Generalized fractional cumulative residual dispersion entropy: A novel feature extraction method for complex signals

Building early-warning systems and cross-asset rankings for financial markets requires complexity measures that respond to regime transitions and stress-driven tail events while remaining stable under heavy-tailed returns and data contamination. We introduce a generalized fractional cumulative residual dispersion entropy (GFCRDE), a unified complexity statistic that combines dispersion-pattern symbolization, cumulative-residual tail aggregation, and fractional-order information weighting on decumulative tail sums. As the fractional order tends to zero, the formulation reduces to classical cumulative-residual entropy, while the same kernel extends naturally to network embeddings so that scalar time-series measures and network-based readouts remain comparable. We assess the proposed measure on synthetic benchmark processes, controlled perturbation stress tests, and daily closing prices from ten major equity indices during 2014–2025, and compare it with several representative entropy-based benchmarks, including cumulative-residual entropy, generalized fractional cumulative-residual entropy, weighted permutation entropy, and refined composite multiscale dispersion entropy. On the equity panel, GFCRDE attains higher adjacent-month ranking stability and yields entropy surges at or ahead of multiple documented stress episodes, including the Greek debt crisis, the 2015–2016 China stock market turmoil, the COVID-19 pandemic shock, and the 2023 Silicon Valley Bank banking stress. Network-level variants preserve concordant orderings across perturbation families, and at small-to-moderate contamination intensities GFCRDE provides improved robustness relative to cumulative-residual entropy while maintaining cross-asset variability comparable to generalized fractional cumulative-residual extensions. Overall, the framework offers a coherent way to monitor structurally complex and incompletely observed financial systems using both scalar and network-based complexity readouts.