We propose a nonparametric framework for analyzing and modeling dynamic postural shifts of human subjects. The postural shifts are represented in the phase space using time-delay embeddings and novel shape-theoretic features are extracted. The proposed multiscale descriptors are used as discriminative features to differentiate dynamical systems. The descriptors are simple and easy to compute, and model the multiscale characteristics of the attractor's multi-dimensional shape measurements. We demonstrate the usefulness of these features by using them to classify subjects into healthy and those affected by Parkinson's disease. We also use these features to assess the severity of the disease. In all these use cases, the proposed multiscale features perform better than their global counterparts.