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.
