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In this study, new approaches for the identification of finite impulse response (FIR) systems using higher-order statistics are proposed. The unknown model parameters are obtained using optimisation algorithms. In fact, the proposed method consists first in defining an optimisation problem and second in using an appropriate algorithm to resolve it. Moreover, a new method is developed for estimating the order of FIR models using only the output cumulants. The results presented in this study illustrate the performance of the proposed methods and compare them with a range of existing approaches.