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

TL;DR

This paper introduces a convex optimization approach using nuclear norm penalization for joint estimation and model order selection of one-dimensional ARMA models, providing a theoretical analysis under Gaussian noise assumptions.

Contribution

It offers a theoretical study of a nuclear norm penalization method for ARMA model estimation, extending previous computational approaches with new analytical insights.

Findings

The method effectively estimates ARMA models with theoretical guarantees.

Nuclear norm penalization facilitates joint model selection and parameter estimation.

Analysis assumes Gaussian noise for theoretical validation.

Abstract

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.