2026/03/24 by von Mallinckrodt, Bernd · 1 voice
Environmental Science · Physics and Astronomy · Economics, Econometrics and Finance · #Ecosystem dynamics and resilience #Chaos control and synchronization #Complex Systems and Time Series Analysis
paper · doi:10.5281/zenodo.19205083
openalex publication_date 2026/03/24 · openalex created_date 2026/03/25 · openalex updated_date 2026/07/01
This technical note investigates boundary conditions of ratio-based composite indicators in the context of early warning signals for critical transitions. Composite indicators of the form T(t) = X1(t) / X2(t) are often interpreted as amplifying signal by combining multiple observables. Using a pre-registered simulation framework and analytically tractable Ornstein–Uhlenbeck-type systems, we show that such ratio constructions are not sign-invariant: the direction and interpretability of the resulting trend depend critically on the assignment of numerator and denominator. Even under conditions where the component observables exhibit structural–dynamic separability, the ratio may suppress or invert the expected signal if the signal-dominant component appears in the denominator. We formalize this phenomenon as a role-assignment constraint and demonstrate that ratio-based composite indicators can exhibit identical magnitude behavior but opposite trend direction depending on formulation (e.g., R/Φ vs. Φ/R). This result is distinct from previously identified coupling-based failure modes and establishes an additional boundary condition for the admissibility of composite indicators. The findings imply that composite early warning indicators should not be evaluated solely on component selection or separability conditions, but also on the functional form of aggregation. In particular, ratio-based indicators require explicit consideration of sign consistency and signal attribution prior to deployment. This work complements earlier falsification-first analyses by identifying a structural limitation of ratio-type composites and provides a methodological basis for evaluating aggregation schemes in complex dynamical systems. composite indicators early warning signals critical transitions ratio indicators sign non-invariance structural–dynamic separability role assignment complex systems Ornstein–Uhlenbeck process covariance structure autocorrelation information redundancy bifurcation analysis multivariate indicators falsification-first