Plausibility of big shocks within a linear state space setting with skewness

In this paper we provide formulae for likelihood function, filtration densities and prediction densities of a linear state space model in which shocks are allowed to be skewed. In particular we work with the closed skew normal distribution, see González-Farías et al. (2004), which nests a normal distribution as a special case. Closure of the csn distribution with respect to all necessary transformations in the state space setting is guaranteed by a simple state dimension reduction procedure which does not influence the value of the likelihood function. Presented formulae allow for estimation, filtration and prediction of vector autoregressions and first order perturbations of DSGE models with skewed shocks. This allows to assess asymmetries in shocks, observed data, impulse responses and forecasts confidence intervals. Some of the advantages of using the outlined approach may involve capturing asymmetric inflation risks in central banks forecasts or producing more plausible probabilities of deep but rare recessionary episodes with DSGE/VAR filtration. Exemplary estimation results are provided which show that within a linear setting with skewness frequency of big shocks can be rather plausibly identifed.