Joint Topology and Parameter Identification of Graphical ARMA Models

Abstract

This paper focuses on the identification of graphical autoregressive moving-average (ARMA) models. Existing methods address the identification problem by estimating the graph topology, moving-average (MA) and autoregressive (AR) parameters in a separate way. To improve the identification efficiency, we design a two-stage identification algorithm, in which the AR and MA parameters are coupled together and can be estimated together with the graphical structure. Since a low-order ARMA model can be approximated by an AR model of appropriate high order, the identification object can be converted to the approximate graphical AR model, whose graph topology is identical to that of the primal graphical ARMA model. Based on l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -type nonsmooth regularized conditional maximum likelihood estimation and information theoretic model selection criterion, the simultaneous identification of the graphical structure and parameters of the approximate graphical AR model can be achieved. Then, the AR and MA parts of the primal graphical ARMA model are decoupled from the estimated parameters. Simulation results illustrate the effectiveness of the proposed algorithm.