Parameter-Covariance Maximum Likelihood Estimation

TL;DR

This paper introduces a convex time-domain approach for vector-ARMA system identification that includes moving average components and supports non-stationarity through regime switching, enhancing model parsimony and flexibility.

Contribution

It presents a novel convex formulation for vector-ARMA identification that incorporates regime switching and can be solved efficiently in the time domain.

Findings

Convex formulation effectively identifies vector-ARMA models.

Method accommodates non-stationary data with regime switching.

Experimental results demonstrate practical applicability.

Abstract

Linear time series modelling is dominated by the use of purely autoregressive models even though incorporating moving average components can greatly improve parsimony. We present a convex formulation for vector-ARMA system identification which respects this fundamental property, thus granting access to the nice properties afforded by convex programming. The identification procedure is done purely in the time domain which can accommodate non-stationarity through regime switching. As a proof of concept, we present experimental results demonstrating this convex program in action. Next, we show how to adapt the expectation-maximization algorithm to support regime switching behavior.