Approximate Recursive Identification of Autoregressive Systems with Skewed Innovations

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-variatenormal–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.