Which sovereign and sector signals statistically predict others? Granger causality tests whether past values of X improve prediction of Y beyond Y's own history. An arrow X→Y means X Granger-causes Y.
Causal Leaders
These entities' signals lead all others
Causal Followers
These entities react to others' movements
Causality Matrix
Row → Column: row entity Granger-causes column entity
| FROM \ TO | 🇺🇸 | 🇪🇺 | 🇩🇪 | 🇫🇷 | 🇮🇹 | 🇨🇳 | 🇷🇴 | 🇹🇷 | 🇯🇵 | 📊 | 📊 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 🇺🇸 United S | — | · | · | · | · | · | · | · | · | · | · |
| 🇪🇺 European | · | — | · | · | · | · | · | · | · | · | · |
| 🇩🇪 Germany | · | · | — | · | · | · | · | · | · | · | · |
| 🇫🇷 France | · | · | · | — | · | · | · | · | · | · | · |
| 🇮🇹 Italy | · | · | · | · | — | · | · | · | · | · | · |
| 🇨🇳 China | · | · | · | · | · | — | · | · | · | · | · |
| 🇷🇴 Romania | · | · | · | · | · | · | — | · | · | · | · |
| 🇹🇷 Turkey | · | · | · | · | · | · | · | — | · | · | · |
| 🇯🇵 Japan | · | · | · | · | · | · | · | · | — | · | · |
| 📊 Banking | · | · | · | · | · | · | · | · | · | — | · |
| 📊 Sovereig | · | · | · | · | · | · | · | · | · | · | — |
Colored cells = p < 0.05 significant at lag-2. F-statistic shown. Red = strong (F>10), amber = moderate (F>5), gold = weak (F>2).
Methodology
VAR(p) Model
Y_t = Σ α_i·Y₀₍t-i₎ + Σ β_i·X₀₍t-i₎ + ε
Fitted via OLS with Gaussian elimination. Lag p=2 by default.
F-Statistic Test
F = [(RSS_r − RSS_u)/p] / [RSS_u/(T−2p−1)]
Compared against F(p, T−2p−1) distribution. p<0.05 = significant.
Series Derivation
32-point quasi-series derived from SIGMA sub-scores and entity text hash. Captures structural risk fingerprint.