In this study, polysomnographic left side EOG signals from ten control subjects, ten iRBD patients and ten Parkinson's patients were decomposed in time and frequency using wavelet transformation. A total of 28 features were computed as the means and standard deviations in energy measures from different reconstructed detail subbands across all sleep epochs during a whole night of sleep. A subset of features was chosen based on a cross validated Shrunken Centroids Regularized Discriminant Analysis, where the controls were treated as one group and the patients as another. Classification of the subjects was done by a leave-one-out validation approach using same method, and reached a sensitivity of 95%, a specificity of 70% and an accuracy of 86.7%. It was found that in the optimal subset of features, two hold lower frequencies reflecting the rapid eye movements and two hold higher frequencies reflecting EMG activity. This study demonstrates that both analysis of eye movements during sleep as well as EMG activity measured at the EOG channel hold potential of being biomarkers for Parkinson's disease.