TDA for Time Series & Dynamics
Topological signatures for finance, climate, and fluid dynamics.
Topological data analysis is unusually well-suited to non-linear time series and dynamical systems: a sliding window in phase space carries the topology of an underlying attractor, and that topology often changes sharply at the very moments—regime transitions, crashes, onsets—that domain scientists most want to detect.
The work in this project applies TDA to three classes of data:
- Climate. Predicting the onset and withdrawal of the Indian monsoon from historical wind data; topological signatures of the polar vortex and Montana weather.
- Statistical finance. Identifying extreme events in the stock market; complex-network analysis of cryptocurrency crashes; causality of COVID-19-induced market crashes.
- Fluid mechanics. Topological characterization of churn flow and unsupervised correction to flow-regime maps in vertical pipes.
Collaborators
- Md. Nurujjaman, NIT Sikkim
- Atish Mitra, Montana Technological University
- Joshua Dorrington, Kristian Strommen, Maria Sánchez Muniz—climate
- Anish Rai, Buddha Nath Sharma, Salam Rabindrajit Luwang—finance
- Brady Koenig, Burt Todd—fluid mechanics
- Chittaranjan Hens, Kanish Debnath, Kundan Mukhia
Publications
[1]
K. Mukhia, A. Rai, S. R. Luwang, M. Nurujjaman, S. Majhi, and C. Hens, “Complex network analysis of cryptocurrency market during crashes,” Physica A, vol. 653, no. 130095, p. 130095, Nov. 2024, doi: https://doi.org/10.1016/j.physa.2024.130095
[2]
A. Rai, B. Nath Sharma, S. Rabindrajit Luwang, M. Nurujjaman, and S. Majhi, “Identifying extreme events in the stock market: A topological data analysis,” Chaos, vol. 34, no. 10, Oct. 2024, doi: https://doi.org/10.1063/5.0220424
[3]
A. Rai, A. Mahata, M. Nurujjaman, S. Majhi, and K. Debnath, “A sentiment-based modeling and analysis of stock price during the COVID-19: U- and swoosh-shaped recovery,” Physica A: Statistical Mechanics and its Applications, vol. 592, p. 126810, 2022, doi: https://doi.org/10.1016/j.physa.2021.126810