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The ARMAX model identification problem is typically solved through nonlinear optimization algorithms, which deliver local optimal solutions. In this thesis, we show that the ARMAX model identification problem is a multiparameter eigenvalue problem and we use the block Macaulay approach to solve it exactly. In contrast to the nonlinear optimization algorithms, our approach, via the block Macaulay matrix, allows us to find the globally optimal point of the identification problem. We started by exploring the available literature related to the multiparameter eigenvalue problem and its application in system identification. There has already been research covering this topic, specifically, Vermeersch & De Moor have provided results for the ARMA problem identification. The current master thesis aims to reach one step further and provide solutions for the more general case, the ARMAX model. Next, we provided a general overview of the multiparameter eigenvalue problem. We started with the standard eigenvalue problem. Then, we moved on to the more complex polynomial eigenvalue problem. Finally, we looked at the multiparameter eigenvalue problem, which is a generalization of the problems previously mentioned. The process to solve these problems can be summarized in three steps: -Use forward shift recursion to create a structured matrix. -Generate the null space of the structured matrix. -Exploit the shift-invariance property of the null space of the structured matrix. After studying the multiparameter eigenvalue problem, we shifted our attention to the identification problem of ARMAX models. We showed that the optimization problem involved to estimate the parameters of the model can be expressed as a multiparameter eigenvalue problem. Then, we developed the procedure to solve this multiparameter eigenvalue problem as a MATLAB toolbox. In addition, we discussed practical elements of the implementation and provided a memory efficient approach based on sparse matrices in MATLAB and the QR decomposition. We compared our method with the default state-of-the-art armax function supported by MATLAB's system identification toolbox. We tested the performance of both methodologies on the models MA(1), MA(2), ARMA(1,1), and ARMAX(1,1,1). We found that, on the one hand, when both methodologies identify the same stationary point, our approach generated a solution with higher precision than its counterpart. On the other hand, when the procedures find different solutions, our method is able to find a stationary local minimal point of the loss function, while the armax function fails to achieve this.