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Electroencephalogram (EEG) signal analysis plays an essential role in detecting and understanding epileptic seizures. It is known that seizure processes are nonlinear and non-stationary, discriminating between rhythmic discharges and dynamic change is a challenging task in EEG-based seizure detection. In this paper, a new time-varying (TV) modeling framework, based on an autoregressive (AR) model structure, is proposed to characterize and analyze EEG signals. The TV parameters of the AR model are approximated through a multi-wavelet basis function expansion (MWBF) approach. An effective ultra-regularized orthogonal forward regression (UROFR) algorithm is employed to significantly reduce and refine the resulting expanded model. Given a time-varying process, the proposed TVAR–MWBF–UROFR method can generate a parsimonious TVAR model, based on which a high-resolution power spectrum density (PSD) estimation can be obtained. Informative features are then defined and extracted from the PSD estimation. The TVAR–MWBF–UROFR method is applied to a number of real EEG datasets; features obtained from these datasets are then used for seizure detection and classification. To make the results more accurate and reliable, a PCA algorithm is adopted to select the optimal feature subset, and a Bayesian optimization technique based on the Gaussian process is performed to determine the coefficients associated with each of the classifiers. The performance of the proposed method is tested on two benchmark datasets, and the experimental results indicate that TVAR–MWBF–UROFR outperforms the compared state-of-the-art classifiers in terms of accuracy, specificity, sensitivity and robustness.