Why Topological Data Analysis Detects Financial Bubbles?

TL;DR

This paper argues that Topological Data Analysis can effectively detect early warning signals of financial bubbles by analyzing the geometric features of price data modeled by the LPPLS framework, demonstrated on Bitcoin prices.

Contribution

It introduces a heuristic connection between TDA and the LPPLS model for early bubble detection in financial time series.

Findings

TDA generates early warning signals when fitting the LPPLS model.

Application to Bitcoin data shows TDA's effectiveness in identifying bubbles.

TDA captures geometric features indicative of critical transitions.

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.