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

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