Is Persistent Entropy Simply a Volatility Proxy? Evidence from the WIG20 Index
Is Persistent Entropy Simply a Volatility Proxy? Evidence from the WIG20 Index

Summary/Abstract: Aim: This article investigates whether persistent homology and persistence entropy capture structural properties of financial time series beyond variance-based risk measures. Using data from the WIG20 index (2019–2024), the study examines whether topological descriptors reflect intrinsic geometric and temporal organization rather than merely volatility intensity. Methodology: Logarithmic returns are embedded using sliding-window delay coordinates and analysed with Vietoris–Rips persistent homology. Betti numbers, persistence diagrams and rolling 𝐻₁ persistence entropy are computed. Relationships with classical risk diagnostics are evaluated using linear correlations, nonlinear dependence measures, regime comparisons and shuffle-based tests. Results: Persistence entropy shows weak association with volatility and second-moment risk. Stronger relationships appear with higher-order distributional characteristics such as skewness and kurtosis. Volatility-based regimes do not significantly separate entropy, whereas a structural split around the 2022 geopolitical shock reveals a significant increase, indicating a shift in return geometry. Shuffle experiments confirm dependence on temporal ordering. Implications: Persistence entropy captures structural and temporal organization of financial returns and may complement classical econometric risk measures. Originality/value: The study shows that persistent homology reflects structural organization of return dynamics rather than acting as a volatility proxy.

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