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Joint estimation and model order selection for one dimensional ARMA models via convex optimization: a nuclear norm penalization approach

The problem of estimating ARMA models is computationally interesting due to the nonconcavity of the log-likelihood function. Recent results were based on the convex minimization. Joint model selection using penalization by a convex norm, e.g. the nuclear norm of a certain matrix related to the state space formulation was extensively studied from a computational viewpoint. The goal of the present short note is to present a theoretical study of a nuclear norm penalization based variant of the method of \cite{Bauer:Automatica05,Bauer:EconTh05} under the assumption of a Gaussian noise process.