  Recently, Fasano, Rebaudo, Durante and Petrone (2019) provided closed-form
expressions for the filtering, predictive and smoothing distributions of
multivariate dynamic probit models, leveraging on unified skew-normal
distribution properties. This allows to develop algorithms to draw independent
and identically distributed samples from such distributions, as well as
sequential Monte Carlo procedures for the filtering and predictive
distributions, allowing to overcome computational bottlenecks that may arise
for large sample sizes. In this paper, we briefly review the above-mentioned
closed-form expressions, mainly focusing on the smoothing distribution of the
univariate dynamic probit. We develop a variational Bayes approach, extending
the partially factorized mean-field variational approximation introduced by
Fasano, Durante and Zanella (2019) for the static binary probit model to the
dynamic setting. Results are shown for a financial application.
