Abstract The Autoregressive moving average (ARMA) model is a very efficient technique for modal parameter identification of mechanical systems, especially when the signal is noisy. However, when significant noise is present in the signal, it is necessary to increase the computational order of the ARMA model. Consequently, this artificial increase of the model order yields to a more difficult identification of the exact number of modal parameters in a given frequency range, especially when we have no prior knowledge of the behaviour of the mechanical system. A new method based on the eigenvalues of a modified covariance matrix is proposed. It is shown that the eigenvalues of the covariance matrix that lead to a minimum and constant value depending on the noise level, correspond to supplementary orders induced by the noise. Thus, the exact order of the mechanical system is revealed from the analysis of the eigenvalue magnitudes with the model order. The analysis of the gradient of the eigenvalue computed at the exact order allows also to select the minimal and necessary order used for computation, without any prior modal parameter identification. This method is robust to noise level and sensitive to the sampling frequency. Thus, the application of the proposed method at different sampling frequencies allows to select the optimal sampling frequency by reducing the lack of accuracy in the identification of modal parameters.