  Normal mean-variance mixture distributions are widely applied to simplify a
model's implementation and improve their computational efficiency under the
Maximum Likelihood (ML) approach. Especially for distributions with normal
mean-variance mixtures representation such as the multivariate skewed variance
gamma (MSVG) distribution, it utilises the expectation-conditional-maximisation
(ECM) algorithm to iteratively obtain the ML estimates. To facilitate
application to financial time series, the mean is further extended to include
autoregressive terms. Techniques are proposed to deal with the unbounded
density for small shape parameter and to speed up the convergence. Simulation
studies are conducted to demonstrate the applicability of this model and
examine estimation properties. Finally, the MSVG model is applied to analyse
the returns of five daily closing price market indices and standard errors for
the estimated parameters are computed using Louis's method.
