Paper: arXiv 2512.02352

Authors: Michał Sikorski

Abstract

Volatility clustering is one of the most robust stylized facts of financial markets, yet it is typically detected using moment-based diagnostics or parametric models such as GARCH. This paper shows that clustered volatility also leaves a clear imprint on the time-reversal symmetry of horizontal visibility graphs (HVGs) constructed on absolute returns in physical time. For each time point, we compute the maximal forward and backward visibility distances, $L^{"+"}(t)$ and $L^{"-"}(t)$, and use their empirical distributions to build a visibility-asymmetry fingerprint comprising the Kolmogorov–Smirnov distance, variance difference, entropy difference, and a ratio of extreme visibility spans. In a Monte Carlo study, these HVG asymmetry features sharply separate volatility-clustered GARCH(1,1) dynamics from i.i.d.\ Gaussian noise and from randomly shuffled GARCH series that preserve the marginal distribution but destroy temporal dependence; a simple linear classifier based on the fingerprint achieves about 90% in-sample accuracy. Applying the method to daily S&P500 data reveals a pronounced forward–backward imbalance, including a variance difference $Δ\mathrm{“Var”}$ that exceeds the simulated GARCH values by two orders of magnitude and vanishes after shuffling. Overall, the visibility-graph asymmetry fingerprint emerges as a simple, model-free, and geometrically interpretable indicator of volatility clustering and time irreversibility in financial time series.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces moderately advanced graph theory and statistical measures (e.g., Kolmogorov-Smirnov, entropy) but lacks implementation details or robust backtesting beyond a single empirical application, placing it between theoretical modeling and limited empirical validation.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Structural Indicator of<br>Volatility Clustering"] --> B["Methodology:<br>Horizontal Visibility Graphs on<br>Absolute Returns"]
  B --> C["Compute Asymmetry Metrics<br>KS Distance / Var Diff / Entropy Diff"]
  C --> D["Simulation:<br>GARCH(1,1) vs. i.i.d. vs. Shuffled Data"]
  D --> E["Application:<br>Real S&amp;P 500 Daily Data"]
  E --> F["Key Outcome:<br>Model-Free Geometric Indicator<br>Identifies Volatility Clustering"]
  F --> G["Key Finding:<br>Imbalance vanishes after shuffling<br>Proves Temporal Dependence"]