Background and objectives: Parkinson's disease is a neurological disorder that affects the motor system producing lack of coordination, resting tremor, and rigidity. Impairments in handwriting are among the main symptoms of the disease. Handwriting analysis can help in supporting the diagnosis and in monitoring the progress of the disease. This paper aims to evaluate the importance of different groups of features to model handwriting deficits that appear due to Parkinson's disease; and how those features are able to discriminate between Parkinson's disease patients and healthy subjects. Methods: Features based on kinematic, geometrical and non-linear dynamics analyses were evaluated to classify Parkinson's disease and healthy subjects. Classifiers based on K-nearest neighbors, support vector machines, and random forest were considered. Results: Accuracies of up to $93.1\%$ were obtained in the classification of patients and healthy control subjects. A relevance analysis of the features indicated that those related to speed, acceleration, and pressure are the most discriminant. The automatic classification of patients in different stages of the disease shows $κ$ indexes between $0.36$ and $0.44$. Accuracies of up to $83.3\%$ were obtained in a different dataset used only for validation purposes. Conclusions: The results confirmed the negative impact of aging in the classification process when we considered different groups of healthy subjects. In addition, the results reported with the separate validation set comprise a step towards the development of automated tools to support the diagnosis process in clinical practice.