Third and fourth moments of vector autoregressions with regime switching

We derive matrix formulae in closed form for the unconditional third and fourth moments of a broad class of vector autoregressive time series with regime switching. First and second moments are well-known. New measures of multivariate skewness and kurtosis are introduced and basic properties are investigated. The knowledge of series level, variation, co-movements, skewness and kurtosis are useful to support model interpretation in real data application. Numerical examples complete the paper.