Abstract: We consider variable selection and shrinkage for Gaussian Dynamic Linear Models (DLM) within a Bayesian framework. In particular, we propose a novel method that accommodates time-varying sparsity, based on an extension of spike-and-slab priors for dynamic models. This is done by assigning appropriate priors for the time-varying coefficients? variances, extending the previous work of Ishwaran and Rao (2005). Our approach is similar to the Normal Gamma Autoregressive (NGAR) process of Kalli and Griffin (2014), nevertheless, we assume a Markov switching structure for the process variances instead of a Gamma Autoregressive (GAR) process. Furthermore, we investigate different priors, including the common Inverted gamma prior for the process variances, and other mixture prior distributions such as Gamma priors for both the spike and the slab, which leads to a mixture of Normal-Gammas priors (Brown and Griffin, 2010) for the coefficients and also different distributions for the spike and the slab. In this sense, our prior can be view as a dynamic variable selection prior which induces either smoothness (through the slab) or shrinkage towards zero (through the spike) at each time point. The MCMC method used for posterior computation uses Markov latent variables that can assume binary regimes at each time point to generate the coefficients? variances. In that way, our model is a dynamic mixture model, thus, we could use the algorithm of Gerlach et al. (2000) to generate the latent processes without conditioning on the states. Finally, our approach is exemplified through simulated examples and a real data application. This is joint work with Paloma Uribe.

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