Nonlinear Autoregressive Modelling: Theory

A relation between the Akaike criterion and reliability of parameter estimates, with application to nonlinear autoregressive modelling of ictal EEG

Jonathan D. Victor and Annemarie Canel

Annals of Biomedical Engineering 20, 167-180 (1992)


The Akaike minimum information criterion provides a means to determine the appropriate number of lags in a linear autoregressive model of a time series. We show that the Akaike criterion is closely related to the reliability estimates of successively determined parameters of an LAR model. A similar criterion may be applied to determine whether the addition of a nonlinear term to an LAR model provides a statistically significant improvement in the description of the time series. As an example, we use this method to identify quadratic contributions to a nonlinear autoregressive characterization of a typical 3/sec spike and wave seizure discharge.

Background on nonlinear autoregressive analysis
Related publication: Further analysis of 3/sec spike and wave seizures
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