Vocal impairments are one of the earliest disrupted modalities in Parkinson's disease (PD). Most of the studies whose aim was to detect Parkinson's disease through acoustic analysis use global parameters. In the meantime, in speaker and speech recognition, analyses are carried out by short-term parameters, and more precisely by Mel-Frequency Cepstral Coefficients (MFCC), combined with Gaussian Mixture Models (GMM). This paper presents an adaptation of the classical methodology used in speaker recognition to the detection of early stages of Parkinson's disease. Automatic analyses were performed during 4 tasks: sustained vowels, fast syllable repetitions, free speech and reading. Men and women were considered separately in order to improve the classification performance. Leave one subject out cross validation exhibits accuracies ranging from 60% to 91% depending on the speech task and on the gender. Best performances are reached during the reading task (91% for men). This accuracy, obtained with a simple and fast methodology, is in line with the best classification results in early PD detection found in literature, obtained with more complex methods.