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Nearly 1% of the world population in all ages suffer from epilepsy. An automatic seizure detection system is an important tool, which helps diagnose epilepsy. In this study, a new approach for epileptic detection based on generalised autoregressive conditional heteroscedasticity (GARCH) model is proposed. First, the electroencephalogram (EEG) signals are decomposed into the frequency sub-bands using wavelet transform. To choose an efficient statistical model for EEG signal wavelet coefficients, the statistical characteristics of these coefficients are studied. The authors show that these coefficients are heteroscedastic. To capture this important property, GARCH model, that is, heteroscedastic, is employed for these coefficients. Moreover, the authors show that GARCH model is compatible with other properties of wavelet coefficients such as heavy tail marginal distribution. GARCH parameters are calculated for each sub-band to represent the wavelet coefficients% distribution of EEG signals. These parameters are then utilised for EEG classification. Next, Markov random field is used to feature selection. The features found are then fed to multilayer perceptron classifier with three discrete outputs: healthy volunteers, epilepsy patients during seizure-free interval and epilepsy patients during seizure. The results clearly indicate that the performance of the new method in classification of EEG signals outperforms previous methods.