Why topological data analysis detects financial bubbles?

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. •We justify the TDA method in terms of a deterministic model for financial bubbles.•Whenever the LPPLS model fits the data, the TDA method yields early warning signals.•We compare the LPPLS model and the TDA method when applied to Bitcoin bubbles.