  We propose a novel recursive system identification algorithm for linear
autoregressive systems with skewed innovations. The algorithm is based on the
variational Bayes approximation of the model with a multivariate normal prior
for the model coefficients, multivariate skew-normally distributed innovations,
and matrix-variate-normal - inverse-Wishart prior for the parameters of the
innovation distribution. The proposed algorithm simultaneously estimates the
model coefficients as well as the parameters of the innovation distribution,
which are both allowed to be slowly time-varying. Through computer simulations,
we compare the proposed method with a variational algorithm based on the
normally-distributed innovations model, and show that modelling the skewness
can provide improvement in identification accuracy.
