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This article is concerned with the identification of autoregressive withexogenous inputs (ARX) models. Most of the existing approaches like predictionerror minimization and state-space framework are widely accepted and utilizedfor the estimation of ARX models but are known to deliver unbiased andconsistent parameter estimates for a correctly supplied guess of input-outputorders and delay.  In this paper, we propose a novel automated framework which recovers orders,delay, output noise distribution along with parameter estimates. The primarytool utilized in the proposed framework is generalized spectral decomposition.The proposed algorithm systematically estimates all the parameters in twosteps. The first step utilizes estimates of the order by examining thegeneralized eigenvalues, and the second step estimates the parameter from thegeneralized eigenvectors. Simulation studies are presented to demonstrate theefficacy of the proposed method and are observed to deliver consistentestimates even at low signal to noise ratio (SNR).

ARX Model Identification using Generalized Spectral Decomposition