Combine these into a composite Early Warning Index (EWI):
EWI(t)=wacAC1(P,t)+wvarVar(P,t)+wskSkew(P,t)+wr1r^t>rc\mathrm{EWI}(t) = w_{ac}\,\mathrm{AC1}(P,t) + w_{var}\,\mathrm{Var}(P,t) + w_{sk}\,\mathrm{Skew}(P,t) + w_r\,\mathbb{1}_{\hat r_t>r_c}
where weights ww are chosen via historical backtesting.
4. Phase diagram construct (operational)
Construct a 2-D phase diagram with axes:
x-axis: policy lever ratio rr (coercion vs relief responsiveness).
y-axis: economic stress EE (normalized index).
Overlay contours of Pr(P>Pc within 30d)\Pr(P>P_c\ \text{within }30\text{d}) from ensemble outputs. The diagram shows regions:
Safe: low rr, low EE containment.
Fragile: moderate rr, moderate EE multistability; sensitive to shocks.
Danger: high rr, high EE high probability of chaotic transition.
This diagram is both diagnostic and prescriptive: moving coordinates left/down (increase relief speed or reduce stress) reduces probability of transition.
5. Spatial & network amplification
Regional heterogeneity and network topology modulate the phase boundary:
