Parkinson's Disease (PD) is a progressive neurodegenerative disease with multiple motor and non-motor characteristics. PD patients commonly face vocal impairments during the early stages of the disease. In this article, the aim is to explain the Unified Parkinson's Disease Rating Scale (UPDRS) as a measure of the progression of Parkinson's disease using a set of covariates obtained from voice signals. In particular, a Support Vector Regression (SVR) model based on a combination of kernel functions is introduced. Theoretically, this proposal, that relies on a mixed kernel (global and local) produces an admissible kernel function. The optimal fitting was obtained for the combination given by the product of radial and polynomial basis. Important results are the non-linear relationships inferred from the features to the response, as well as a considerable improvement in prediction performance metrics, when compared to other learning approaches. Furthermore, with knowledge on factors such as age and gender, it is possible to describe the dynamics of patients' UPDRS from the data collected during their monitoring. In summary, these advances could expand learning processes and intelligent systems to assist in monitoring the evolution of Parkinson's disease.