Approximate Recursive Identification of Autoregressive Systems with Skewed Innovations

TL;DR

This paper introduces a recursive identification algorithm for linear autoregressive systems with skewed innovations, improving accuracy by modeling skewness in the innovations using variational Bayes approximation.

Contribution

The paper presents a novel recursive algorithm that estimates both system coefficients and skewed innovation parameters, allowing for time-varying dynamics and enhanced identification accuracy.

Findings

Modeling skewness improves identification accuracy.

The proposed method outperforms Gaussian-based variational algorithms.

Simulations demonstrate effectiveness in dynamic settings.

Abstract

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.