This paper focuses on a classification problem for volatile time series. One of the most popular approaches for time series classification is dynamic time warping and feature-based machine learning architectures. In many previous studies, these algorithms have performed satisfactorily on various datasets. However, most of these methods are not suitable for chaotic time series because the superficial changes in measured values are not essential for chaotic time series. In general, most time series datasets include both chaotic and non-chaotic time series; thus, it is necessary to extract the more essential features of a time series. In this paper, we propose a new approach for volatile time series classification. Our approach generates a novel feature by extracting the structure of the attractor using topological data analysis to represent the transition rules of the time series. As this feature represents the essential property of systems of the time series, our approach is effective for both chaotic and non-chaotic types. We applied a learning architecture inspired by a convolutional neural network to this feature and found that the proposed approach improves performance in a human activity recognition problem by 18.5% compared with conventional approaches.