<p>Blind system identification, which has been a focus of research efforts throughout the years, evolves into a highly challenging problem in the context of colored output noise. The aim of this paper is to jointly identify the AutoRegressive with eXogenous inputs (ARX) model and input using output data, where the unknown input is modeled as a filtered white noise. By converting the output data into a multivariate AutoRegressive Moving Average model, an identification protocol is established to obtain all possible combinations of the system model and input model. The optimal ARX model and input model are determined from these candidate combinations through a variant of the maximum likelihood method and information criterion. In addition, identifiability analysis and uncertainty bound are provided. The performance of the proposed identification method is finally demonstrated via numerical and real examples. The obtained results show that the proposed method can return consistent estimates of the ARX model and the input model, and outperforms the four reference methods.</p>