Why Topological Data Analysis Detects Financial Bubbles?

Author

Marian Gidea

Published

December 8, 2023

Topological Data Analysis (TDA) has been applied in recent years to detect critical transitions in financial time series, particularly financial bubbles. Most of the evidence so far on the adeptness of TDA to detect financial bubbles has been empirical. In this work we propose, for the first time, a heuristic argument for why TDA detects financial bubbles. There are models from economics that assert that the time series exhibits certain oscillatory patterns when approaching the tipping point. From a topological view-point, these oscillations determine holes in the point-clouds. When approaching the tipping point of a bubble, there are significant changes in the nature of the oscillations, and consequently in the TDA output. These changes can be captured via persistence homology and yield early warning signals.

This is based on joint work with S.W. Akingbade, M. Manzi, and V. Nateghi.