ARMA model order estimation based on the eigenvalues of the covariance matrix

Parametric Modelling of EEG Data for the Identification of Mental Tasks

“…By contrast, they decrease significantly for orders which are greater than the true order (Liang et al, 1993). Hence if (,)…”

“…Another group of methods, which do not require prior estimation of model parameters, use eigendecomposition of the input/output data covariance matrix to estimate the model order. This approach, based on the Minimum Description Length criterion, was applied to univariate ARMA and ARX models by Liang et al (1993). The method was shown to be able to estimate the correct model order even in the presence of limited noise conditions.…”

“…They utilize a Bayesian approach and are normally very demanding computationally. The work presented in this section, which is based on the second group of methods, proposes a modified criterion to that of (Liang et al, 1993) which leads to a lower probability of error for model order estimation. As in (Lardies & Larbi, 2001), which extended Liang's method to multivariate AR models, this work will not be restricted to univariate models.…”

“…A multivariate ARMA model is given by the difference equation represents the input to the model which is a white Gaussian noise process having zero mean and covariance C, and n t R υ ∈ , which represents observation or modeling error, is also a random white noise process having covariance Q υ . Extending the approach of (Liang et al, 1993) to the multivariate case, assuming that N time samples of the output data are available, Equation (13) A and 0 B assumed to be identity matrices. In order to compose the input/output matrix , pq D , the unknown input signal t e needs to be estimated.…”

“…For the univariate case, (Liang et al, 1993) generate a column ratio (CR) and a row ratio (RR) table to identify the transition between the two regions shown in Figure 5. …”