# Topological Data Analysis (TDA) for Time Series

**Authors:** Nalini Ravishanker, Renjie Chen  
**arXiv:** [1909.10604](https://arxiv.org/abs/1909.10604)  
**Date:** 2019-09-23  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1909.10604v1/

## Key points

- Topological Data Analysis (TDA) is a set of powerful tools that utilize topological features in data
- TDA has gained considerable momentum in recent years
- TDA can be applied to time series analysis
- The authors describe a method where they apply TDA independently to each daily log-price cryptocurrency time series
- Feature vectors used for K-means clustering include log-price time series, first difference of log-price values, and L1 norm
- This method has the potential to recognize critical transitions in cryptocurrency markets before market crashes
- Potential research extensions for TDA include exploring its applications for multivariate time series analysis, using summary statistics and dissimilarity measures, and improving computation tools in computational topology
- Ongoing research areas include computational homology and statistical inference to enhance capabilities of TDA in analyzing complex datasets and making predictions based on topological features
- TDA is useful in measuring topological features of time series data and its applications include pattern detection, clustering, classification, and structural break detection.

## Summary

This article provides a comprehensive overview of Topological Data Analysis (TDA) for time series. TDA is a set of powerful tools that utilize topological features in data, such as connected components, tunnels, and voids. While the study of topology is traditionally a topic in pure mathematics, TDA has gained considerable momentum in recent years. The authors focus on the application of TDA to time series analysis. They describe a method where they apply TDA independently to each daily log-price cryptocurrency time series. They use a combination of the log-price time series, the first difference of the log-price values, and the L1 norm as feature vectors for K-means clustering with 18 clusters. By identifying topologically distinct regimes before market crashes, this method has the potential to recognize critical transitions in cryptocurrency markets. The paper also discusses potential research extensions for TDA such as exploring its applications for multivariate time series analysis; using summary statistics and dissimilarity measures for TDA; and improving computation tools in computational topology. The authors highlight ongoing research areas such as computational homology which involves studying topological summaries and statistical inference to enhance capabilities of TDA in analyzing complex datasets and making predictions based on topological features. In summary, this article highlights the usefulness of TDA in measuring topological features of time series data and its applications in pattern detection, clustering, classification and structural break detection.