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The true model orders are noted for different speakers.

The estimated model orders are presented after the error of the ARopt in parenthesis.

The range of the model orders are noted for the different speakers.

For all subjects, the used simulation AR model orders are shown in the first line, e.g., order 49 was given for the first male speaker, M 1(49).

In both ESPRIT and root MUSIC, the model orders are set as K, and the covariance matrix orders are M/ 2 according to [32].

In this paper, the corresponding covariance expressions for the system matrix estimates at multiple model orders are derived and successfully applied on real vibration data.

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Ten-second model orders were adopted to account for delay that may arise due to differences between time series in the hemodynamic response.

The BIC matrix calculations show that the best ARIMAX model order are equal to (1, 0, 2).

Important issues concerning the generation of the data set and the estimation of the model order are discussed.

Commonly used information criteria to estimate the model order are inadequate, as we demonstrated in this study.

(3) The best AR model order is determined based on the final prediction error (FPE) and the Akaike's information criteria (AIC).

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