There have been many studies on intelligent robotic systems for patients with motor impairments, where different sensor types and different human-machine interface (HMI) methods have been developed. However, these studies fail to achieve complex activity detection at the minimum sensing level. In this paper, exploratory approaches are adopted to investigate ocular activity dynamics and complex activity estimation using a single-channel EOG device. First, the stationarity of ocular activities during a static motion is investigated and some activities are found to be non-stationary. Further, no statistical difference is found between the envelope sequences in the temporal domain. However, when utilized as an alternative to a low-pass filter, high-frequency harmonic components in the frequency domain are found to improve contrasting ocular activities and the performance of the EOG-HMI-based activity detection system substantially. The activities are trained with different classifiers and their prediction success is evaluated with leave-one-session-out cross-validation. Accordingly, the two-dimensional CNN model achieved the highest performance with the accuracy of 72.35\%. Furthermore, the clustering performance is assessed using unsupervised learning and the results are evaluated in terms of how well the feature sets are grouped. The system is further tested in real-time with the graphical user interface and the scores and survey data of the subjects are used to verify the effectiveness.