Time-varying parameter (TVP) structural vector autoregressive models with stochastic volatility (SVAR-SV) usually assume Gaussian innovations and a smooth or discrete path for the coefficients. To account for possible skewness and fat tails, this work introduces a semiparametric mixture of multivariate restricted skew-t innovation distributions, also permitting the inference of clusters of asymmetry across data series. Moreover, a dynamic shrinkage prior is designed for the coefficients of the contemporaneous and lagged variables to model the path of the parameters flexibly. Inference in high-dimensional settings is performed via a Markov chain Monte Carlo algorithm that leverages the stochastic representation of the skew-t distribution for obtaining a conditional linear Gaussian state-space model. Then, the algorithm alternates between the centred and non-centred parametrizations to improve the mixing and samples from the joint smoothed distribution without loops. The proposed semiparametric approach is combined with a sparsification method to extract time-varying Granger-causal networks in different applications regarding the COVID-19 pandemic across Europe and financial contagion transmission in Europe and the world.
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