A closed-form filter for binary time series

Non-Gaussian state-space models arise in several applications, and within this framework the binary time series setting provides a relevant example. However, unlike for Gaussian - where filtering, predictive smoothing distributions are available closed form require approximations or sequential Monte Carlo strategies inference prediction. This is due to apparent absence of conjugacy between states likelihood induced by observation equation data. In article we prove that dynamic probit with state variables are, fact, belong class unified skew-normals (SUN) whose parameters can be updated recursively via analytical expressions. Also key functionals these principle, available, but their calculation requires evaluation multivariate cumulative distribution functions. Leveraging SUN properties, address issue novel methods based on independent samples from distribution, easily adapted filtering case, thus improving state-of-the-art approximate small-to-moderate dimensional studies. Novel procedures exploit properties also developed deal online high dimensions. Performance gains over competitors outlined financial application.