  The new class of Markov processes is proposed to realize the flexible
shrinkage effects for the dynamic models. The transition density of the new
process consists of two penalty functions, similarly to Bayesian fused LASSO in
its functional form, that shrink the current state variable to its previous
value and zero. The normalizing constant of the density, which is not ignorable
in the posterior computation, is shown to be essentially the log-geometric
mixture of double-exponential densities. This process comprises the state
equation of the dynamic regression models, which is shown to be conditionally
Gaussian and linear in state variables and utilize the forward filtering and
backward sampling in posterior computation by Gibbs sampler. The problem of
overshrinkage that is inherent in lasso is moderated by considering the
hierarchical extension, which can even realize the shrinkage of horseshoe
priors marginally. The new prior is compared with the standard
double-exponential prior in the estimation of and prediction by the dynamic
linear models for illustration. It is also applied to the time-varying vector
autoregressive models for the US macroeconomic data, where we examine the
(dis)similarity of the additional shrinkage effect to dynamic variable
selection or, specifically, the latent threshold models.
