Finding how human brains work has always been fascinating and challenging to researchers for a long time. As the computer technology advances in the last several decades, brain computer interface (BCI) is now an important area for brain research and practice. Neurological phenomena that are special features of brain activity appearing the brain signals is the source for controlling BCI systems. Various methods have been used to capture the brain signals and analyze the neurological phenomena. One of the method is Electroencephalography (EEG) that is the recording of electrical activities along the surface of scalp. The EEG signals are usually contaminated with artifacts due to noise and biological reasons such as eye movements. These artifacts need to be detected and removed so that the signal data are clean for further analysis. In this paper, we investigate the problem of detecting closed and open eyes from EEG signals. There are a lot of eye blink detection research in the literature but most of those studies used EEG devices with multiple channels. Using a multi-channel EEG device helps increasing the accuracy but some operations such as feature selection or mounting the EEG device into the subject's head, become more complex and time consuming. In this study, we focus on analyzing ocular activity using an EEG device with only one channel.