Why Topological Data Analysis Detects Financial Bubbles?
Statistical Finance
2023-04-17 v1 Dynamical Systems
Physics and Society
Abstract
We present a heuristic argument for the propensity of Topological Data Analysis (TDA) to detect early warning signals of critical transitions in financial time series. Our argument is based on the Log-Periodic Power Law Singularity (LPPLS) model, which characterizes financial bubbles as super-exponential growth (or decay) of an asset price superimposed with oscillations increasing in frequency and decreasing in amplitude when approaching a critical transition (tipping point). We show that whenever the LPPLS model is fitting with the data, TDA generates early warning signals. As an application, we illustrate this approach on a sample of positive and negative bubbles in the Bitcoin historical price.
Keywords
Cite
@article{arxiv.2304.06877,
title = {Why Topological Data Analysis Detects Financial Bubbles?},
author = {Samuel W. Akingbade and Marian Gidea and Matteo Manzi and Vahid Nateghi},
journal= {arXiv preprint arXiv:2304.06877},
year = {2023}
}