A Rate Mismatch Criterion for Early Warning of Critical Transitions: Cross-Domain Validation, Boundary Conditions, and a Variance–Autocorrelation Coupling Framework for Criterion Applicability
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2026
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| _version_ | 1866901565337501696 |
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| author | Malone, Ryan |
| author_facet | Malone, Ryan |
| contents | <p>Critical slowing down (CSD) theory predicts that systems approaching catastrophic tipping points<br>exhibit rising variance and rising lag-1 autocorrelation (AR1) in observable time series. Joint early<br>warning criteria based on simultaneous elevation of both signals have been applied across complex<br>systems, but a systematic test of the assumption underlying all joint criteria — that variance and<br>AR1 are positively coupled before transitions — has not been reported across diverse system types.<br>We address two gaps. First, we apply the Rate Mismatch Criterion (RMC), a single operationalised<br>joint criterion, to 187 documented collapse events across 14 mechanistically distinct domains<br>spanning physical, biological, ecological, and financial systems, evaluating performance with hit<br>rates (Wilson 95% CIs), false positive rates, and ROC-based AUC metrics. Hit rates ranged from<br>100% in theoretical models (Ising, climate) to 0% in snap-transition domains (ecological, sepsis),<br>with warning times from 38 minutes (epileptic seizures) to 305 days (corporate fraud). Second, we<br>directly test the coupling assumption by computing variance–AR1 correlations across four domain<br>types with bootstrap confidence intervals. We identify three empirically distinct coupling regimes:<br>near-zero in financial time series (r = 0.039, CI [0.035, 0.043], N = 8,785) and within-subject sleep<br>EEG (r = 0.044, CI [−0.014, 0.103]); significant negative in cross-subject physiological variation<br>(r = −0.236, CI [−0.339, −0.149]); and strong positive in epileptic brain dynamics (r = 0.682, CI<br>[0.568, 0.764] in one subject; heterogeneous across subjects). We derive a mean-reversion<br>boundary condition from the Ornstein-Uhlenbeck model that predicts variance-only precursors in<br>financially mean-reverting systems, confirmed by ROC analysis (variance-only AUC = 0.86–0.88<br>vs. joint RMC AUC = 0.51–0.60). These results establish coupling structure as a system-level<br>diagnostic property and motivate a pre-screening framework: characterise coupling before<br>applying any joint early warning criterion, and select the criterion variant appropriate to the<br>observed regime.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19817224 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Rate Mismatch Criterion for Early Warning of Critical Transitions: Cross-Domain Validation, Boundary Conditions, and a Variance–Autocorrelation Coupling Framework for Criterion Applicability Malone, Ryan critical slowing down early warning signals rate mismatch criterion variance autocorrelation tipping points complex systems financial markets epiliepsy cross domain <p>Critical slowing down (CSD) theory predicts that systems approaching catastrophic tipping points<br>exhibit rising variance and rising lag-1 autocorrelation (AR1) in observable time series. Joint early<br>warning criteria based on simultaneous elevation of both signals have been applied across complex<br>systems, but a systematic test of the assumption underlying all joint criteria — that variance and<br>AR1 are positively coupled before transitions — has not been reported across diverse system types.<br>We address two gaps. First, we apply the Rate Mismatch Criterion (RMC), a single operationalised<br>joint criterion, to 187 documented collapse events across 14 mechanistically distinct domains<br>spanning physical, biological, ecological, and financial systems, evaluating performance with hit<br>rates (Wilson 95% CIs), false positive rates, and ROC-based AUC metrics. Hit rates ranged from<br>100% in theoretical models (Ising, climate) to 0% in snap-transition domains (ecological, sepsis),<br>with warning times from 38 minutes (epileptic seizures) to 305 days (corporate fraud). Second, we<br>directly test the coupling assumption by computing variance–AR1 correlations across four domain<br>types with bootstrap confidence intervals. We identify three empirically distinct coupling regimes:<br>near-zero in financial time series (r = 0.039, CI [0.035, 0.043], N = 8,785) and within-subject sleep<br>EEG (r = 0.044, CI [−0.014, 0.103]); significant negative in cross-subject physiological variation<br>(r = −0.236, CI [−0.339, −0.149]); and strong positive in epileptic brain dynamics (r = 0.682, CI<br>[0.568, 0.764] in one subject; heterogeneous across subjects). We derive a mean-reversion<br>boundary condition from the Ornstein-Uhlenbeck model that predicts variance-only precursors in<br>financially mean-reverting systems, confirmed by ROC analysis (variance-only AUC = 0.86–0.88<br>vs. joint RMC AUC = 0.51–0.60). These results establish coupling structure as a system-level<br>diagnostic property and motivate a pre-screening framework: characterise coupling before<br>applying any joint early warning criterion, and select the criterion variant appropriate to the<br>observed regime.</p> |
| title | A Rate Mismatch Criterion for Early Warning of Critical Transitions: Cross-Domain Validation, Boundary Conditions, and a Variance–Autocorrelation Coupling Framework for Criterion Applicability |
| topic | critical slowing down early warning signals rate mismatch criterion variance autocorrelation tipping points complex systems financial markets epiliepsy cross domain |
| url | https://doi.org/10.5281/zenodo.19817224 |