Here we introduce Local Topological Recurrence Analysis (LoTRA), a simple computational approach for analyzing time-series data. Its versatility is elucidated using simulated data, Parkinsonian gait, and in vivo brain dynamics. We also show that this algorithm can be used to build a remarkably simple machine-learning model capable of outperforming deep-learning models in detecting Parkinson’s disease from a single digital handwriting test.