This study offers a novel and efficient measure based on a higher order version of autocorrelative signal memory that can identify nonlinearities in a single time series . The suggested method was applied to simultaneously recorded subthalamic nucleus (STN) local field potentials (LFP) and magnetoencephalography (MEG) from fourteen Parkinson's Disease (PD) patients who underwent surgery for deep brain stimulation . Recordings were obtained during rest for both OFF and ON dopaminergic medication states . We analyzed the bilateral LFP channels that had the maximum beta power in the OFF state and the cortical sources that had the maximum coherence with the selected LFP channels in the alpha band . Our findings revealed the inherent nonlinearity in the PD data as subcortical high beta (20 - 30 Hz) band and cortical alpha (8 - 12 Hz) band activities . While the former was discernible without medication (p=0.015), the latter was induced upon the dopaminergic medication (p <6.10). The degree of subthalamic nonlinearity was correlated with contralateral tremor severity (r=0.45, p=0.02). Conversely, for the cortical signals nonlinearity was present for the ON medication state with a peak in the alpha band and correlated with contralateral akinesia and rigidity (r=0.46, p=0.02). This correlation appeared to be independent from that of alpha power and the two measures combined explained 34% of the variance in contralateral akinesia scores . Our findings suggest that particular frequency bands and brain regions display nonlinear features closely associated with distinct motor symptoms and functions.