We derive Lagrange Multiplier and Likelihood Ratio specifi cation tests for the null hypotheses of multivariate normal and Student t innovations using the Generalised Hyperbolic distribution as our alternative hypothesis. We decompose the corresponding Lagrange Multiplier-type tests into...

We derive specification tests for the null hypotheses of multivariate normal and Student t innovations using the Generalised Hyperbolic distribution as our alternative hypothesis. In both cases, we decompose the corresponding Lagrange Multiplier-type tests into skewness and kurtosis components,...