Rest tremor is a most common symptom of Parkinson’s Disease (PD), with diagnosis and severity estimation often being hindered by subjectivity and limitations of existing methods. Additionally, treatment strategies for PD face challenges in monitoring symptom fluctuations with clinical methods, like the MDS-UPDRS and motor diaries, suffering from subjectivity, limited sensitivity, and infrequent sampling, potentially impacting treatment effectiveness. Hence, methods that can yield explainable biomarkers that accurately describe properties of PD rest tremor, while accounting for the presence of ongoing treatments, such as Deep Brain Stimulation (DBS) and medication, are important for integration in accurate AI-powered wearable systems. To that end, a Higher Order Spectrum (HOS)-based analysis to extract features from index finger velocity recordings of 16 PD patients is proposed. Two different scenarios are implemented for characterizing and classifying treatment (medication/DBS) effectiveness and tremor severity (Low-/High- Amplitude (LAT/HAT)), by means of statistical tests and a leave-one-subject-out cross-validation classification scheme, respectively. The proposed analysis resulted in area under the Receiver Operating Characteristics curve (AUC) score of 0.94 for the Medication treatment classification, 0.71 for the DBS treatment and 0.83 for LAT/HAT prediction. Our results demonstrate that the proposed approach can effectively assess the influence of medication and DBS and recognize rest tremor severity. Finally, our HOS-based methodology enables the establishment of new rest tremor classes, based on its nonlinearity and allows for new insights about the dynamic nature of the resting tremor production system.