Abstract In the paper, we first thoroughly examine and prove properties of the participation index of spatio-temporal sequential patterns. Then, we introduce notions of a closure of a spatio-temporal sequential pattern and a closed spatio-temporal sequential pattern, as well as investigate and prove their properties. In particular, we prove that the set of all participation index strong closed spatio-temporal sequential patterns constitues a lossless representation of all participation index strong spatio-temporal sequential patterns. We also propose an algorithm, called CST-SPMiner, for discovering all participation index strong closed spatio-temporal sequential patterns. CST-SPMiner is an adaptation of the STBFM algorithm, which was proposed recently for the discovery of spatio-temporal sequential patterns with high participation index. While STBFM uses the CSP-tree structure for time-efficient candidate patterns generation and evaluation, CST-SPMiner uses it also for fast identification of closed patterns. Efficiency and effectiveness of our algorithm were verified on real crime data for Boston.