Paper: arXiv 2304.06877

Authors: Samuel W. Akingbade, Marian Gidea, Matteo Manzi, Vahid Nateghi

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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper offers an intriguing theoretical bridge between Topological Data Analysis (TDA) and the Log-Periodic Power Law Singularity (LPPLS) model to explain why TDA works for bubble detection. While the heuristic argument is mathematically solid and illustrated via a Bitcoin case study, the empirical section remains primarily illustrative rather than a exhaustive, large-sample backtest.

Research Flowchart

  flowchart TD
    A[Research Goal: Explain why TDA detects financial bubbles] --> B[Input Data: Bitcoin historical price series]
    B --> C[Fit Log-Periodic Power Law Singularity LPPLS Model]
    C --> D[Analyze Super-Exponential Growth & High-Frequency Oscillations]
    D --> E[Apply Topological Data Analysis TDA]
    E --> F[Generate Early Warning Signals for Critical Transitions]
    F --> G[Outcome: LPPLS fit guarantees TDA early warning signal detection]