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Cassini / Earth Magnometer Correlation Findings

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  1. ======================================================================
  2. TEST 1: Day-of-Week Effect in SKR
  3. ======================================================================
  4.  
  5. Kruskal-Wallis H = 21339.0, p = 0.00e+00
  6. N = 363,357 records
  7.  
  8. Day Mean deviation (dex) N
  9. ------------------------------------------
  10. Mon +0.0883 53,039 ← max
  11. Tue +0.0526 53,047
  12. Sun +0.0298 51,389
  13. Wed -0.0002 52,881
  14. Sat -0.0018 49,637
  15. Thu -0.0413 52,719
  16. Fri -0.0549 50,645 ← min
  17.  
  18. Shuffle null (1000 iterations)...
  19. Observed H = 21339.0
  20. Null H: mean = 5.9, max = 19.3
  21. Empirical p = 0.0000 (1000 shuffles)
  22. → Saved: test1_dow_skr.png
  23.  
  24. ======================================================================
  25. TEST 2: 16-Minute Comb in Autocorrelation
  26. ======================================================================
  27. Median sample spacing: 60.0 seconds
  28. Computing ACF to lag 200...
  29. Envelope fit: dual-exponential (residual σ = 0.01856)
  30.  
  31. After removing smooth ACF envelope:
  32. Mean excess at multiples of 16: 0.43521
  33. Std of non-16 residuals: 0.01856
  34. Z-score of 16-min comb: 23.45
  35.  
  36. Lag Raw ACF Envelope Excess Z
  37. ---------------------------------------------
  38. 16 +0.7059 +0.1902 +0.51574 +27.8
  39. 32 +0.6730 +0.1811 +0.49186 +26.5
  40. 48 +0.6522 +0.1753 +0.47681 +25.7
  41. 64 +0.6305 +0.1701 +0.46045 +24.8
  42. 80 +0.6168 +0.1653 +0.45151 +24.3
  43. 96 +0.5985 +0.1608 +0.43766 +23.6
  44. 112 +0.5820 +0.1568 +0.42522 +22.9
  45. 128 +0.5687 +0.1530 +0.41568 +22.4
  46.  
  47. Phase-randomized surrogate null (1000 iterations)...
  48. Observed excess at 16-multiples: 0.43521
  49. Null excess: mean = 0.43499, std = 0.00009
  50. Empirical p = 0.0000
  51.  
  52. Raw ratio (for reference): 3.6× (spike/background without envelope removal)
  53. → Saved: test2_16min_comb.png
  54.  
  55. ======================================================================
  56. TEST 3: SKR–Earth Mutual Information (station: BRW)
  57. ======================================================================
  58. Common hourly bins: 6036
  59. Computing MI at 169 lags (0–336h, step=2h)...
  60. Using 24 bins, rank-transformed data, 500 shuffles/lag
  61.  
  62. Complementary Spearman correlation test...
  63. Effective sample size: 857 / 6036 (ratio = 0.142)
  64.  
  65. === MI Results ===
  66. Lags with z > 3 (block-shuffle): 0 / 169
  67. Mean z-score: 0.21
  68. Max z-score: 2.60 at lag 100h
  69.  
  70. === Spearman Results ===
  71. Lags with p < 0.001 (raw): 72 / 169
  72. Lags with p < 0.001 (n_eff adj): 0 / 169
  73. Max |r| = +0.1009 at lag 76h (p_raw = 5.76e-15, p_adj = 3.28e-03)
  74. → Saved: test3_mi_BRW.png
  75.  
  76. ======================================================================
  77. TEST 4: Directional Asymmetry (station: BRW)
  78. ======================================================================
  79. Computing directional MI at 83 lags...
  80.  
  81. Mean MI level: 0.00783 bits
  82.  
  83. Directional asymmetry (positive = SKR leads):
  84. Short lags (1–70h): -0.00118 (-15.0% of mean MI)
  85. Long lags (130–200h): -0.00268 (-34.2% of mean MI)
  86. → No sign reversal
  87. Shuffle null (200 iterations)...
  88. Overall mean asymmetry: -0.00129 (z = -3.13)
  89. Short-lag z: -2.53, Long-lag z: -4.55
  90. Null reversal rate: 44.0% (observed: NO)
  91. → Saved: test4_direction_BRW.png
  92.  
  93. ======================================================================
  94. TEST 5: SKR → Earth Prediction (station: BRW)
  95. ======================================================================
  96. Channels: 115 total, split into thirds (38 each)
  97.  
  98. Scanning 4 bands × 3 metrics × 113 lags (0–336h, 3h steps)
  99. Total valid combinations: 1356
  100.  
  101. Raw p < 0.05: 52/1356 (expected by chance: 67.8)
  102. BH-FDR q < 0.05: 1/1356
  103. BH-FDR q < 0.10: 4/1356
  104.  
  105. All combinations with raw p < 0.05:
  106. Band Metric Lag t p(raw) p(BH) d N
  107. ----------------------------------------------------------------------------
  108. high_third |dH/dt| 120h +4.668 0.000011 0.0149 +0.1716 88 *
  109. high_third |dH/dt| 102h +4.136 0.000081 0.0546 +0.1690 89
  110. high_third hourly_range 33h +3.886 0.000193 0.0740 +0.1712 92
  111. mid_third hourly_std 123h -3.849 0.000218 0.0740 -0.2549 93
  112. mid_third hourly_range 9h -3.578 0.000554 0.1502 -0.2597 93
  113. high_third hourly_range 132h +3.167 0.002126 0.4806 +0.1422 88
  114. high_third |dH/dt| 117h +3.062 0.002928 0.5658 +0.1339 88
  115. high_third |dH/dt| 132h +2.989 0.003645 0.5658 +0.1312 87
  116. high_third hourly_std 144h +2.974 0.003755 0.5658 +0.1444 93
  117. high_third hourly_std 117h +2.849 0.005404 0.6395 +0.1248 93
  118. high_third hourly_range 57h +2.834 0.005677 0.6395 +0.1608 91
  119. mid_third hourly_range 147h -2.808 0.006150 0.6395 -0.1930 88
  120. high_third hourly_std 129h +2.799 0.006250 0.6395 +0.1262 93
  121. mid_third hourly_range 33h -2.780 0.006603 0.6395 -0.1876 92
  122. high_third hourly_range 129h +2.738 0.007489 0.6738 +0.1298 89
  123. mid_third hourly_std 195h -2.694 0.008424 0.6738 -0.1911 91
  124. high_third hourly_std 132h +2.692 0.008448 0.6738 +0.1110 93
  125. high_third hourly_range 30h +2.653 0.009393 0.7076 +0.1360 93
  126. mid_third hourly_std 126h -2.618 0.010335 0.7376 -0.2150 93
  127. high_third |dH/dt| 279h +2.530 0.013307 0.8599 +0.1125 84
  128. mid_third |dH/dt| 39h -2.501 0.014191 0.8599 -0.1834 91
  129. mid_third hourly_std 198h -2.487 0.014727 0.8599 -0.1923 91
  130. mid_third |dH/dt| 195h -2.480 0.015144 0.8599 -0.1816 85
  131. high_third hourly_std 87h +2.459 0.015797 0.8599 +0.1096 94
  132. high_third |dH/dt| 15h +2.443 0.016484 0.8599 +0.1166 92
  133. high_third hourly_std 51h +2.442 0.016488 0.8599 +0.1211 95
  134. high_third hourly_range 63h +2.411 0.017930 0.8842 +0.1224 91
  135. mid_third hourly_std 273h -2.402 0.018421 0.8842 -0.1843 89
  136. mid_third |dH/dt| 297h -2.394 0.018909 0.8842 -0.2245 84
  137. high_third |dH/dt| 60h +2.370 0.019956 0.9020 +0.1184 90
  138. high_third hourly_range 6h +2.323 0.022403 0.9436 +0.1145 93
  139. mid_third hourly_range 195h -2.310 0.023263 0.9436 -0.1749 87
  140. high_third |dH/dt| 315h +2.305 0.023658 0.9436 +0.1051 84
  141. mid_third hourly_std 9h -2.304 0.023397 0.9436 -0.1895 96
  142. high_third |dH/dt| 3h +2.271 0.025469 0.9867 +0.1144 93
  143. high_third hourly_std 114h +2.199 0.030369 0.9880 +0.1102 93
  144. mid_third hourly_range 150h -2.195 0.030817 0.9880 -0.1553 88
  145. high_third hourly_range 66h +2.193 0.030861 0.9880 +0.0954 91
  146. broadband hourly_std 87h +2.183 0.031571 0.9880 +0.1911 94
  147. mid_third hourly_std 120h -2.167 0.032800 0.9880 -0.1780 93
  148. high_third |dH/dt| 45h +2.160 0.033410 0.9880 +0.0897 91
  149. high_third |dH/dt| 129h +2.154 0.033975 0.9880 +0.1089 88
  150. high_third hourly_range 45h +2.143 0.034777 0.9880 +0.1005 92
  151. high_third hourly_std 24h +2.130 0.035731 0.9880 +0.0958 96
  152. broadband hourly_std 9h -2.125 0.036201 0.9880 -0.1693 96
  153. mid_third hourly_range 297h -2.038 0.044662 0.9880 -0.1832 86
  154. high_third hourly_range 87h +2.036 0.044733 0.9880 +0.1060 90
  155. mid_third hourly_range 126h -2.030 0.045376 0.9880 -0.1672 89
  156. mid_third |dH/dt| 177h -2.005 0.048100 0.9880 -0.1661 86
  157. high_third hourly_range 201h +1.999 0.048818 0.9880 +0.1001 87
  158. broadband hourly_range 87h +1.997 0.048875 0.9880 +0.1869 90
  159. high_third hourly_range 54h +1.989 0.049705 0.9880 +0.0963 92
  160.  
  161. Shuffle null (1000 iterations) for 4 results with BH q < 0.10:
  162. Band Metric Lag t p(BH) p(shuf) d
  163. ----------------------------------------------------------------------------
  164. high_third |dH/dt| 120h +4.668 0.0149 0.0000 +0.1716
  165. high_third |dH/dt| 102h +4.136 0.0546 0.0030 +0.1690
  166. high_third hourly_range 33h +3.886 0.0740 0.0030 +0.1712
  167. mid_third hourly_std 123h -3.849 0.0740 0.0010 -0.2549
  168.  
  169. Lag curve: high_third → |dH/dt|
  170. Lag t p d N
  171. ----------------------------------------
  172. 0h +1.586 0.1161 +0.0781 93
  173. 3h +2.271 0.0255 +0.1144 93 *
  174. 6h +1.616 0.1096 +0.1247 92
  175. 9h +0.262 0.7939 +0.0232 92
  176. 12h +0.456 0.6493 +0.0243 92
  177. 15h +2.443 0.0165 +0.1166 92 *
  178. 18h +0.837 0.4047 +0.0679 92
  179. 21h +0.966 0.3368 +0.0527 92
  180. 24h +0.230 0.8188 +0.0124 92
  181. 27h +0.638 0.5251 +0.0333 92
  182. 30h +0.501 0.6173 +0.0389 92
  183. 33h +1.234 0.2202 +0.1078 91
  184. 36h +0.842 0.4020 +0.0458 91
  185. 39h +1.094 0.2768 +0.0782 91
  186. 42h -0.869 0.3873 -0.1932 91
  187. 45h +2.160 0.0334 +0.0897 91 *
  188. 48h +1.517 0.1328 +0.0767 91
  189. 51h +1.178 0.2417 +0.0622 91
  190. 54h +1.430 0.1562 +0.0720 91
  191. 57h +0.592 0.5554 +0.0365 90
  192. 60h +2.370 0.0200 +0.1184 90 *
  193. 63h +1.394 0.1668 +0.0814 90
  194. 66h -1.166 0.2466 -0.2525 90
  195. 69h +1.538 0.1275 +0.0733 90
  196. 72h -0.119 0.9055 -0.0069 90
  197. 75h +1.081 0.2826 +0.0585 90
  198. 78h +0.161 0.8724 +0.0209 90
  199. 81h +1.635 0.1057 +0.0904 89
  200. 84h +0.620 0.5367 +0.0426 89
  201. 87h +1.193 0.2360 +0.0643 89
  202. 90h -0.346 0.7303 -0.0211 89
  203. 93h +0.046 0.9637 +0.0029 89
  204. 96h +1.361 0.1771 +0.0620 89
  205. 99h +0.528 0.5986 +0.0306 89
  206. 102h +4.136 0.0001 +0.1690 89 *
  207. 105h +1.759 0.0820 +0.1028 89
  208. 108h +0.910 0.3654 +0.0754 88
  209. 111h +1.784 0.0779 +0.0983 88
  210. 114h +1.676 0.0973 +0.0823 88
  211. 117h +3.062 0.0029 +0.1339 88 *
  212. 120h +4.668 0.0000 +0.1716 88 *
  213. 123h +0.651 0.5168 +0.0421 88
  214. 126h +0.103 0.9183 +0.0155 88
  215. 129h +2.154 0.0340 +0.1089 88 *
  216. 132h +2.989 0.0036 +0.1312 87 *
  217. 135h +0.567 0.5720 +0.0435 87
  218. 138h +0.990 0.3251 +0.0579 87
  219. 141h +0.417 0.6779 +0.0222 87
  220. 144h +1.817 0.0727 +0.0900 87
  221. 147h +0.935 0.3525 +0.0496 87
  222. 150h +1.282 0.2034 +0.0703 87
  223. 153h +1.515 0.1334 +0.0825 87
  224. 156h +0.692 0.4908 +0.0412 87
  225. 159h -0.886 0.3781 -0.0581 87
  226. 162h -0.100 0.9209 -0.0062 86
  227. 165h -0.839 0.4040 -0.0505 86
  228. 168h +0.544 0.5880 +0.0303 86
  229. 171h +0.272 0.7864 +0.0165 86
  230. 174h +1.038 0.3023 +0.0547 86
  231. 177h +1.323 0.1894 +0.0633 86
  232. 180h +1.511 0.1346 +0.0713 86
  233. 183h +1.055 0.2944 +0.0514 86
  234. 186h +1.016 0.3124 +0.0568 85
  235. 189h +0.487 0.6273 +0.0297 85
  236. 192h -0.209 0.8353 -0.0130 85
  237. 195h +0.881 0.3809 +0.0491 85
  238. 198h +0.814 0.4178 +0.0469 85
  239. 201h +1.423 0.1585 +0.0788 85
  240. 204h -0.046 0.9633 -0.0034 85
  241. 207h +0.406 0.6854 +0.0227 85
  242. 210h +0.386 0.7001 +0.0254 85
  243. 213h -0.730 0.4675 -0.1168 85
  244. 216h -0.395 0.6939 -0.0441 85
  245. 219h -0.114 0.9096 -0.0105 85
  246. 222h -1.185 0.2392 -0.1350 85
  247. 225h -0.233 0.8160 -0.0145 85
  248. 228h -0.976 0.3320 -0.0571 85
  249. 231h +0.517 0.6067 +0.0264 85
  250. 234h +1.106 0.2720 +0.0687 84
  251. 237h +0.707 0.4818 +0.0775 84
  252. 240h +0.118 0.9065 +0.0151 84
  253. 243h -0.737 0.4635 -0.0795 84
  254. 246h -0.578 0.5646 -0.0596 84
  255. 249h -0.790 0.4319 -0.1837 84
  256. 252h -1.102 0.2735 -0.1034 84
  257. 255h +1.157 0.2506 +0.0592 84
  258. 258h +0.330 0.7421 +0.0191 84
  259. 261h +0.046 0.9635 +0.0037 84
  260. 264h +0.045 0.9644 +0.0052 84
  261. 267h +0.350 0.7269 +0.0211 84
  262. 270h +0.873 0.3852 +0.0562 84
  263. 273h -0.568 0.5719 -0.0544 84
  264. 276h +0.748 0.4563 +0.0790 84
  265. 279h +2.530 0.0133 +0.1125 84 *
  266. 282h +0.481 0.6315 +0.0242 84
  267. 285h -0.478 0.6338 -0.0398 84
  268. 288h -0.369 0.7133 -0.0358 84
  269. 291h +0.250 0.8033 +0.0164 84
  270. 294h +0.536 0.5932 +0.0305 84
  271. 297h -0.791 0.4311 -0.0806 84
  272. 300h +0.883 0.3799 +0.0454 84
  273. 303h +0.976 0.3317 +0.0565 84
  274. 306h +1.362 0.1768 +0.0757 84
  275. 309h +0.787 0.4338 +0.0647 84
  276. 312h +0.114 0.9093 +0.0108 84
  277. 315h +2.305 0.0237 +0.1051 84 *
  278. 318h +1.723 0.0887 +0.0826 84
  279. 321h +0.573 0.5685 +0.0474 84
  280. 324h +1.411 0.1620 +0.0755 84
  281. 327h -0.220 0.8267 -0.0160 84
  282. 330h -1.183 0.2403 -0.0974 84
  283. 333h -0.736 0.4639 -0.0748 84
  284. 336h +0.031 0.9753 +0.0030 84
  285.  
  286. Events: N=93, spacing mean=65.4h, median=31.5h, min=24h, max=375h
  287.  
  288. Cross-band comparison (same events from |dH/dt|)
  289.  
  290. Band lag curve correlations:
  291. broadband vs low_third: r = +0.876, p = 0.000000
  292. broadband vs mid_third: r = +0.669, p = 0.000000
  293. broadband vs high_third: r = +0.520, p = 0.000000
  294. low_third vs mid_third: r = +0.358, p = 0.000097
  295. low_third vs high_third: r = +0.348, p = 0.000158
  296. mid_third vs high_third: r = +0.053, p = 0.580123
  297.  
  298. → Saved: test5_prediction_BRW.png
  299.  
  300. ======================================================================
  301. TEST 3: SKR–Earth Mutual Information (station: YKC)
  302. ======================================================================
  303. Common hourly bins: 5459
  304. Computing MI at 169 lags (0–336h, step=2h)...
  305. Using 24 bins, rank-transformed data, 500 shuffles/lag
  306.  
  307. Complementary Spearman correlation test...
  308. Effective sample size: 417 / 5459 (ratio = 0.077)
  309.  
  310. === MI Results ===
  311. Lags with z > 3 (block-shuffle): 66 / 169
  312. Mean z-score: 2.41
  313. Max z-score: 4.99 at lag 158h
  314.  
  315. === Spearman Results ===
  316. Lags with p < 0.001 (raw): 28 / 169
  317. Lags with p < 0.001 (n_eff adj): 0 / 169
  318. Max |r| = +0.0587 at lag 260h (p_raw = 2.31e-05, p_adj = 2.44e-01)
  319. → Saved: test3_mi_YKC.png
  320.  
  321. ======================================================================
  322. TEST 4: Directional Asymmetry (station: YKC)
  323. ======================================================================
  324. Computing directional MI at 83 lags...
  325.  
  326. Mean MI level: 0.00054 bits
  327.  
  328. Directional asymmetry (positive = SKR leads):
  329. Short lags (1–70h): -0.00006 (-11.5% of mean MI)
  330. Long lags (130–200h): +0.00016 (+29.6% of mean MI)
  331. → SIGN REVERSAL: direction flips with timescale
  332. Shuffle null (200 iterations)...
  333. Overall mean asymmetry: -0.00002 (z = -0.35)
  334. Short-lag z: -0.68, Long-lag z: 1.76
  335. Null reversal rate: 52.0% (observed: YES)
  336. → Saved: test4_direction_YKC.png
  337.  
  338. ======================================================================
  339. TEST 5: SKR → Earth Prediction (station: YKC)
  340. ======================================================================
  341. Channels: 115 total, split into thirds (38 each)
  342.  
  343. Scanning 4 bands × 3 metrics × 113 lags (0–336h, 3h steps)
  344. Total valid combinations: 1356
  345.  
  346. Raw p < 0.05: 74/1356 (expected by chance: 67.8)
  347. BH-FDR q < 0.05: 2/1356
  348. BH-FDR q < 0.10: 4/1356
  349.  
  350. All combinations with raw p < 0.05:
  351. Band Metric Lag t p(raw) p(BH) d N
  352. ----------------------------------------------------------------------------
  353. mid_third |dH/dt| 306h -4.727 0.000069 0.0468 -0.4066 27 *
  354. high_third hourly_std 324h +4.406 0.000031 0.0423 +0.1645 84 *
  355. high_third hourly_std 6h +3.853 0.000221 0.0970 +0.1612 89
  356. high_third hourly_range 324h +3.814 0.000286 0.0970 +0.1604 73
  357. high_third hourly_std 24h +3.655 0.000436 0.1025 +0.1580 89
  358. high_third hourly_std 318h +3.652 0.000454 0.1025 +0.1661 84
  359. high_third hourly_range 318h +3.584 0.000612 0.1186 +0.1764 73
  360. high_third |dH/dt| 135h +3.449 0.001931 0.2619 +0.1777 27
  361. mid_third hourly_std 30h -3.426 0.000933 0.1581 -0.2924 89
  362. high_third |dH/dt| 144h +3.356 0.002439 0.2756 +0.1745 27
  363. high_third hourly_std 321h +3.248 0.001679 0.2529 +0.1533 84
  364. high_third |dH/dt| 201h +3.227 0.003366 0.3497 +0.2151 27
  365. mid_third |dH/dt| 168h -3.189 0.003704 0.3497 -0.3621 27
  366. high_third hourly_std 327h +3.154 0.002240 0.2756 +0.1186 84
  367. high_third hourly_std 309h +2.972 0.003868 0.3497 +0.1196 84
  368. high_third hourly_range 93h +2.959 0.004126 0.3497 +0.1298 76
  369. high_third |dH/dt| 285h +2.900 0.007499 0.4771 +0.2088 27
  370. high_third |dH/dt| 255h +2.886 0.007740 0.4771 +0.1746 27
  371. mid_third |dH/dt| 150h -2.863 0.008189 0.4828 -0.2805 27
  372. mid_third |dH/dt| 153h -2.840 0.008645 0.4885 -0.3248 27
  373. high_third hourly_range 24h +2.816 0.006192 0.4728 +0.1299 77
  374. high_third hourly_std 126h +2.803 0.006276 0.4728 +0.1320 86
  375. high_third |dH/dt| 117h +2.759 0.010476 0.5682 +0.1616 27
  376. high_third hourly_range 114h +2.753 0.007418 0.4771 +0.1383 75
  377. high_third hourly_std 300h +2.751 0.007285 0.4771 +0.1114 84
  378. mid_third |dH/dt| 165h -2.730 0.011213 0.5848 -0.3178 27
  379. mid_third |dH/dt| 156h -2.650 0.013528 0.6436 -0.2550 27
  380. mid_third |dH/dt| 177h -2.627 0.014238 0.6436 -0.2957 27
  381. high_third hourly_range 111h +2.565 0.012335 0.6195 +0.1214 75
  382. high_third hourly_range 126h +2.515 0.014069 0.6436 +0.1201 75
  383. high_third hourly_range 321h +2.499 0.014741 0.6448 +0.1337 73
  384. mid_third hourly_range 30h -2.472 0.015674 0.6642 -0.2536 77
  385. high_third hourly_range 309h +2.451 0.016684 0.6840 +0.1111 73
  386. mid_third |dH/dt| 42h -2.451 0.021302 0.7931 -0.2368 27
  387. high_third hourly_range 6h +2.426 0.017654 0.6840 +0.1180 77
  388. mid_third hourly_std 21h -2.419 0.017642 0.6840 -0.1662 89
  389. high_third |dH/dt| 288h +2.392 0.024303 0.8340 +0.1471 27
  390. high_third |dH/dt| 306h +2.345 0.026948 0.8340 +0.2027 27
  391. high_third hourly_std 111h +2.339 0.021642 0.7931 +0.1062 87
  392. high_third |dH/dt| 153h +2.329 0.027893 0.8340 +0.1556 27
  393. high_third |dH/dt| 282h +2.323 0.028248 0.8340 +0.1620 27
  394. low_third hourly_std 315h -2.318 0.022935 0.8184 -0.2021 84
  395. high_third |dH/dt| 225h +2.312 0.028960 0.8340 +0.1480 27
  396. high_third |dH/dt| 162h +2.304 0.029497 0.8340 +0.1777 27
  397. broadband hourly_range 78h +2.281 0.025371 0.8340 +0.2622 76
  398. mid_third |dH/dt| 219h -2.277 0.031266 0.8340 -0.2716 27
  399. high_third |dH/dt| 198h +2.247 0.033359 0.8340 +0.1440 27
  400. mid_third hourly_std 153h -2.229 0.028486 0.8340 -0.1955 86
  401. mid_third hourly_std 27h -2.228 0.028459 0.8340 -0.1929 89
  402. high_third hourly_range 66h +2.193 0.031409 0.8340 +0.1071 76
  403. mid_third hourly_std 18h -2.185 0.031531 0.8340 -0.1935 89
  404. mid_third hourly_range 306h -2.179 0.032623 0.8340 -0.2259 73
  405. mid_third |dH/dt| 231h -2.165 0.039725 0.8340 -0.2182 27
  406. high_third |dH/dt| 114h +2.163 0.039942 0.8340 +0.1484 27
  407. mid_third |dH/dt| 210h -2.156 0.040492 0.8340 -0.2396 27
  408. broadband hourly_range 315h -2.153 0.034656 0.8340 -0.2100 73
  409. high_third |dH/dt| 303h +2.149 0.041091 0.8340 +0.1507 27
  410. high_third hourly_std 294h +2.148 0.034665 0.8340 +0.1172 84
  411. high_third hourly_range 327h +2.143 0.035455 0.8340 +0.0982 73
  412. high_third |dH/dt| 264h +2.141 0.041801 0.8340 +0.1442 27
  413. high_third |dH/dt| 177h +2.141 0.041821 0.8340 +0.1788 27
  414. broadband hourly_std 315h -2.137 0.035574 0.8340 -0.1872 84
  415. broadband hourly_range 201h -2.131 0.036497 0.8340 -0.1731 74
  416. mid_third hourly_range 192h -2.128 0.036690 0.8340 -0.1728 74
  417. mid_third hourly_std 291h -2.126 0.036476 0.8340 -0.1589 84
  418. mid_third |dH/dt| 120h -2.124 0.043333 0.8516 -0.2766 27
  419. mid_third |dH/dt| 96h -2.096 0.045982 0.8732 -0.2409 27
  420. high_third hourly_std 63h +2.095 0.039045 0.8340 +0.1007 88
  421. high_third |dH/dt| 60h +2.092 0.046363 0.8732 +0.1524 27
  422. low_third hourly_range 315h -2.088 0.040355 0.8340 -0.2021 73
  423. mid_third |dH/dt| 180h -2.071 0.048400 0.8980 -0.2374 27
  424. low_third hourly_std 186h -2.069 0.041661 0.8340 -0.1925 85
  425. low_third hourly_range 78h +2.044 0.044476 0.8616 +0.2681 76
  426. mid_third hourly_range 291h -2.002 0.049006 0.8980 -0.1616 73
  427.  
  428. Shuffle null (1000 iterations) for 4 results with BH q < 0.10:
  429. Band Metric Lag t p(BH) p(shuf) d
  430. ----------------------------------------------------------------------------
  431. mid_third |dH/dt| 306h -4.727 0.0468 0.0070 -0.4066
  432. high_third hourly_std 324h +4.406 0.0423 0.0040 +0.1645
  433. high_third hourly_std 6h +3.853 0.0970 0.0050 +0.1612
  434. high_third hourly_range 324h +3.814 0.0970 0.0070 +0.1604
  435.  
  436. Lag curve: mid_third → |dH/dt|
  437. Lag t p d N
  438. ----------------------------------------
  439. 0h -0.286 0.7775 -0.0488 27
  440. 3h -0.278 0.7829 -0.0502 27
  441. 6h -0.391 0.6993 -0.0719 27
  442. 9h -0.796 0.4330 -0.0994 27
  443. 12h -1.934 0.0640 -0.2150 27
  444. 15h -0.701 0.4892 -0.1227 27
  445. 18h -0.172 0.8644 -0.0320 27
  446. 21h +0.573 0.5713 +0.1196 27
  447. 24h +0.181 0.8578 +0.0344 27
  448. 27h -0.866 0.3945 -0.1040 27
  449. 30h +0.853 0.4012 +0.1855 27
  450. 33h +0.815 0.4223 +0.1868 27
  451. 36h -0.526 0.6036 -0.0688 27
  452. 39h -0.819 0.4202 -0.1001 27
  453. 42h -2.451 0.0213 -0.2368 27 *
  454. 45h -0.609 0.5477 -0.0685 27
  455. 48h -0.244 0.8088 -0.0496 27
  456. 51h -0.308 0.7603 -0.0592 27
  457. 54h -0.032 0.9751 -0.0055 27
  458. 57h +0.280 0.7816 +0.0564 27
  459. 60h +0.296 0.7694 +0.0599 27
  460. 63h +0.232 0.8180 +0.0337 27
  461. 66h +0.080 0.9372 +0.0143 27
  462. 69h -1.545 0.1345 -0.1918 27
  463. 72h -1.215 0.2351 -0.1423 27
  464. 75h -0.796 0.4335 -0.1005 27
  465. 78h -0.015 0.9881 -0.0026 27
  466. 81h +0.710 0.4843 +0.1806 27
  467. 84h +0.651 0.5205 +0.1458 27
  468. 87h +0.035 0.9720 +0.0066 27
  469. 90h +0.822 0.4186 +0.1781 27
  470. 93h -0.185 0.8550 -0.0338 27
  471. 96h -2.096 0.0460 -0.2409 27 *
  472. 99h -1.414 0.1691 -0.1706 27
  473. 102h -0.801 0.4304 -0.1184 27
  474. 105h +0.004 0.9971 +0.0007 27
  475. 108h +0.068 0.9465 +0.0119 27
  476. 111h -0.483 0.6333 -0.0766 27
  477. 114h -0.024 0.9809 -0.0050 27
  478. 117h -0.350 0.7289 -0.0646 27
  479. 120h -2.124 0.0433 -0.2766 27 *
  480. 123h -1.434 0.1634 -0.2159 27
  481. 126h -1.471 0.1534 -0.1965 27
  482. 129h -0.600 0.5536 -0.0968 27
  483. 132h -1.089 0.2863 -0.1618 27
  484. 135h +0.026 0.9794 +0.0048 27
  485. 138h -0.295 0.7705 -0.0518 27
  486. 141h -1.245 0.2244 -0.1693 27
  487. 144h -0.690 0.4962 -0.0890 27
  488. 147h -0.763 0.4525 -0.1110 27
  489. 150h -2.863 0.0082 -0.2805 27 *
  490. 153h -2.840 0.0086 -0.3248 27 *
  491. 156h -2.650 0.0135 -0.2550 27 *
  492. 159h -1.106 0.2790 -0.1623 27
  493. 162h -0.851 0.4026 -0.1533 27
  494. 165h -2.730 0.0112 -0.3178 27 *
  495. 168h -3.189 0.0037 -0.3621 27 *
  496. 171h -1.324 0.1970 -0.1837 27
  497. 174h -1.131 0.2683 -0.1637 27
  498. 177h -2.627 0.0142 -0.2957 27 *
  499. 180h -2.071 0.0484 -0.2374 27 *
  500. 183h -0.702 0.4891 -0.1116 27
  501. 186h -1.109 0.2776 -0.1881 27
  502. 189h -0.284 0.7788 -0.0449 27
  503. 192h -1.073 0.2932 -0.1753 27
  504. 195h -1.032 0.3118 -0.1909 27
  505. 198h -1.609 0.1196 -0.2135 27
  506. 201h -1.955 0.0614 -0.2239 27
  507. 204h +0.519 0.6079 +0.0888 27
  508. 207h -1.653 0.1103 -0.2188 27
  509. 210h -2.156 0.0405 -0.2396 27 *
  510. 213h -0.215 0.8317 -0.0371 27
  511. 216h -0.981 0.3355 -0.1513 27
  512. 219h -2.277 0.0313 -0.2716 27 *
  513. 222h -1.499 0.1460 -0.2208 27
  514. 225h -1.213 0.2362 -0.1780 27
  515. 228h -1.243 0.2251 -0.1573 27
  516. 231h -2.165 0.0397 -0.2182 27 *
  517. 234h -1.211 0.2369 -0.1651 27
  518. 237h -0.971 0.3407 -0.1277 27
  519. 240h -1.462 0.1558 -0.1668 27
  520. 243h +0.230 0.8199 +0.0375 27
  521. 246h +0.183 0.8566 +0.0321 27
  522. 249h -0.335 0.7405 -0.0584 27
  523. 252h -0.202 0.8417 -0.0316 27
  524. 255h -1.130 0.2688 -0.1413 27
  525. 258h +0.794 0.4345 +0.1129 27
  526. 261h -0.038 0.9702 -0.0060 27
  527. 264h -0.535 0.5970 -0.0963 27
  528. 267h -0.100 0.9210 -0.0186 27
  529. 270h -0.283 0.7793 -0.0504 27
  530. 273h -0.475 0.6389 -0.0931 27
  531. 276h -0.124 0.9020 -0.0236 27
  532. 279h -1.074 0.2925 -0.1248 27
  533. 282h -0.756 0.4567 -0.1332 27
  534. 285h -0.305 0.7626 -0.0524 27
  535. 288h -0.992 0.3305 -0.1309 27
  536. 291h -0.587 0.5621 -0.0969 27
  537. 294h -0.608 0.5484 -0.0883 27
  538. 297h -0.997 0.3282 -0.1705 27
  539. 300h -0.512 0.6129 -0.0786 27
  540. 303h +0.240 0.8119 +0.0359 27
  541. 306h -4.727 0.0001 -0.4066 27 *
  542. 309h -0.699 0.4910 -0.1145 27
  543. 312h -0.863 0.3960 -0.1129 27
  544. 315h -1.048 0.3041 -0.1344 27
  545. 318h -0.451 0.6554 -0.0750 27
  546. 321h -0.879 0.3874 -0.1389 27
  547. 324h -0.003 0.9980 -0.0005 27
  548. 327h -0.576 0.5697 -0.0879 27
  549. 330h -0.744 0.4638 -0.1198 27
  550. 333h -0.504 0.6184 -0.0793 27
  551. 336h -1.726 0.0962 -0.2399 27
  552.  
  553. Events: N=27, spacing mean=125.4h, median=29.0h, min=24h, max=1291h
  554.  
  555. Cross-band comparison (same events from |dH/dt|)
  556.  
  557. Band lag curve correlations:
  558. broadband vs low_third: r = +0.861, p = 0.000000
  559. broadband vs mid_third: r = +0.448, p = 0.000001
  560. broadband vs high_third: r = +0.442, p = 0.000001
  561. low_third vs mid_third: r = +0.024, p = 0.802805
  562. low_third vs high_third: r = +0.334, p = 0.000296
  563. mid_third vs high_third: r = -0.082, p = 0.385008
  564.  
  565. → Saved: test5_prediction_YKC.png
  566.  
  567. ======================================================================
  568. TEST 3: SKR–Earth Mutual Information (station: MEA)
  569. ======================================================================
  570. Common hourly bins: 6030
  571. Computing MI at 169 lags (0–336h, step=2h)...
  572. Using 24 bins, rank-transformed data, 500 shuffles/lag
  573.  
  574. Complementary Spearman correlation test...
  575. Effective sample size: 879 / 6030 (ratio = 0.146)
  576.  
  577. === MI Results ===
  578. Lags with z > 3 (block-shuffle): 0 / 169
  579. Mean z-score: 0.39
  580. Max z-score: 2.78 at lag 96h
  581.  
  582. === Spearman Results ===
  583. Lags with p < 0.001 (raw): 90 / 169
  584. Lags with p < 0.001 (n_eff adj): 0 / 169
  585. Max |r| = -0.1066 at lag 186h (p_raw = 3.15e-16, p_adj = 1.84e-03)
  586. → Saved: test3_mi_MEA.png
  587.  
  588. ======================================================================
  589. TEST 4: Directional Asymmetry (station: MEA)
  590. ======================================================================
  591. Computing directional MI at 83 lags...
  592.  
  593. Mean MI level: 0.00591 bits
  594.  
  595. Directional asymmetry (positive = SKR leads):
  596. Short lags (1–70h): +0.00034 (+5.7% of mean MI)
  597. Long lags (130–200h): -0.00105 (-17.8% of mean MI)
  598. → SIGN REVERSAL: direction flips with timescale
  599. Shuffle null (200 iterations)...
  600. Overall mean asymmetry: -0.00055 (z = -0.44)
  601. Short-lag z: 0.77, Long-lag z: -0.41
  602. Null reversal rate: 50.0% (observed: YES)
  603. → Saved: test4_direction_MEA.png
  604.  
  605. ======================================================================
  606. TEST 5: SKR → Earth Prediction (station: MEA)
  607. ======================================================================
  608. Channels: 115 total, split into thirds (38 each)
  609.  
  610. Scanning 4 bands × 3 metrics × 113 lags (0–336h, 3h steps)
  611. Total valid combinations: 1356
  612.  
  613. Raw p < 0.05: 112/1356 (expected by chance: 67.8)
  614. BH-FDR q < 0.05: 0/1356
  615. BH-FDR q < 0.10: 0/1356
  616.  
  617. All combinations with raw p < 0.05:
  618. Band Metric Lag t p(raw) p(BH) d N
  619. ----------------------------------------------------------------------------
  620. mid_third |dH/dt| 171h -4.046 0.000127 0.1345 -0.2852 75
  621. mid_third hourly_range 30h -3.874 0.000243 0.1345 -0.3881 69
  622. mid_third hourly_std 18h -3.830 0.000298 0.1345 -0.2944 64
  623. mid_third hourly_range 18h -3.705 0.000427 0.1447 -0.2681 69
  624. high_third hourly_std 24h +3.276 0.001716 0.3309 +0.1696 64
  625. broadband hourly_range 192h -3.211 0.002030 0.3309 -0.2624 68
  626. low_third |dH/dt| 198h -3.208 0.001984 0.3309 -0.2928 74
  627. mid_third hourly_std 27h -3.198 0.002164 0.3309 -0.2734 64
  628. mid_third |dH/dt| 168h -3.173 0.002196 0.3309 -0.2344 75
  629. broadband |dH/dt| 198h -3.046 0.003222 0.3813 -0.2434 74
  630. broadband hourly_std 186h -2.996 0.003928 0.3813 -0.2472 63
  631. broadband hourly_range 186h -2.972 0.004106 0.3813 -0.2734 68
  632. high_third hourly_range 24h +2.955 0.004296 0.3813 +0.1437 69
  633. mid_third hourly_std 30h -2.946 0.004503 0.3813 -0.3653 64
  634. high_third |dH/dt| 123h +2.938 0.004383 0.3813 +0.1503 76
  635. mid_third hourly_range 186h -2.913 0.004856 0.3813 -0.2553 68
  636. high_third |dH/dt| 45h +2.882 0.005128 0.3813 +0.1442 77
  637. mid_third |dH/dt| 174h -2.872 0.005313 0.3813 -0.2347 75
  638. high_third |dH/dt| 36h +2.868 0.005342 0.3813 +0.1267 77
  639. mid_third |dH/dt| 30h -2.846 0.005683 0.3853 -0.2877 77
  640. mid_third hourly_range 171h -2.819 0.006325 0.4006 -0.2171 68
  641. low_third hourly_std 195h -2.806 0.006695 0.4006 -0.2810 63
  642. mid_third hourly_std 165h -2.800 0.006796 0.4006 -0.2771 63
  643. broadband hourly_range 204h -2.760 0.007440 0.4204 -0.2020 68
  644. low_third hourly_range 192h -2.720 0.008308 0.4315 -0.2643 68
  645. mid_third |dH/dt| 21h -2.720 0.008094 0.4315 -0.1992 77
  646. low_third hourly_std 186h -2.714 0.008591 0.4315 -0.2666 63
  647. low_third |dH/dt| 195h -2.687 0.008913 0.4317 -0.2809 74
  648. broadband hourly_range 198h -2.678 0.009295 0.4346 -0.2236 68
  649. low_third hourly_range 204h -2.654 0.009922 0.4404 -0.2421 68
  650. low_third hourly_range 198h -2.643 0.010226 0.4404 -0.2724 68
  651. high_third hourly_std 39h +2.642 0.010392 0.4404 +0.1232 64
  652. high_third |dH/dt| 126h +2.606 0.011035 0.4465 +0.1376 76
  653. high_third hourly_std 333h +2.605 0.011484 0.4465 +0.1432 63
  654. mid_third hourly_std 171h -2.579 0.012311 0.4465 -0.2070 63
  655. mid_third hourly_range 168h -2.578 0.012136 0.4465 -0.2263 68
  656. broadband hourly_std 195h -2.572 0.012529 0.4465 -0.2473 63
  657. low_third |dH/dt| 201h -2.571 0.012177 0.4465 -0.2580 74
  658. low_third hourly_std 183h -2.540 0.013592 0.4465 -0.2477 63
  659. mid_third hourly_range 21h -2.535 0.013541 0.4465 -0.1946 69
  660. broadband hourly_range 315h -2.518 0.014212 0.4465 -0.2088 68
  661. mid_third hourly_range 192h -2.515 0.014314 0.4465 -0.2428 68
  662. high_third |dH/dt| 93h +2.510 0.014196 0.4465 +0.1192 77
  663. mid_third hourly_range 165h -2.503 0.014741 0.4465 -0.2364 68
  664. low_third hourly_range 207h -2.501 0.014818 0.4465 -0.2913 68
  665. broadband hourly_range 201h -2.482 0.015580 0.4499 -0.2030 68
  666. low_third hourly_range 195h -2.480 0.015648 0.4499 -0.2432 68
  667. broadband |dH/dt| 204h -2.466 0.016001 0.4499 -0.1868 74
  668. low_third |dH/dt| 123h +2.451 0.016595 0.4499 +0.2759 76
  669. low_third |dH/dt| 204h -2.431 0.017492 0.4499 -0.2182 74
  670. broadband hourly_std 174h -2.428 0.018088 0.4499 -0.2374 63
  671. low_third |dH/dt| 183h -2.427 0.017652 0.4499 -0.2414 75
  672. mid_third hourly_std 21h -2.423 0.018267 0.4499 -0.2076 64
  673. low_third hourly_std 198h -2.420 0.018461 0.4499 -0.2688 63
  674. mid_third hourly_std 168h -2.418 0.018581 0.4499 -0.2239 63
  675. mid_third |dH/dt| 27h -2.407 0.018524 0.4499 -0.2234 77
  676. broadband |dH/dt| 252h +2.374 0.020219 0.4724 +0.2660 74
  677. mid_third |dH/dt| 36h -2.374 0.020113 0.4724 -0.1945 77
  678. high_third |dH/dt| 159h +2.362 0.020810 0.4724 +0.1153 75
  679. high_third |dH/dt| 24h +2.359 0.020904 0.4724 +0.1184 77
  680. low_third hourly_range 318h -2.342 0.022177 0.4764 -0.2144 68
  681. broadband |dH/dt| 201h -2.333 0.022422 0.4764 -0.1910 74
  682. broadband |dH/dt| 186h -2.330 0.022548 0.4764 -0.1886 74
  683. broadband hourly_range 207h -2.329 0.022886 0.4764 -0.2784 68
  684. low_third hourly_range 42h -2.327 0.022935 0.4764 -0.2494 69
  685. low_third |dH/dt| 192h -2.319 0.023186 0.4764 -0.2098 74
  686. high_third hourly_std 111h +2.300 0.024777 0.4924 +0.1177 64
  687. low_third |dH/dt| 318h -2.299 0.024376 0.4924 -0.2104 74
  688. broadband hourly_range 195h -2.292 0.025054 0.4924 -0.2106 68
  689. high_third hourly_std 171h +2.258 0.027463 0.5159 +0.1089 63
  690. low_third hourly_range 186h -2.252 0.027585 0.5159 -0.2466 68
  691. low_third hourly_range 201h -2.250 0.027727 0.5159 -0.2341 68
  692. mid_third hourly_std 144h -2.248 0.028060 0.5159 -0.1892 64
  693. broadband |dH/dt| 174h -2.237 0.028270 0.5159 -0.2021 75
  694. broadband hourly_std 198h -2.235 0.029013 0.5159 -0.2188 63
  695. broadband hourly_range 252h +2.228 0.029209 0.5159 +0.2556 68
  696. broadband |dH/dt| 93h +2.221 0.029296 0.5159 +0.2134 77
  697. broadband |dH/dt| 123h +2.214 0.029879 0.5194 +0.2234 76
  698. low_third hourly_std 318h -2.206 0.031110 0.5273 -0.2055 63
  699. broadband |dH/dt| 192h -2.205 0.030627 0.5257 -0.1642 74
  700. broadband hourly_range 318h -2.190 0.031993 0.5356 -0.1822 68
  701. mid_third hourly_std 33h -2.178 0.033177 0.5405 -0.2144 64
  702. low_third hourly_std 207h -2.158 0.034811 0.5405 -0.2580 63
  703. low_third hourly_std 180h -2.155 0.035036 0.5405 -0.2375 63
  704. mid_third hourly_std 153h -2.154 0.035074 0.5405 -0.2035 64
  705. broadband |dH/dt| 195h -2.153 0.034582 0.5405 -0.2646 74
  706. high_third |dH/dt| 69h +2.151 0.034622 0.5405 +0.1250 77
  707. mid_third |dH/dt| 186h -2.150 0.034840 0.5405 -0.1778 74
  708. low_third hourly_std 174h -2.140 0.036321 0.5501 -0.2379 63
  709. broadband hourly_std 87h +2.128 0.037298 0.5501 +0.2357 64
  710. mid_third hourly_std 189h -2.112 0.038750 0.5501 -0.2087 63
  711. low_third hourly_range 315h -2.106 0.038975 0.5501 -0.2023 68
  712. high_third hourly_std 327h +2.105 0.039366 0.5501 +0.1043 63
  713. broadband hourly_std 117h +2.102 0.039534 0.5501 +0.1935 64
  714. broadband hourly_range 174h -2.096 0.039848 0.5501 -0.1984 68
  715. mid_third hourly_std 312h -2.095 0.040259 0.5501 -0.1853 63
  716. low_third |dH/dt| 252h +2.094 0.039748 0.5501 +0.2574 74
  717. broadband |dH/dt| 183h -2.087 0.040375 0.5501 -0.1819 75
  718. broadband hourly_range 168h -2.084 0.040936 0.5501 -0.1867 68
  719. mid_third hourly_std 186h -2.083 0.041379 0.5501 -0.2123 63
  720. broadband |dH/dt| 207h -2.082 0.040880 0.5501 -0.2333 74
  721. mid_third hourly_range 27h -2.081 0.041169 0.5501 -0.2066 69
  722. mid_third hourly_std 174h -2.057 0.043866 0.5577 -0.1965 63
  723. high_third hourly_std 87h +2.057 0.043803 0.5577 +0.1056 64
  724. high_third hourly_std 45h +2.056 0.043896 0.5577 +0.1359 64
  725. mid_third hourly_range 174h -2.052 0.044083 0.5577 -0.1841 68
  726. broadband hourly_std 90h +2.051 0.044417 0.5577 +0.2170 64
  727. low_third |dH/dt| 207h -2.049 0.044020 0.5577 -0.2179 74
  728. high_third hourly_range 258h -2.039 0.045379 0.5645 -0.1809 68
  729. broadband hourly_std 210h -2.032 0.046476 0.5712 -0.2272 63
  730. high_third |dH/dt| 105h +2.021 0.046756 0.5712 +0.0954 77
  731. broadband hourly_std 180h -2.017 0.047989 0.5810 -0.2039 63
  732.  
  733. No results survived BH q < 0.10. Shuffle testing top 5 by |t|:
  734. Band Metric Lag t p(BH) p(shuf) d
  735. ----------------------------------------------------------------------------
  736. mid_third |dH/dt| 171h -4.046 0.1345 0.0010 -0.2852
  737. mid_third hourly_range 30h -3.874 0.1345 0.0060 -0.3881
  738. mid_third hourly_std 18h -3.830 0.1345 0.0020 -0.2944
  739. mid_third hourly_range 18h -3.705 0.1447 0.0050 -0.2681
  740. high_third hourly_std 24h +3.276 0.3309 0.0150 +0.1696
  741.  
  742. Lag curve: mid_third → |dH/dt|
  743. Lag t p d N
  744. ----------------------------------------
  745. 0h -0.992 0.3244 -0.0907 78
  746. 3h -1.145 0.2558 -0.1207 78
  747. 6h -0.577 0.5655 -0.0666 77
  748. 9h -0.526 0.6006 -0.0587 77
  749. 12h +0.158 0.8747 +0.0173 77
  750. 15h -0.426 0.6713 -0.0439 77
  751. 18h -1.333 0.1866 -0.1260 77
  752. 21h -2.720 0.0081 -0.1992 77 *
  753. 24h -1.770 0.0808 -0.1568 77
  754. 27h -2.407 0.0185 -0.2234 77 *
  755. 30h -2.846 0.0057 -0.2877 77 *
  756. 33h -1.644 0.1044 -0.1633 77
  757. 36h -2.374 0.0201 -0.1945 77 *
  758. 39h -0.723 0.4721 -0.0758 77
  759. 42h -0.867 0.3887 -0.0888 77
  760. 45h -1.566 0.1215 -0.1356 77
  761. 48h +0.289 0.7734 +0.0351 77
  762. 51h +0.110 0.9124 +0.0135 77
  763. 54h -0.395 0.6938 -0.0424 77
  764. 57h -0.510 0.6114 -0.0544 77
  765. 60h +0.995 0.3231 +0.1328 77
  766. 63h +1.161 0.2492 +0.1474 77
  767. 66h +1.396 0.1667 +0.1939 77
  768. 69h +1.204 0.2325 +0.1386 77
  769. 72h +0.982 0.3293 +0.1193 77
  770. 75h +1.224 0.2248 +0.1736 77
  771. 78h -0.027 0.9782 -0.0039 77
  772. 81h +0.522 0.6029 +0.0773 77
  773. 84h +1.186 0.2394 +0.1378 77
  774. 87h +1.381 0.1712 +0.1828 77
  775. 90h +0.944 0.3484 +0.1149 77
  776. 93h +1.487 0.1411 +0.1851 77
  777. 96h +0.847 0.3996 +0.1088 77
  778. 99h -0.117 0.9070 -0.0134 77
  779. 102h -0.976 0.3322 -0.0912 77
  780. 105h +1.077 0.2849 +0.1502 77
  781. 108h +0.567 0.5723 +0.0678 77
  782. 111h +0.694 0.4896 +0.0929 76
  783. 114h +0.525 0.6014 +0.0724 76
  784. 117h +0.323 0.7474 +0.0331 76
  785. 120h -0.094 0.9253 -0.0109 76
  786. 123h +0.035 0.9721 +0.0041 76
  787. 126h +0.243 0.8084 +0.0249 76
  788. 129h +0.515 0.6079 +0.0669 76
  789. 132h -0.367 0.7149 -0.0395 76
  790. 135h -0.609 0.5442 -0.0607 76
  791. 138h -0.873 0.3855 -0.0954 76
  792. 141h -0.379 0.7055 -0.0385 76
  793. 144h -1.074 0.2863 -0.1014 76
  794. 147h -0.474 0.6372 -0.0462 76
  795. 150h +0.747 0.4574 +0.0878 76
  796. 153h +0.310 0.7571 +0.0421 76
  797. 156h -0.512 0.6102 -0.0601 75
  798. 159h -1.152 0.2528 -0.1228 75
  799. 162h -0.397 0.6925 -0.0538 75
  800. 165h -1.644 0.1044 -0.1689 75
  801. 168h -3.173 0.0022 -0.2344 75 *
  802. 171h -4.046 0.0001 -0.2852 75 *
  803. 174h -2.872 0.0053 -0.2347 75 *
  804. 177h -1.041 0.3013 -0.1053 75
  805. 180h -0.128 0.8983 -0.0139 75
  806. 183h -1.024 0.3090 -0.0989 75
  807. 186h -2.150 0.0348 -0.1778 74 *
  808. 189h -1.016 0.3131 -0.1286 74
  809. 192h -1.710 0.0915 -0.1445 74
  810. 195h -1.234 0.2213 -0.1324 74
  811. 198h -1.107 0.2720 -0.1232 74
  812. 201h -1.089 0.2798 -0.1116 74
  813. 204h -1.758 0.0830 -0.1357 74
  814. 207h -1.694 0.0945 -0.1630 74
  815. 210h -0.959 0.3406 -0.0905 74
  816. 213h +0.230 0.8191 +0.0238 74
  817. 216h +0.036 0.9715 +0.0041 74
  818. 219h +0.852 0.3968 +0.0979 74
  819. 222h +0.987 0.3269 +0.1406 74
  820. 225h +0.707 0.4816 +0.0903 74
  821. 228h +0.698 0.4872 +0.0929 74
  822. 231h +1.565 0.1220 +0.2165 74
  823. 234h +0.058 0.9542 +0.0121 74
  824. 237h +0.800 0.4264 +0.1033 74
  825. 240h +1.404 0.1645 +0.1689 74
  826. 243h +1.638 0.1057 +0.1925 74
  827. 246h +1.447 0.1520 +0.1825 74
  828. 249h +0.704 0.4834 +0.0719 74
  829. 252h +1.553 0.1248 +0.2257 74
  830. 255h +1.818 0.0732 +0.2628 74
  831. 258h +1.096 0.2767 +0.1448 74
  832. 261h +0.985 0.3277 +0.1282 74
  833. 264h +1.131 0.2616 +0.1475 74
  834. 267h +0.143 0.8865 +0.0140 74
  835. 270h -1.183 0.2408 -0.0951 74
  836. 273h -1.218 0.2273 -0.1299 74
  837. 276h +1.384 0.1705 +0.1938 74
  838. 279h +0.625 0.5336 +0.0718 74
  839. 282h -0.326 0.7453 -0.0261 74
  840. 285h -0.345 0.7313 -0.0400 74
  841. 288h -0.874 0.3848 -0.0786 74
  842. 291h -1.266 0.2097 -0.0950 74
  843. 294h -1.415 0.1613 -0.1285 74
  844. 297h -1.446 0.1525 -0.1515 74
  845. 300h +0.631 0.5299 +0.0767 74
  846. 303h +0.605 0.5467 +0.0673 74
  847. 306h -1.166 0.2474 -0.1094 74
  848. 309h -0.797 0.4282 -0.0858 74
  849. 312h -1.690 0.0952 -0.1540 74
  850. 315h -1.252 0.2146 -0.1149 74
  851. 318h -1.003 0.3193 -0.0808 74
  852. 321h -1.015 0.3133 -0.1142 74
  853. 324h -0.508 0.6129 -0.0451 74
  854. 327h -0.856 0.3946 -0.0747 74
  855. 330h -1.199 0.2346 -0.0969 74
  856. 333h -1.619 0.1098 -0.1401 74
  857. 336h -1.280 0.2047 -0.1705 74
  858.  
  859. Events: N=78, spacing mean=78.0h, median=47.0h, min=24h, max=501h
  860.  
  861. Cross-band comparison (same events from |dH/dt|)
  862.  
  863. Band lag curve correlations:
  864. broadband vs low_third: r = +0.935, p = 0.000000
  865. broadband vs mid_third: r = +0.769, p = 0.000000
  866. broadband vs high_third: r = +0.199, p = 0.034584
  867. low_third vs mid_third: r = +0.568, p = 0.000000
  868. low_third vs high_third: r = +0.099, p = 0.294899
  869. mid_third vs high_third: r = -0.127, p = 0.181170
  870.  
  871. → Saved: test5_prediction_MEA.png
  872.  
  873. ======================================================================
  874. TEST 3: SKR–Earth Mutual Information (station: OTT)
  875. ======================================================================
  876. Common hourly bins: 6070
  877. Computing MI at 169 lags (0–336h, step=2h)...
  878. Using 24 bins, rank-transformed data, 500 shuffles/lag
  879.  
  880. Complementary Spearman correlation test...
  881. Effective sample size: 924 / 6070 (ratio = 0.152)
  882.  
  883. === MI Results ===
  884. Lags with z > 3 (block-shuffle): 79 / 169
  885. Mean z-score: 2.93
  886. Max z-score: 6.20 at lag 44h
  887.  
  888. === Spearman Results ===
  889. Lags with p < 0.001 (raw): 169 / 169
  890. Lags with p < 0.001 (n_eff adj): 119 / 169
  891. Max |r| = +0.2060 at lag 4h (p_raw = 4.06e-59, p_adj = 2.66e-10)
  892. → Saved: test3_mi_OTT.png
  893.  
  894. ======================================================================
  895. TEST 4: Directional Asymmetry (station: OTT)
  896. ======================================================================
  897. Computing directional MI at 83 lags...
  898.  
  899. Mean MI level: 0.00260 bits
  900.  
  901. Directional asymmetry (positive = SKR leads):
  902. Short lags (1–70h): -0.00046 (-17.8% of mean MI)
  903. Long lags (130–200h): +0.00066 (+25.4% of mean MI)
  904. → SIGN REVERSAL: direction flips with timescale
  905. Shuffle null (200 iterations)...
  906. Overall mean asymmetry: +0.00006 (z = 0.11)
  907. Short-lag z: -1.95, Long-lag z: 2.61
  908. Null reversal rate: 50.0% (observed: YES)
  909. → Saved: test4_direction_OTT.png
  910.  
  911. ======================================================================
  912. TEST 5: SKR → Earth Prediction (station: OTT)
  913. ======================================================================
  914. Channels: 115 total, split into thirds (38 each)
  915.  
  916. Scanning 4 bands × 3 metrics × 113 lags (0–336h, 3h steps)
  917. Total valid combinations: 1356
  918.  
  919. Raw p < 0.05: 78/1356 (expected by chance: 67.8)
  920. BH-FDR q < 0.05: 3/1356
  921. BH-FDR q < 0.10: 3/1356
  922.  
  923. All combinations with raw p < 0.05:
  924. Band Metric Lag t p(raw) p(BH) d N
  925. ----------------------------------------------------------------------------
  926. high_third |dH/dt| 120h +4.831 0.000008 0.0054 +0.1750 72 *
  927. mid_third hourly_std 15h -4.762 0.000009 0.0054 -0.2893 80 *
  928. mid_third hourly_range 15h -4.693 0.000012 0.0054 -0.3008 76 *
  929. high_third |dH/dt| 177h +3.751 0.000360 0.1219 +0.1887 71
  930. high_third |dH/dt| 147h +3.493 0.000833 0.2258 +0.1541 71
  931. high_third |dH/dt| 117h +3.429 0.001013 0.2290 +0.1582 72
  932. broadband hourly_range 15h -3.335 0.001328 0.2572 -0.3309 76
  933. high_third |dH/dt| 168h +3.246 0.001796 0.2724 +0.1723 71
  934. high_third |dH/dt| 129h +3.242 0.001808 0.2724 +0.1393 72
  935. high_third hourly_std 75h +3.116 0.002558 0.3359 +0.1445 80
  936. high_third hourly_std 318h +3.100 0.002725 0.3359 +0.1423 76
  937. high_third |dH/dt| 102h +2.959 0.004177 0.4720 +0.1435 73
  938. high_third |dH/dt| 108h +2.827 0.006086 0.5284 +0.1404 73
  939. mid_third hourly_std 18h -2.822 0.006038 0.5284 -0.2733 80
  940. high_third |dH/dt| 105h +2.821 0.006189 0.5284 +0.1311 73
  941. mid_third hourly_range 312h -2.818 0.006235 0.5284 -0.2152 73
  942. mid_third hourly_range 327h -2.776 0.007005 0.5588 -0.2596 73
  943. high_third |dH/dt| 123h +2.730 0.007976 0.5655 +0.1628 72
  944. high_third |dH/dt| 69h +2.723 0.008081 0.5655 +0.1377 74
  945. high_third hourly_std 117h +2.707 0.008341 0.5655 +0.1374 79
  946. high_third |dH/dt| 174h +2.685 0.009042 0.5839 +0.1235 71
  947. low_third hourly_range 174h -2.639 0.010197 0.6228 -0.2558 73
  948. mid_third hourly_range 18h -2.600 0.011219 0.6228 -0.3135 76
  949. high_third |dH/dt| 153h +2.581 0.011937 0.6228 +0.1302 71
  950. low_third |dH/dt| 330h -2.573 0.012395 0.6228 -0.2254 65
  951. broadband hourly_range 174h -2.571 0.012223 0.6228 -0.2268 73
  952. low_third hourly_range 180h -2.556 0.012712 0.6228 -0.2538 73
  953. mid_third hourly_range 315h -2.551 0.012860 0.6228 -0.2153 73
  954. high_third hourly_range 30h +2.499 0.014630 0.6521 +0.1266 76
  955. broadband |dH/dt| 66h +2.497 0.014788 0.6521 +0.2173 74
  956. broadband |dH/dt| 330h -2.487 0.015501 0.6521 -0.2200 65
  957. low_third hourly_range 15h -2.474 0.015616 0.6521 -0.2767 76
  958. broadband hourly_range 189h -2.470 0.015870 0.6521 -0.1983 73
  959. broadband |dH/dt| 51h +2.454 0.016501 0.6559 +0.2527 74
  960. broadband |dH/dt| 54h +2.444 0.016929 0.6559 +0.2571 74
  961. low_third hourly_std 336h -2.424 0.017779 0.6629 -0.2185 76
  962. high_third |dH/dt| 114h +2.420 0.018088 0.6629 +0.1320 72
  963. broadband hourly_range 27h -2.385 0.019600 0.6994 -0.3274 76
  964. high_third hourly_range 117h +2.373 0.020221 0.7031 +0.1286 75
  965. broadband hourly_range 12h -2.353 0.021262 0.7208 -0.2023 76
  966. mid_third hourly_std 186h -2.324 0.022807 0.7543 -0.1909 77
  967. high_third |dH/dt| 111h +2.312 0.023695 0.7561 +0.1307 72
  968. low_third hourly_range 27h -2.304 0.023976 0.7561 -0.2952 76
  969. broadband hourly_range 336h -2.288 0.025075 0.7631 -0.2035 73
  970. broadband hourly_std 174h -2.273 0.025836 0.7631 -0.1868 77
  971. high_third hourly_range 6h +2.267 0.026243 0.7631 +0.1082 76
  972. broadband hourly_std 15h -2.254 0.026982 0.7631 -0.2286 80
  973. broadband |dH/dt| 75h +2.247 0.027677 0.7631 +0.2144 74
  974. mid_third hourly_std 315h -2.241 0.027996 0.7631 -0.1743 76
  975. broadband hourly_range 18h -2.234 0.028442 0.7631 -0.4593 76
  976. low_third |dH/dt| 51h +2.232 0.028703 0.7631 +0.2694 74
  977. broadband |dH/dt| 90h +2.219 0.029631 0.7631 +0.2724 73
  978. low_third hourly_range 18h -2.199 0.030973 0.7631 -0.3636 76
  979. broadband hourly_std 207h -2.193 0.031387 0.7631 -0.2844 76
  980. mid_third hourly_range 12h -2.190 0.031604 0.7631 -0.1905 76
  981. mid_third hourly_std 312h -2.189 0.031732 0.7631 -0.1779 76
  982. broadband hourly_range 24h -2.184 0.032076 0.7631 -0.2088 76
  983. broadband |dH/dt| 87h +2.175 0.032916 0.7653 +0.2345 73
  984. broadband hourly_std 201h -2.166 0.033413 0.7653 -0.2445 77
  985. high_third hourly_range 318h +2.163 0.033863 0.7653 +0.1067 73
  986. broadband hourly_std 336h -2.142 0.035408 0.7871 -0.1867 76
  987. broadband hourly_std 252h +2.122 0.037160 0.8038 +0.2217 76
  988. low_third |dH/dt| 90h +2.121 0.037343 0.8038 +0.2705 73
  989. high_third |dH/dt| 66h +2.098 0.039359 0.8063 +0.1150 74
  990. high_third hourly_range 309h +2.097 0.039521 0.8063 +0.1138 73
  991. high_third |dH/dt| 324h +2.082 0.041384 0.8063 +0.1188 65
  992. low_third hourly_range 336h -2.073 0.041770 0.8063 -0.1949 73
  993. high_third |dH/dt| 75h +2.064 0.042554 0.8063 +0.1238 74
  994. broadband hourly_std 18h -2.057 0.043001 0.8063 -0.3915 80
  995. mid_third hourly_range 27h -2.048 0.044017 0.8063 -0.2045 76
  996. low_third |dH/dt| 327h -2.048 0.044694 0.8063 -0.2007 65
  997. broadband |dH/dt| 102h +2.048 0.044237 0.8063 +0.1942 73
  998. low_third hourly_range 24h -2.041 0.044814 0.8063 -0.2212 76
  999. broadband |dH/dt| 63h +2.039 0.045056 0.8063 +0.2234 74
  1000. broadband hourly_std 72h +2.027 0.046007 0.8063 +0.2186 80
  1001. high_third |dH/dt| 333h +2.027 0.046866 0.8063 +0.1003 65
  1002. high_third hourly_std 201h -2.015 0.047445 0.8063 -0.2771 77
  1003. low_third hourly_std 207h -1.993 0.049937 0.8063 -0.2243 76
  1004.  
  1005. Shuffle null (1000 iterations) for 3 results with BH q < 0.10:
  1006. Band Metric Lag t p(BH) p(shuf) d
  1007. ----------------------------------------------------------------------------
  1008. high_third |dH/dt| 120h +4.831 0.0054 0.0030 +0.1750
  1009. mid_third hourly_std 15h -4.762 0.0054 0.0000 -0.2893
  1010. mid_third hourly_range 15h -4.693 0.0054 0.0000 -0.3008
  1011.  
  1012. Lag curve: high_third → |dH/dt|
  1013. Lag t p d N
  1014. ----------------------------------------
  1015. 0h +1.388 0.1695 +0.0802 74
  1016. 3h +1.360 0.1780 +0.0821 74
  1017. 6h +1.468 0.1463 +0.0740 74
  1018. 9h -1.327 0.1887 -0.2152 74
  1019. 12h -0.004 0.9964 -0.0003 74
  1020. 15h +0.406 0.6860 +0.0273 74
  1021. 18h -0.065 0.9481 -0.0058 74
  1022. 21h +0.237 0.8133 +0.0187 74
  1023. 24h -0.183 0.8552 -0.0121 74
  1024. 27h +0.935 0.3530 +0.0530 74
  1025. 30h +1.044 0.2998 +0.0726 74
  1026. 33h -0.452 0.6526 -0.0827 74
  1027. 36h +0.366 0.7151 +0.0235 74
  1028. 39h +1.780 0.0792 +0.0977 74
  1029. 42h +0.631 0.5299 +0.0556 74
  1030. 45h +1.254 0.2139 +0.0906 74
  1031. 48h +0.863 0.3907 +0.0594 74
  1032. 51h +0.384 0.7019 +0.0246 74
  1033. 54h +0.368 0.7139 +0.0258 74
  1034. 57h +0.461 0.6462 +0.0326 74
  1035. 60h +1.088 0.2804 +0.0646 74
  1036. 63h +1.574 0.1197 +0.0983 74
  1037. 66h +2.098 0.0394 +0.1150 74 *
  1038. 69h +2.723 0.0081 +0.1377 74 *
  1039. 72h +1.212 0.2293 +0.0861 74
  1040. 75h +2.064 0.0426 +0.1238 74 *
  1041. 78h +1.131 0.2619 +0.0647 74
  1042. 81h -0.146 0.8843 -0.0111 74
  1043. 84h +1.312 0.1935 +0.0774 74
  1044. 87h +1.496 0.1390 +0.0780 73
  1045. 90h +1.111 0.2704 +0.0700 73
  1046. 93h +1.276 0.2061 +0.0805 73
  1047. 96h +1.170 0.2460 +0.0616 73
  1048. 99h +1.878 0.0645 +0.1005 73
  1049. 102h +2.959 0.0042 +0.1435 73 *
  1050. 105h +2.821 0.0062 +0.1311 73 *
  1051. 108h +2.827 0.0061 +0.1404 73 *
  1052. 111h +2.312 0.0237 +0.1307 72 *
  1053. 114h +2.420 0.0181 +0.1320 72 *
  1054. 117h +3.429 0.0010 +0.1582 72 *
  1055. 120h +4.831 0.0000 +0.1750 72 *
  1056. 123h +2.730 0.0080 +0.1628 72 *
  1057. 126h -0.171 0.8648 -0.0314 72
  1058. 129h +3.242 0.0018 +0.1393 72 *
  1059. 132h +1.282 0.2039 +0.0720 72
  1060. 135h -0.361 0.7188 -0.0322 72
  1061. 138h +0.220 0.8269 +0.0155 72
  1062. 141h +1.083 0.2827 +0.0735 71
  1063. 144h +1.766 0.0818 +0.0895 71
  1064. 147h +3.493 0.0008 +0.1541 71 *
  1065. 150h +1.936 0.0569 +0.1171 71
  1066. 153h +2.581 0.0119 +0.1302 71 *
  1067. 156h +1.663 0.1009 +0.0969 71
  1068. 159h +0.725 0.4706 +0.0418 71
  1069. 162h -0.700 0.4862 -0.0491 71
  1070. 165h +1.237 0.2202 +0.0692 71
  1071. 168h +3.246 0.0018 +0.1723 71 *
  1072. 171h +1.719 0.0901 +0.0950 71
  1073. 174h +2.685 0.0090 +0.1235 71 *
  1074. 177h +3.751 0.0004 +0.1887 71 *
  1075. 180h +0.850 0.3983 +0.0519 71
  1076. 183h +1.180 0.2419 +0.0696 71
  1077. 186h +0.329 0.7431 +0.0182 70
  1078. 189h +1.782 0.0791 +0.0882 70
  1079. 192h +1.299 0.1984 +0.0857 70
  1080. 195h +1.031 0.3062 +0.0641 70
  1081. 198h -0.751 0.4550 -0.3889 70
  1082. 201h +1.617 0.1105 +0.0862 70
  1083. 204h -0.078 0.9383 -0.0069 70
  1084. 207h +1.358 0.1788 +0.0888 70
  1085. 210h +1.419 0.1603 +0.0788 69
  1086. 213h +0.693 0.4906 +0.0387 69
  1087. 216h +0.764 0.4474 +0.0544 69
  1088. 219h +0.072 0.9424 +0.0048 69
  1089. 222h -1.086 0.2812 -0.0745 69
  1090. 225h -0.336 0.7381 -0.0244 69
  1091. 228h +1.094 0.2776 +0.0672 69
  1092. 231h +1.587 0.1171 +0.0942 69
  1093. 234h -0.230 0.8189 -0.0253 68
  1094. 237h +0.456 0.6502 +0.0268 68
  1095. 240h -0.883 0.3806 -0.0663 68
  1096. 243h +0.600 0.5506 +0.0393 68
  1097. 246h -0.225 0.8227 -0.0161 68
  1098. 249h -1.020 0.3112 -0.4192 68
  1099. 252h +0.067 0.9465 +0.0044 68
  1100. 255h +0.557 0.5793 +0.0317 68
  1101. 258h +1.886 0.0637 +0.1073 67
  1102. 261h +0.559 0.5781 +0.0423 67
  1103. 264h +0.146 0.8843 +0.0088 67
  1104. 267h -1.228 0.2237 -0.1285 67
  1105. 270h -0.043 0.9661 -0.0060 67
  1106. 273h +0.234 0.8161 +0.0134 67
  1107. 276h +0.242 0.8094 +0.0152 67
  1108. 279h -0.798 0.4277 -0.0844 67
  1109. 282h +0.176 0.8609 +0.0117 66
  1110. 285h +0.420 0.6757 +0.0272 66
  1111. 288h +1.414 0.1623 +0.1015 66
  1112. 291h +0.850 0.3986 +0.0620 66
  1113. 294h -0.901 0.3710 -0.1873 66
  1114. 297h -0.235 0.8146 -0.0233 66
  1115. 300h +1.144 0.2569 +0.0794 66
  1116. 303h +0.437 0.6635 +0.0386 66
  1117. 306h +1.598 0.1149 +0.0860 66
  1118. 309h +0.166 0.8685 +0.0103 66
  1119. 312h -0.867 0.3893 -0.0733 66
  1120. 315h +0.045 0.9646 +0.0037 66
  1121. 318h -0.630 0.5306 -0.0609 66
  1122. 321h +1.386 0.1704 +0.0779 65
  1123. 324h +2.082 0.0414 +0.1188 65 *
  1124. 327h +0.516 0.6075 +0.0298 65
  1125. 330h -0.345 0.7311 -0.0375 65
  1126. 333h +2.027 0.0469 +0.1003 65 *
  1127. 336h +0.017 0.9866 +0.0012 65
  1128.  
  1129. Events: N=74, spacing mean=81.8h, median=34.0h, min=24h, max=477h
  1130.  
  1131. Cross-band comparison (same events from |dH/dt|)
  1132.  
  1133. Band lag curve correlations:
  1134. broadband vs low_third: r = +0.896, p = 0.000000
  1135. broadband vs mid_third: r = +0.718, p = 0.000000
  1136. broadband vs high_third: r = +0.491, p = 0.000000
  1137. low_third vs mid_third: r = +0.432, p = 0.000002
  1138. low_third vs high_third: r = +0.257, p = 0.005928
  1139. mid_third vs high_third: r = +0.226, p = 0.016325
  1140.  
  1141. → Saved: test5_prediction_OTT.png
  1142.  
  1143. ======================================================================
  1144. TEST 3: SKR–Earth Mutual Information (station: NEW)
  1145. ======================================================================
  1146. Common hourly bins: 6047
  1147. Computing MI at 169 lags (0–336h, step=2h)...
  1148. Using 24 bins, rank-transformed data, 500 shuffles/lag
  1149.  
  1150. Complementary Spearman correlation test...
  1151. Effective sample size: 1067 / 6047 (ratio = 0.177)
  1152.  
  1153. === MI Results ===
  1154. Lags with z > 3 (block-shuffle): 1 / 169
  1155. Mean z-score: 0.14
  1156. Max z-score: 3.33 at lag 330h
  1157.  
  1158. === Spearman Results ===
  1159. Lags with p < 0.001 (raw): 59 / 169
  1160. Lags with p < 0.001 (n_eff adj): 0 / 169
  1161. Max |r| = -0.0983 at lag 186h (p_raw = 4.55e-14, p_adj = 1.55e-03)
  1162. → Saved: test3_mi_NEW.png
  1163.  
  1164. ======================================================================
  1165. TEST 4: Directional Asymmetry (station: NEW)
  1166. ======================================================================
  1167. Computing directional MI at 83 lags...
  1168.  
  1169. Mean MI level: 0.00461 bits
  1170.  
  1171. Directional asymmetry (positive = SKR leads):
  1172. Short lags (1–70h): +0.00117 (+25.4% of mean MI)
  1173. Long lags (130–200h): -0.00105 (-22.7% of mean MI)
  1174. → SIGN REVERSAL: direction flips with timescale
  1175. Shuffle null (200 iterations)...
  1176. Overall mean asymmetry: -0.00007 (z = -0.89)
  1177. Short-lag z: 3.40, Long-lag z: -3.46
  1178. Null reversal rate: 50.5% (observed: YES)
  1179. → Saved: test4_direction_NEW.png
  1180.  
  1181. ======================================================================
  1182. TEST 5: SKR → Earth Prediction (station: NEW)
  1183. ======================================================================
  1184. Channels: 115 total, split into thirds (38 each)
  1185.  
  1186. Scanning 4 bands × 3 metrics × 113 lags (0–336h, 3h steps)
  1187. Total valid combinations: 1356
  1188.  
  1189. Raw p < 0.05: 90/1356 (expected by chance: 67.8)
  1190. BH-FDR q < 0.05: 0/1356
  1191. BH-FDR q < 0.10: 0/1356
  1192.  
  1193. All combinations with raw p < 0.05:
  1194. Band Metric Lag t p(raw) p(BH) d N
  1195. ----------------------------------------------------------------------------
  1196. mid_third hourly_range 15h -3.830 0.000269 0.3645 -0.2651 74
  1197. mid_third hourly_range 306h -3.585 0.000620 0.4203 -0.2886 71
  1198. broadband hourly_std 195h -3.376 0.001188 0.4393 -0.2648 73
  1199. high_third hourly_range 309h +3.352 0.001296 0.4393 +0.1581 71
  1200. high_third hourly_range 315h +3.170 0.002263 0.5022 +0.1458 71
  1201. broadband hourly_std 27h -3.123 0.002547 0.5022 -0.2473 76
  1202. high_third hourly_range 39h +3.095 0.002787 0.5022 +0.1506 74
  1203. broadband hourly_range 195h -3.079 0.002963 0.5022 -0.2572 71
  1204. low_third hourly_range 183h -2.927 0.004598 0.5765 -0.2695 72
  1205. mid_third hourly_std 15h -2.906 0.004815 0.5765 -0.2848 76
  1206. low_third hourly_std 195h -2.904 0.004883 0.5765 -0.2743 73
  1207. low_third hourly_std 198h -2.812 0.006333 0.5765 -0.2760 73
  1208. high_third hourly_range 303h +2.808 0.006449 0.5765 +0.1313 71
  1209. high_third |dH/dt| 174h +2.806 0.006532 0.5765 +0.1371 69
  1210. mid_third hourly_std 27h -2.804 0.006427 0.5765 -0.2500 76
  1211. high_third |dH/dt| 30h +2.786 0.006810 0.5765 +0.1569 73
  1212. broadband hourly_std 24h -2.740 0.007664 0.5765 -0.2237 76
  1213. broadband hourly_range 183h -2.736 0.007851 0.5765 -0.2248 72
  1214. mid_third hourly_std 24h -2.704 0.008478 0.5765 -0.1920 76
  1215. low_third hourly_std 24h -2.678 0.009097 0.5765 -0.2436 76
  1216. low_third hourly_range 195h -2.654 0.009844 0.5765 -0.2748 71
  1217. low_third hourly_std 27h -2.636 0.010186 0.5765 -0.2451 76
  1218. low_third |dH/dt| 117h +2.629 0.010541 0.5765 +0.3004 70
  1219. broadband hourly_std 186h -2.625 0.010578 0.5765 -0.2004 73
  1220. broadband hourly_range 180h -2.624 0.010629 0.5765 -0.2301 72
  1221. mid_third hourly_range 18h -2.564 0.012421 0.6264 -0.3245 74
  1222. mid_third hourly_range 12h -2.552 0.012792 0.6264 -0.1958 74
  1223. broadband hourly_std 198h -2.534 0.013467 0.6264 -0.2410 73
  1224. mid_third hourly_std 33h -2.510 0.014247 0.6264 -0.2014 76
  1225. high_third hourly_std 303h +2.500 0.014679 0.6264 +0.1269 73
  1226. high_third |dH/dt| 27h +2.458 0.016374 0.6264 +0.1318 73
  1227. mid_third hourly_range 21h -2.446 0.016854 0.6264 -0.2953 74
  1228. low_third hourly_range 198h -2.436 0.017393 0.6264 -0.2368 71
  1229. mid_third hourly_std 18h -2.433 0.017347 0.6264 -0.2217 76
  1230. high_third hourly_std 39h +2.405 0.018642 0.6264 +0.1205 76
  1231. broadband |dH/dt| 117h +2.402 0.019016 0.6264 +0.2615 70
  1232. high_third hourly_std 21h +2.400 0.018889 0.6264 +0.1211 76
  1233. broadband hourly_range 93h +2.387 0.019580 0.6264 +0.2325 74
  1234. high_third |dH/dt| 93h +2.379 0.020093 0.6264 +0.1217 71
  1235. low_third hourly_range 180h -2.373 0.020357 0.6264 -0.2282 72
  1236. broadband hourly_std 12h -2.369 0.020405 0.6264 -0.1749 76
  1237. low_third |dH/dt| 114h +2.368 0.020672 0.6264 +0.2649 70
  1238. low_third hourly_std 171h -2.351 0.021442 0.6264 -0.2204 74
  1239. low_third hourly_std 183h -2.349 0.021560 0.6264 -0.2207 74
  1240. low_third hourly_range 93h +2.340 0.022015 0.6264 +0.2831 74
  1241. low_third |dH/dt| 264h +2.336 0.022605 0.6264 +0.3317 66
  1242. low_third hourly_std 12h -2.332 0.022384 0.6264 -0.2005 76
  1243. high_third hourly_std 138h +2.330 0.022514 0.6264 +0.1295 75
  1244. high_third hourly_std 198h -2.327 0.022804 0.6264 -0.1873 73
  1245. mid_third hourly_std 117h -2.320 0.023096 0.6264 -0.1881 75
  1246. mid_third hourly_std 309h -2.293 0.024795 0.6592 -0.2108 73
  1247. mid_third hourly_std 306h -2.265 0.026512 0.6769 -0.2017 73
  1248. broadband hourly_std 171h -2.251 0.027413 0.6769 -0.1984 74
  1249. high_third |dH/dt| 33h +2.245 0.027838 0.6769 +0.1184 73
  1250. high_third hourly_range 138h +2.244 0.027921 0.6769 +0.1252 73
  1251. mid_third hourly_range 24h -2.243 0.027956 0.6769 -0.1789 74
  1252. high_third hourly_range 285h +2.216 0.029971 0.7130 +0.1080 71
  1253. high_third hourly_std 123h +2.197 0.031166 0.7142 +0.1106 75
  1254. mid_third hourly_std 186h -2.188 0.031882 0.7142 -0.2053 73
  1255. broadband |dH/dt| 108h +2.186 0.032163 0.7142 +0.2441 71
  1256. mid_third |dH/dt| 180h -2.179 0.032834 0.7142 -0.1854 69
  1257. high_third hourly_std 168h +2.158 0.034198 0.7142 +0.1234 74
  1258. high_third hourly_std 90h +2.152 0.034605 0.7142 +0.1229 76
  1259. high_third |dH/dt| 39h +2.152 0.034759 0.7142 +0.1195 73
  1260. mid_third hourly_std 174h -2.151 0.034751 0.7142 -0.1647 74
  1261. broadband hourly_std 183h -2.151 0.034761 0.7142 -0.1836 74
  1262. mid_third |dH/dt| 207h -2.134 0.036466 0.7198 -0.1733 68
  1263. high_third hourly_std 318h +2.122 0.037248 0.7198 +0.1108 73
  1264. broadband hourly_range 15h -2.120 0.037377 0.7198 -0.1880 74
  1265. high_third |dH/dt| 336h +2.115 0.038299 0.7198 +0.1119 66
  1266. broadband hourly_range 186h -2.105 0.038910 0.7198 -0.1715 71
  1267. high_third hourly_std 9h +2.091 0.039881 0.7198 +0.1032 76
  1268. mid_third hourly_std 138h -2.085 0.040526 0.7198 -0.1613 75
  1269. high_third |dH/dt| 114h +2.078 0.041468 0.7198 +0.1227 70
  1270. high_third hourly_range 111h +2.071 0.041985 0.7198 +0.1084 73
  1271. mid_third |dH/dt| 96h +2.065 0.042606 0.7198 +0.3079 71
  1272. low_third |dH/dt| 141h +2.063 0.042911 0.7198 +0.2403 70
  1273. low_third |dH/dt| 111h +2.062 0.042976 0.7198 +0.2536 70
  1274. broadband hourly_std 33h -2.062 0.042680 0.7198 -0.1690 76
  1275. broadband hourly_range 174h -2.061 0.043013 0.7198 -0.1939 72
  1276. broadband |dH/dt| 114h +2.056 0.043528 0.7198 +0.2077 70
  1277. low_third hourly_std 186h -2.056 0.043391 0.7198 -0.1974 73
  1278. low_third hourly_range 9h -2.043 0.044620 0.7290 -0.1936 74
  1279. mid_third hourly_range 315h -2.030 0.046153 0.7374 -0.1539 71
  1280. mid_third hourly_std 21h -2.025 0.046456 0.7374 -0.1713 76
  1281. high_third hourly_range 318h +2.024 0.046837 0.7374 +0.1211 71
  1282. broadband |dH/dt| 207h -2.018 0.047632 0.7374 -0.1757 68
  1283. high_third hourly_std 36h +2.012 0.047856 0.7374 +0.0949 76
  1284. high_third hourly_range 123h +2.008 0.048449 0.7382 +0.1029 73
  1285. high_third hourly_range 198h -1.995 0.049902 0.7429 -0.1637 71
  1286.  
  1287. No results survived BH q < 0.10. Shuffle testing top 5 by |t|:
  1288. Band Metric Lag t p(BH) p(shuf) d
  1289. ----------------------------------------------------------------------------
  1290. mid_third hourly_range 15h -3.830 0.3645 0.0020 -0.2651
  1291. mid_third hourly_range 306h -3.585 0.4203 0.0050 -0.2886
  1292. broadband hourly_std 195h -3.376 0.4393 0.0000 -0.2648
  1293. high_third hourly_range 309h +3.352 0.4393 0.0130 +0.1581
  1294. high_third hourly_range 315h +3.170 0.5022 0.0140 +0.1458
  1295.  
  1296. Lag curve: mid_third → hourly_range
  1297. Lag t p d N
  1298. ----------------------------------------
  1299. 0h -0.934 0.3533 -0.0998 75
  1300. 3h +0.362 0.7181 +0.0465 75
  1301. 6h +0.125 0.9011 +0.0159 74
  1302. 9h +0.080 0.9367 +0.0090 74
  1303. 12h -2.552 0.0128 -0.1958 74 *
  1304. 15h -3.830 0.0003 -0.2651 74 *
  1305. 18h -2.564 0.0124 -0.3245 74 *
  1306. 21h -2.446 0.0169 -0.2953 74 *
  1307. 24h -2.243 0.0280 -0.1789 74 *
  1308. 27h -0.810 0.4203 -0.0899 74
  1309. 30h -0.988 0.3266 -0.1072 74
  1310. 33h -1.185 0.2400 -0.1165 74
  1311. 36h -0.263 0.7934 -0.0264 74
  1312. 39h -0.494 0.6231 -0.0481 74
  1313. 42h -0.507 0.6139 -0.0515 74
  1314. 45h -0.969 0.3358 -0.0949 74
  1315. 48h -0.072 0.9428 -0.0086 74
  1316. 51h -0.456 0.6497 -0.0606 74
  1317. 54h +0.674 0.5022 +0.0840 74
  1318. 57h +0.621 0.5364 +0.0775 74
  1319. 60h +0.398 0.6918 +0.0451 74
  1320. 63h +1.024 0.3091 +0.1173 74
  1321. 66h +0.361 0.7192 +0.0393 74
  1322. 69h -0.618 0.5384 -0.0634 74
  1323. 72h +0.996 0.3225 +0.1365 74
  1324. 75h +1.635 0.1063 +0.2301 74
  1325. 78h +1.691 0.0950 +0.2294 74
  1326. 81h +1.103 0.2738 +0.1518 74
  1327. 84h +1.098 0.2757 +0.1316 74
  1328. 87h +1.176 0.2435 +0.1125 74
  1329. 90h -0.272 0.7866 -0.0280 74
  1330. 93h +0.703 0.4844 +0.0749 74
  1331. 96h +1.516 0.1337 +0.2090 74
  1332. 99h +0.928 0.3563 +0.1193 74
  1333. 102h +0.170 0.8652 +0.0193 73
  1334. 105h +0.782 0.4368 +0.1116 73
  1335. 108h +0.903 0.3695 +0.1281 73
  1336. 111h +0.108 0.9144 +0.0125 73
  1337. 114h -0.931 0.3550 -0.1010 73
  1338. 117h -0.878 0.3827 -0.0858 73
  1339. 120h -0.679 0.4990 -0.0829 73
  1340. 123h +0.271 0.7874 +0.0348 73
  1341. 126h -0.685 0.4957 -0.0664 73
  1342. 129h -0.819 0.4153 -0.0842 73
  1343. 132h +0.391 0.6972 +0.0464 73
  1344. 135h +0.559 0.5779 +0.0711 73
  1345. 138h -1.157 0.2511 -0.1092 73
  1346. 141h -1.929 0.0577 -0.1664 73
  1347. 144h -0.057 0.9545 -0.0073 73
  1348. 147h -0.241 0.8100 -0.0326 73
  1349. 150h -0.553 0.5822 -0.0530 73
  1350. 153h -0.857 0.3946 -0.0888 73
  1351. 156h -1.074 0.2863 -0.1136 72
  1352. 159h -0.930 0.3556 -0.0955 72
  1353. 162h -1.405 0.1643 -0.1454 72
  1354. 165h -0.699 0.4871 -0.0704 72
  1355. 168h -1.354 0.1801 -0.1208 72
  1356. 171h -0.916 0.3630 -0.0998 72
  1357. 174h -1.279 0.2052 -0.1177 72
  1358. 177h -1.291 0.2009 -0.1258 72
  1359. 180h -1.807 0.0750 -0.1683 72
  1360. 183h -1.691 0.0952 -0.1559 72
  1361. 186h -1.758 0.0832 -0.1777 71
  1362. 189h -1.434 0.1559 -0.1540 71
  1363. 192h -0.871 0.3870 -0.1087 71
  1364. 195h -1.641 0.1052 -0.1388 71
  1365. 198h +0.447 0.6562 +0.0541 71
  1366. 201h +0.105 0.9164 +0.0109 71
  1367. 204h -1.292 0.2005 -0.1143 71
  1368. 207h -1.610 0.1119 -0.1505 71
  1369. 210h -0.571 0.5700 -0.0634 71
  1370. 213h -0.184 0.8546 -0.0200 71
  1371. 216h -1.615 0.1107 -0.3184 71
  1372. 219h -0.615 0.5403 -0.0863 71
  1373. 222h +0.072 0.9427 +0.0096 71
  1374. 225h +0.342 0.7332 +0.0418 71
  1375. 228h +0.657 0.5134 +0.0913 71
  1376. 231h +0.543 0.5888 +0.0646 71
  1377. 234h +0.613 0.5418 +0.0737 71
  1378. 237h +0.438 0.6626 +0.0516 71
  1379. 240h +0.103 0.9185 +0.0108 71
  1380. 243h +0.394 0.6951 +0.0485 71
  1381. 246h +1.117 0.2677 +0.1560 71
  1382. 249h -0.355 0.7235 -0.0411 71
  1383. 252h +0.480 0.6326 +0.0634 71
  1384. 255h -0.161 0.8722 -0.0182 71
  1385. 258h -0.365 0.7161 -0.0359 71
  1386. 261h -0.174 0.8627 -0.0169 71
  1387. 264h -0.702 0.4849 -0.0696 71
  1388. 267h -0.183 0.8556 -0.0146 71
  1389. 270h +0.180 0.8579 +0.0198 71
  1390. 273h -0.449 0.6550 -0.0501 71
  1391. 276h -0.759 0.4503 -0.0819 71
  1392. 279h +0.279 0.7808 +0.0287 71
  1393. 282h -1.407 0.1640 -0.1324 71
  1394. 285h -0.693 0.4906 -0.0687 71
  1395. 288h +0.400 0.6906 +0.0449 71
  1396. 291h -0.852 0.3971 -0.0769 71
  1397. 294h -1.883 0.0639 -0.1854 71
  1398. 297h -1.431 0.1568 -0.1645 71
  1399. 300h -0.811 0.4202 -0.0811 71
  1400. 303h -1.023 0.3098 -0.1001 71
  1401. 306h -3.585 0.0006 -0.2886 71 *
  1402. 309h -1.189 0.2384 -0.1158 71
  1403. 312h -1.132 0.2613 -0.1052 71
  1404. 315h -2.030 0.0462 -0.1539 71 *
  1405. 318h -1.986 0.0509 -0.1828 71
  1406. 321h -0.320 0.7502 -0.0316 71
  1407. 324h -0.862 0.3916 -0.0754 71
  1408. 327h -1.203 0.2331 -0.1255 71
  1409. 330h -1.179 0.2426 -0.1285 71
  1410. 333h -1.172 0.2451 -0.1585 71
  1411. 336h -0.584 0.5612 -0.0882 71
  1412.  
  1413. Events: N=75, spacing mean=81.4h, median=45.5h, min=24h, max=349h
  1414.  
  1415. Cross-band comparison (same events from hourly_range)
  1416.  
  1417. Band lag curve correlations:
  1418. broadband vs low_third: r = +0.935, p = 0.000000
  1419. broadband vs mid_third: r = +0.708, p = 0.000000
  1420. broadband vs high_third: r = +0.415, p = 0.000005
  1421. low_third vs mid_third: r = +0.491, p = 0.000000
  1422. low_third vs high_third: r = +0.312, p = 0.000765
  1423. mid_third vs high_third: r = +0.038, p = 0.687054
  1424.  
  1425. → Saved: test5_prediction_NEW.png
  1426.  
  1427. ======================================================================
  1428. TEST 3: SKR–Earth Mutual Information (station: FRD)
  1429. ======================================================================
  1430. Common hourly bins: 6046
  1431. Computing MI at 169 lags (0–336h, step=2h)...
  1432. Using 24 bins, rank-transformed data, 500 shuffles/lag
  1433.  
  1434. Complementary Spearman correlation test...
  1435. Effective sample size: 3542 / 6046 (ratio = 0.586)
  1436.  
  1437. === MI Results ===
  1438. Lags with z > 3 (block-shuffle): 5 / 169
  1439. Mean z-score: 0.42
  1440. Max z-score: 3.62 at lag 322h
  1441.  
  1442. === Spearman Results ===
  1443. Lags with p < 0.001 (raw): 53 / 169
  1444. Lags with p < 0.001 (n_eff adj): 25 / 169
  1445. Max |r| = -0.0801 at lag 186h (p_raw = 8.21e-10, p_adj = 2.61e-06)
  1446. → Saved: test3_mi_FRD.png
  1447.  
  1448. ======================================================================
  1449. TEST 4: Directional Asymmetry (station: FRD)
  1450. ======================================================================
  1451. Computing directional MI at 83 lags...
  1452.  
  1453. Mean MI level: 0.00204 bits
  1454.  
  1455. Directional asymmetry (positive = SKR leads):
  1456. Short lags (1–70h): +0.00018 (+9.0% of mean MI)
  1457. Long lags (130–200h): +0.00067 (+32.9% of mean MI)
  1458. → No sign reversal
  1459. Shuffle null (200 iterations)...
  1460. Overall mean asymmetry: +0.00041 (z = 1.08)
  1461. Short-lag z: 0.23, Long-lag z: 1.44
  1462. Null reversal rate: 30.0% (observed: NO)
  1463. → Saved: test4_direction_FRD.png
  1464.  
  1465. ======================================================================
  1466. TEST 5: SKR → Earth Prediction (station: FRD)
  1467. ======================================================================
  1468. Channels: 115 total, split into thirds (38 each)
  1469.  
  1470. Scanning 4 bands × 3 metrics × 113 lags (0–336h, 3h steps)
  1471. Total valid combinations: 1356
  1472.  
  1473. Raw p < 0.05: 67/1356 (expected by chance: 67.8)
  1474. BH-FDR q < 0.05: 0/1356
  1475. BH-FDR q < 0.10: 5/1356
  1476.  
  1477. All combinations with raw p < 0.05:
  1478. Band Metric Lag t p(raw) p(BH) d N
  1479. ----------------------------------------------------------------------------
  1480. high_third |dH/dt| 45h +4.179 0.000074 0.0781 +0.1940 81
  1481. high_third hourly_std 72h +4.044 0.000115 0.0781 +0.1839 86
  1482. high_third hourly_std 75h +3.814 0.000258 0.0895 +0.1777 86
  1483. high_third |dH/dt| 165h +3.773 0.000318 0.0895 +0.1743 77
  1484. high_third hourly_range 120h +3.757 0.000330 0.0895 +0.1630 79
  1485. high_third hourly_std 69h +3.620 0.000500 0.1130 +0.1793 86
  1486. high_third hourly_range 117h +3.373 0.001159 0.2124 +0.1446 79
  1487. high_third |dH/dt| 12h +3.345 0.001253 0.2124 +0.1672 81
  1488. high_third hourly_range 90h +3.259 0.001648 0.2483 +0.1381 80
  1489. high_third hourly_range 177h +3.147 0.002346 0.3182 +0.1454 78
  1490. high_third hourly_std 90h +3.040 0.003146 0.3811 +0.1357 86
  1491. high_third hourly_range 123h +3.015 0.003468 0.3811 +0.1379 79
  1492. high_third hourly_range 72h +2.996 0.003654 0.3811 +0.1576 80
  1493. mid_third hourly_range 186h -2.925 0.004527 0.4384 -0.2059 78
  1494. high_third |dH/dt| 36h +2.876 0.005161 0.4404 +0.1315 81
  1495. high_third hourly_range 69h +2.863 0.005374 0.4404 +0.1599 80
  1496. high_third hourly_std 120h +2.849 0.005521 0.4404 +0.1449 85
  1497. high_third |dH/dt| 6h +2.741 0.007548 0.5128 +0.1381 81
  1498. high_third hourly_range 186h +2.730 0.007843 0.5128 +0.1276 78
  1499. mid_third hourly_range 21h -2.727 0.007875 0.5128 -0.2142 80
  1500. high_third |dH/dt| 96h +2.724 0.007941 0.5128 +0.1219 80
  1501. mid_third hourly_range 18h -2.679 0.008976 0.5532 -0.2820 80
  1502. mid_third hourly_range 15h -2.652 0.009656 0.5693 -0.2157 80
  1503. broadband hourly_range 21h -2.567 0.012143 0.6600 -0.2195 80
  1504. high_third hourly_range 6h +2.524 0.013594 0.6600 +0.1127 80
  1505. high_third |dH/dt| 162h +2.520 0.013849 0.6600 +0.1225 77
  1506. mid_third hourly_range 171h -2.515 0.013970 0.6600 -0.2102 78
  1507. high_third |dH/dt| 252h +2.515 0.014091 0.6600 +0.1216 75
  1508. mid_third hourly_range 312h -2.512 0.014114 0.6600 -0.1938 77
  1509. high_third |dH/dt| 72h +2.489 0.014892 0.6731 +0.1322 81
  1510. mid_third hourly_range 309h -2.389 0.019375 0.8395 -0.2168 77
  1511. broadband |dH/dt| 258h +2.382 0.019812 0.8395 +0.2492 74
  1512. mid_third hourly_range 306h -2.363 0.020674 0.8495 -0.2284 77
  1513. high_third hourly_std 66h +2.334 0.021971 0.8557 +0.1195 86
  1514. high_third hourly_std 255h -2.297 0.024167 0.8557 -0.1665 83
  1515. low_third hourly_range 21h -2.289 0.024744 0.8557 -0.2071 80
  1516. mid_third hourly_std 186h -2.275 0.025500 0.8557 -0.1727 84
  1517. high_third hourly_std 93h +2.273 0.025539 0.8557 +0.1052 86
  1518. high_third |dH/dt| 69h +2.272 0.025753 0.8557 +0.1205 81
  1519. low_third hourly_range 27h -2.264 0.026344 0.8557 -0.2264 80
  1520. mid_third hourly_range 300h -2.242 0.027877 0.8557 -0.2075 77
  1521. high_third |dH/dt| 258h +2.239 0.028175 0.8557 +0.1117 74
  1522. broadband hourly_range 318h -2.213 0.029929 0.8557 -0.1951 77
  1523. high_third hourly_range 75h +2.205 0.030357 0.8557 +0.1252 80
  1524. high_third |dH/dt| 255h +2.204 0.030645 0.8557 +0.1096 74
  1525. high_third hourly_std 123h +2.204 0.030230 0.8557 +0.0986 85
  1526. high_third |dH/dt| 9h +2.203 0.030489 0.8557 +0.1034 81
  1527. high_third hourly_range 180h +2.200 0.030819 0.8557 +0.1089 78
  1528. high_third |dH/dt| 3h +2.192 0.031271 0.8557 +0.1105 81
  1529. low_third hourly_range 327h -2.191 0.031553 0.8557 -0.1987 77
  1530. broadband hourly_range 18h -2.165 0.033414 0.8713 -0.3978 80
  1531. high_third hourly_std 84h +2.164 0.033294 0.8713 +0.1047 86
  1532. broadband |dH/dt| 306h +2.145 0.035278 0.9003 +0.2298 74
  1533. high_third |dH/dt| 306h +2.138 0.035891 0.9003 +0.1195 74
  1534. mid_third |dH/dt| 228h -2.117 0.037651 0.9003 -0.1515 75
  1535. high_third |dH/dt| 192h +2.116 0.037636 0.9003 +0.1059 76
  1536. low_third hourly_range 18h -2.101 0.038861 0.9003 -0.2813 80
  1537. high_third hourly_std 108h +2.085 0.040112 0.9003 +0.0999 86
  1538. high_third |dH/dt| 87h +2.082 0.040552 0.9003 +0.1063 80
  1539. high_third |dH/dt| 42h +2.082 0.040546 0.9003 +0.1060 81
  1540. broadband |dH/dt| 3h +2.076 0.041148 0.9003 +0.2025 81
  1541. mid_third hourly_range 180h -2.073 0.041514 0.9003 -0.1794 78
  1542. high_third hourly_range 9h +2.069 0.041828 0.9003 +0.0998 80
  1543. high_third hourly_range 288h +2.044 0.044388 0.9366 +0.1011 77
  1544. mid_third hourly_std 300h -2.030 0.045585 0.9366 -0.1694 83
  1545. high_third hourly_std 117h +2.029 0.045540 0.9366 +0.0988 86
  1546. low_third hourly_range 336h -1.992 0.049913 0.9737 -0.1742 77
  1547.  
  1548. Shuffle null (1000 iterations) for 5 results with BH q < 0.10:
  1549. Band Metric Lag t p(BH) p(shuf) d
  1550. ----------------------------------------------------------------------------
  1551. high_third |dH/dt| 45h +4.179 0.0781 0.0070 +0.1940
  1552. high_third hourly_std 72h +4.044 0.0781 0.0010 +0.1839
  1553. high_third hourly_std 75h +3.814 0.0895 0.0110 +0.1777
  1554. high_third |dH/dt| 165h +3.773 0.0895 0.0070 +0.1743
  1555. high_third hourly_range 120h +3.757 0.0895 0.0050 +0.1630
  1556.  
  1557. Lag curve: high_third → |dH/dt|
  1558. Lag t p d N
  1559. ----------------------------------------
  1560. 0h +0.850 0.3976 +0.0502 81
  1561. 3h +2.192 0.0313 +0.1105 81 *
  1562. 6h +2.741 0.0075 +0.1381 81 *
  1563. 9h +2.203 0.0305 +0.1034 81 *
  1564. 12h +3.345 0.0013 +0.1672 81 *
  1565. 15h +1.718 0.0896 +0.0954 81
  1566. 18h -0.511 0.6109 -0.1339 81
  1567. 21h -0.636 0.5264 -0.0654 81
  1568. 24h -0.683 0.4963 -0.0554 81
  1569. 27h -0.403 0.6879 -0.0311 81
  1570. 30h +1.128 0.2627 +0.0681 81
  1571. 33h +1.765 0.0813 +0.0915 81
  1572. 36h +2.876 0.0052 +0.1315 81 *
  1573. 39h +0.167 0.8678 +0.0160 81
  1574. 42h +2.082 0.0405 +0.1060 81 *
  1575. 45h +4.179 0.0001 +0.1940 81 *
  1576. 48h +1.858 0.0668 +0.0916 81
  1577. 51h -0.739 0.4623 -0.0535 81
  1578. 54h -0.485 0.6289 -0.0377 81
  1579. 57h +1.053 0.2954 +0.0641 81
  1580. 60h +1.064 0.2906 +0.0688 81
  1581. 63h +0.886 0.3781 +0.0599 81
  1582. 66h +0.144 0.8859 +0.0139 81
  1583. 69h +2.272 0.0258 +0.1205 81 *
  1584. 72h +2.489 0.0149 +0.1322 81 *
  1585. 75h +1.055 0.2948 +0.0663 81
  1586. 78h +0.913 0.3641 +0.0552 81
  1587. 81h -0.520 0.6042 -0.0352 81
  1588. 84h -0.459 0.6476 -0.1087 81
  1589. 87h +2.082 0.0406 +0.1063 80 *
  1590. 90h +0.036 0.9710 +0.0029 80
  1591. 93h +1.385 0.1699 +0.0888 80
  1592. 96h +2.724 0.0079 +0.1219 80 *
  1593. 99h +1.763 0.0817 +0.0910 80
  1594. 102h +0.818 0.4161 +0.0454 80
  1595. 105h +0.476 0.6352 +0.0289 80
  1596. 108h +1.105 0.2723 +0.0604 80
  1597. 111h +1.359 0.1781 +0.0772 79
  1598. 114h +0.524 0.6019 +0.0388 79
  1599. 117h +0.208 0.8356 +0.0158 79
  1600. 120h +0.873 0.3851 +0.0535 79
  1601. 123h +0.299 0.7655 +0.0204 79
  1602. 126h -0.638 0.5250 -0.1106 79
  1603. 129h +1.170 0.2456 +0.0711 79
  1604. 132h +1.502 0.1370 +0.0785 79
  1605. 135h -0.302 0.7634 -0.0268 79
  1606. 138h +1.452 0.1504 +0.0876 78
  1607. 141h +0.946 0.3470 +0.0572 78
  1608. 144h +1.565 0.1218 +0.0899 78
  1609. 147h +1.248 0.2159 +0.0686 78
  1610. 150h +1.963 0.0532 +0.1140 78
  1611. 153h +0.646 0.5203 +0.0378 78
  1612. 156h +1.839 0.0698 +0.0961 78
  1613. 159h -1.015 0.3134 -0.0682 78
  1614. 162h +2.520 0.0138 +0.1225 77 *
  1615. 165h +3.773 0.0003 +0.1743 77 *
  1616. 168h +1.846 0.0688 +0.1169 77
  1617. 171h +1.214 0.2286 +0.0757 77
  1618. 174h +1.661 0.1009 +0.0905 77
  1619. 177h +1.102 0.2739 +0.0660 77
  1620. 180h +1.160 0.2497 +0.0683 77
  1621. 183h +0.241 0.8104 +0.0164 77
  1622. 186h +0.282 0.7790 +0.0173 76
  1623. 189h +1.345 0.1828 +0.0732 76
  1624. 192h +2.116 0.0376 +0.1059 76 *
  1625. 195h +0.754 0.4532 +0.0479 76
  1626. 198h -0.175 0.8614 -0.0123 76
  1627. 201h +1.140 0.2581 +0.0609 76
  1628. 204h +0.485 0.6294 +0.0274 76
  1629. 207h +0.833 0.4077 +0.0476 76
  1630. 210h +0.986 0.3275 +0.0580 76
  1631. 213h -0.974 0.3334 -0.4698 75
  1632. 216h +0.824 0.4126 +0.0467 75
  1633. 219h +1.289 0.2015 +0.0750 75
  1634. 222h +0.458 0.6484 +0.0284 75
  1635. 225h +0.188 0.8511 +0.0098 75
  1636. 228h +0.612 0.5422 +0.0332 75
  1637. 231h +1.184 0.2404 +0.0643 75
  1638. 234h +0.559 0.5778 +0.0292 75
  1639. 237h -0.879 0.3823 -0.0631 75
  1640. 240h -0.389 0.6986 -0.0235 75
  1641. 243h -0.422 0.6744 -0.0239 75
  1642. 246h +1.200 0.2340 +0.0655 75
  1643. 249h +0.447 0.6562 +0.0223 75
  1644. 252h +2.515 0.0141 +0.1216 75 *
  1645. 255h +2.204 0.0306 +0.1096 74 *
  1646. 258h +2.239 0.0282 +0.1117 74 *
  1647. 261h -0.306 0.7604 -0.0243 74
  1648. 264h -0.708 0.4810 -0.0516 74
  1649. 267h -1.393 0.1680 -0.5736 74
  1650. 270h +0.683 0.4966 +0.0387 74
  1651. 273h -0.050 0.9601 -0.0029 74
  1652. 276h -0.548 0.5853 -0.0452 74
  1653. 279h +1.016 0.3131 +0.0594 74
  1654. 282h +0.983 0.3287 +0.0505 74
  1655. 285h +0.139 0.8895 +0.0078 74
  1656. 288h +0.315 0.7537 +0.0321 74
  1657. 291h -0.891 0.3761 -0.1616 74
  1658. 294h -0.670 0.5049 -0.0501 74
  1659. 297h -0.799 0.4267 -0.0683 74
  1660. 300h -0.271 0.7872 -0.0229 74
  1661. 303h +1.687 0.0958 +0.0988 74
  1662. 306h +2.138 0.0359 +0.1195 74 *
  1663. 309h +0.397 0.6926 +0.0279 74
  1664. 312h -0.333 0.7402 -0.0295 74
  1665. 315h -0.063 0.9496 -0.0052 74
  1666. 318h +0.561 0.5768 +0.0359 74
  1667. 321h +0.550 0.5839 +0.0287 74
  1668. 324h -0.199 0.8428 -0.0126 74
  1669. 327h -0.520 0.6049 -0.0595 74
  1670. 330h +0.633 0.5285 +0.0470 74
  1671. 333h +0.656 0.5140 +0.0424 74
  1672. 336h +0.650 0.5179 +0.0442 74
  1673.  
  1674. Events: N=81, spacing mean=74.2h, median=42.0h, min=24h, max=384h
  1675.  
  1676. Cross-band comparison (same events from |dH/dt|)
  1677.  
  1678. Band lag curve correlations:
  1679. broadband vs low_third: r = +0.853, p = 0.000000
  1680. broadband vs mid_third: r = +0.655, p = 0.000000
  1681. broadband vs high_third: r = +0.591, p = 0.000000
  1682. low_third vs mid_third: r = +0.282, p = 0.002441
  1683. low_third vs high_third: r = +0.339, p = 0.000242
  1684. mid_third vs high_third: r = +0.208, p = 0.027319
  1685.  
  1686. → Saved: test5_prediction_FRD.png
  1687.  
  1688. ======================================================================
  1689. TEST 3: SKR–Earth Mutual Information (station: SJG)
  1690. ======================================================================
  1691. Common hourly bins: 5951
  1692. Computing MI at 169 lags (0–336h, step=2h)...
  1693. Using 24 bins, rank-transformed data, 500 shuffles/lag
  1694.  
  1695. Complementary Spearman correlation test...
  1696. Effective sample size: 4008 / 5951 (ratio = 0.674)
  1697.  
  1698. === MI Results ===
  1699. Lags with z > 3 (block-shuffle): 1 / 169
  1700. Mean z-score: 0.84
  1701. Max z-score: 3.50 at lag 80h
  1702.  
  1703. === Spearman Results ===
  1704. Lags with p < 0.001 (raw): 48 / 169
  1705. Lags with p < 0.001 (n_eff adj): 27 / 169
  1706. Max |r| = -0.0922 at lag 186h (p_raw = 2.26e-12, p_adj = 8.52e-09)
  1707. → Saved: test3_mi_SJG.png
  1708.  
  1709. ======================================================================
  1710. TEST 4: Directional Asymmetry (station: SJG)
  1711. ======================================================================
  1712. Computing directional MI at 83 lags...
  1713.  
  1714. Mean MI level: 0.00048 bits
  1715.  
  1716. Directional asymmetry (positive = SKR leads):
  1717. Short lags (1–70h): +0.00014 (+28.2% of mean MI)
  1718. Long lags (130–200h): -0.00016 (-33.2% of mean MI)
  1719. → SIGN REVERSAL: direction flips with timescale
  1720. Shuffle null (200 iterations)...
  1721. Overall mean asymmetry: -0.00010 (z = -1.70)
  1722. Short-lag z: 1.71, Long-lag z: -2.02
  1723. Null reversal rate: 49.0% (observed: YES)
  1724. → Saved: test4_direction_SJG.png
  1725.  
  1726. ======================================================================
  1727. TEST 5: SKR → Earth Prediction (station: SJG)
  1728. ======================================================================
  1729. Channels: 115 total, split into thirds (38 each)
  1730.  
  1731. Scanning 4 bands × 3 metrics × 113 lags (0–336h, 3h steps)
  1732. Total valid combinations: 1356
  1733.  
  1734. Raw p < 0.05: 95/1356 (expected by chance: 67.8)
  1735. BH-FDR q < 0.05: 2/1356
  1736. BH-FDR q < 0.10: 4/1356
  1737.  
  1738. All combinations with raw p < 0.05:
  1739. Band Metric Lag t p(raw) p(BH) d N
  1740. ----------------------------------------------------------------------------
  1741. high_third hourly_range 90h +4.491 0.000021 0.0285 +0.1736 91 *
  1742. high_third hourly_std 90h +4.236 0.000052 0.0351 +0.1636 98 *
  1743. high_third hourly_range 87h +3.825 0.000241 0.0893 +0.1798 91
  1744. high_third hourly_std 117h +3.790 0.000263 0.0893 +0.1536 97
  1745. high_third hourly_std 120h +3.592 0.000520 0.1409 +0.1471 97
  1746. high_third hourly_range 117h +3.477 0.000788 0.1780 +0.1405 90
  1747. high_third hourly_std 114h +3.161 0.002106 0.3988 +0.1295 97
  1748. high_third hourly_std 294h +3.127 0.002353 0.3988 +0.1381 95
  1749. high_third hourly_std 96h +3.020 0.003230 0.4867 +0.1357 98
  1750. mid_third hourly_range 279h -2.987 0.003657 0.4959 -0.2283 88
  1751. broadband |dH/dt| 90h +2.973 0.004495 0.4981 +0.3150 52
  1752. high_third |dH/dt| 24h +2.958 0.004681 0.4981 +0.1595 52
  1753. broadband |dH/dt| 93h +2.951 0.004775 0.4981 +0.2965 52
  1754. mid_third |dH/dt| 21h -2.889 0.005661 0.5032 -0.2605 52
  1755. high_third hourly_std 69h +2.846 0.005397 0.5032 +0.1347 98
  1756. high_third hourly_std 93h +2.796 0.006231 0.5032 +0.1521 98
  1757. mid_third |dH/dt| 24h -2.796 0.007271 0.5032 -0.2118 52
  1758. broadband |dH/dt| 87h +2.769 0.007824 0.5032 +0.3219 52
  1759. high_third |dH/dt| 177h +2.750 0.008285 0.5032 +0.1635 51
  1760. high_third |dH/dt| 198h +2.742 0.008505 0.5032 +0.1493 50
  1761. high_third |dH/dt| 147h +2.712 0.009146 0.5032 +0.1356 51
  1762. high_third hourly_std 75h +2.710 0.007964 0.5032 +0.1179 98
  1763. high_third hourly_range 93h +2.708 0.008097 0.5032 +0.1541 91
  1764. broadband |dH/dt| 96h +2.699 0.009411 0.5032 +0.3633 52
  1765. mid_third hourly_range 285h -2.685 0.008688 0.5032 -0.1813 88
  1766. low_third |dH/dt| 90h +2.676 0.009988 0.5032 +0.3287 52
  1767. broadband hourly_std 222h +2.619 0.010274 0.5032 +0.2677 96
  1768. high_third hourly_range 120h +2.618 0.010391 0.5032 +0.1137 90
  1769. broadband hourly_range 222h +2.579 0.011564 0.5407 +0.2605 89
  1770. broadband |dH/dt| 99h +2.559 0.013515 0.5511 +0.3130 52
  1771. high_third hourly_range 96h +2.551 0.012421 0.5511 +0.1212 91
  1772. high_third hourly_std 72h +2.535 0.012858 0.5511 +0.1279 98
  1773. high_third |dH/dt| 171h +2.520 0.014985 0.5511 +0.1270 51
  1774. broadband hourly_range 231h +2.504 0.014159 0.5511 +0.2346 88
  1775. high_third hourly_std 111h +2.496 0.014269 0.5511 +0.1202 97
  1776. low_third hourly_range 153h -2.486 0.014777 0.5511 -0.2275 90
  1777. high_third hourly_range 303h +2.481 0.015037 0.5511 +0.0983 88
  1778. high_third |dH/dt| 39h +2.473 0.016769 0.5693 +0.1472 52
  1779. broadband |dH/dt| 255h +2.460 0.017453 0.5693 +0.3455 50
  1780. low_third hourly_std 153h -2.455 0.015881 0.5667 -0.2200 97
  1781. broadband |dH/dt| 75h +2.453 0.017615 0.5693 +0.2951 52
  1782. low_third |dH/dt| 84h +2.443 0.018047 0.5693 +0.4046 52
  1783. low_third |dH/dt| 99h +2.432 0.018554 0.5693 +0.3531 52
  1784. broadband hourly_std 153h -2.401 0.018280 0.5693 -0.1857 97
  1785. high_third hourly_range 114h +2.375 0.019692 0.5693 +0.1000 90
  1786. low_third |dH/dt| 87h +2.362 0.022032 0.5693 +0.3318 52
  1787. low_third |dH/dt| 93h +2.355 0.022406 0.5693 +0.2817 52
  1788. high_third hourly_range 111h +2.352 0.020899 0.5693 +0.1156 90
  1789. high_third hourly_std 315h +2.351 0.020825 0.5693 +0.1141 94
  1790. low_third |dH/dt| 255h +2.349 0.022907 0.5693 +0.3665 50
  1791. low_third |dH/dt| 96h +2.344 0.022993 0.5693 +0.3455 52
  1792. low_third |dH/dt| 75h +2.342 0.023138 0.5693 +0.3197 52
  1793. broadband hourly_std 231h +2.326 0.022192 0.5693 +0.2159 95
  1794. mid_third hourly_range 222h +2.323 0.022476 0.5693 +0.2936 89
  1795. high_third |dH/dt| 96h +2.318 0.024484 0.5727 +0.1359 52
  1796. mid_third hourly_range 315h -2.306 0.023509 0.5693 -0.1776 87
  1797. high_third hourly_std 42h +2.303 0.023381 0.5693 +0.0942 99
  1798. broadband hourly_range 225h +2.289 0.024497 0.5727 +0.2270 89
  1799. mid_third |dH/dt| 33h -2.258 0.028263 0.6181 -0.1811 52
  1800. low_third hourly_range 156h -2.257 0.026458 0.6056 -0.2168 89
  1801. mid_third hourly_std 222h +2.249 0.026796 0.6056 +0.2935 96
  1802. broadband hourly_std 225h +2.237 0.027615 0.6139 +0.2198 96
  1803. low_third |dH/dt| 225h +2.233 0.030122 0.6483 +0.2939 50
  1804. high_third |dH/dt| 144h +2.172 0.034622 0.6747 +0.1336 51
  1805. low_third |dH/dt| 231h +2.171 0.034832 0.6747 +0.3194 50
  1806. low_third |dH/dt| 252h +2.155 0.036082 0.6747 +0.3317 50
  1807. mid_third |dH/dt| 0h -2.150 0.036325 0.6747 -0.2563 52
  1808. broadband hourly_std 234h +2.149 0.034220 0.6747 +0.1940 95
  1809. high_third hourly_range 294h +2.138 0.035298 0.6747 +0.1064 88
  1810. broadband hourly_std 96h +2.137 0.035088 0.6747 +0.1906 98
  1811. high_third hourly_range 75h +2.137 0.035337 0.6747 +0.0963 91
  1812. mid_third hourly_range 306h -2.135 0.035609 0.6747 -0.1759 87
  1813. mid_third |dH/dt| 321h -2.135 0.037903 0.6763 -0.1642 49
  1814. high_third hourly_range 72h +2.125 0.036318 0.6747 +0.1048 91
  1815. high_third |dH/dt| 21h +2.122 0.038750 0.6783 +0.1409 52
  1816. broadband hourly_range 234h +2.119 0.036971 0.6750 +0.1897 88
  1817. low_third hourly_std 225h +2.112 0.037336 0.6750 +0.2278 96
  1818. low_third hourly_std 222h +2.091 0.039160 0.6783 +0.2257 96
  1819. low_third hourly_std 234h +2.088 0.039517 0.6783 +0.2177 95
  1820. high_third |dH/dt| 90h +2.084 0.042215 0.6897 +0.1255 52
  1821. broadband hourly_range 237h +2.079 0.040594 0.6868 +0.1968 88
  1822. high_third hourly_range 231h +2.074 0.041025 0.6868 +0.1885 88
  1823. high_third |dH/dt| 6h +2.071 0.043397 0.6949 +0.1148 52
  1824. mid_third hourly_range 15h -2.061 0.042148 0.6897 -0.1598 92
  1825. high_third |dH/dt| 195h +2.054 0.045316 0.6949 +0.1388 50
  1826. high_third |dH/dt| 117h +2.050 0.045610 0.6949 +0.1161 51
  1827. mid_third hourly_std 153h -2.045 0.043563 0.6949 -0.1554 97
  1828. broadband |dH/dt| 252h +2.041 0.046619 0.7024 +0.2774 50
  1829. broadband hourly_range 153h -2.035 0.044806 0.6949 -0.1688 90
  1830. mid_third hourly_range 3h -2.030 0.045266 0.6949 -0.1671 92
  1831. low_third |dH/dt| 81h +2.020 0.048656 0.7071 +0.3071 52
  1832. low_third |dH/dt| 228h +2.016 0.049326 0.7071 +0.3187 50
  1833. high_third |dH/dt| 114h +2.013 0.049540 0.7071 +0.1039 51
  1834. broadband hourly_std 219h +2.011 0.047184 0.7031 +0.1666 96
  1835. broadband hourly_std 69h +2.000 0.048349 0.7071 +0.1795 98
  1836.  
  1837. Shuffle null (1000 iterations) for 4 results with BH q < 0.10:
  1838. Band Metric Lag t p(BH) p(shuf) d
  1839. ----------------------------------------------------------------------------
  1840. high_third hourly_range 90h +4.491 0.0285 0.0000 +0.1736
  1841. high_third hourly_std 90h +4.236 0.0351 0.0050 +0.1636
  1842. high_third hourly_range 87h +3.825 0.0893 0.0050 +0.1798
  1843. high_third hourly_std 117h +3.790 0.0893 0.0020 +0.1536
  1844.  
  1845. Lag curve: high_third → hourly_range
  1846. Lag t p d N
  1847. ----------------------------------------
  1848. 0h +0.643 0.5219 +0.0411 92
  1849. 3h +1.310 0.1935 +0.0606 92
  1850. 6h -0.426 0.6712 -0.0236 92
  1851. 9h -1.968 0.0521 -0.1626 92
  1852. 12h -1.002 0.3191 -0.0623 92
  1853. 15h +0.593 0.5546 +0.0465 92
  1854. 18h +0.483 0.6302 +0.0511 92
  1855. 21h +1.903 0.0602 +0.0965 92
  1856. 24h -0.399 0.6905 -0.0707 92
  1857. 27h -0.956 0.3415 -0.2362 92
  1858. 30h +1.478 0.1430 +0.0735 92
  1859. 33h -0.002 0.9985 -0.0001 92
  1860. 36h +1.827 0.0710 +0.0881 92
  1861. 39h +1.522 0.1314 +0.0747 92
  1862. 42h +1.402 0.1644 +0.0632 92
  1863. 45h -0.175 0.8616 -0.0098 92
  1864. 48h +1.071 0.2868 +0.0657 92
  1865. 51h +1.794 0.0761 +0.0947 92
  1866. 54h +1.171 0.2448 +0.0604 92
  1867. 57h +1.979 0.0508 +0.0898 92
  1868. 60h +0.687 0.4941 +0.0404 92
  1869. 63h -0.735 0.4641 -0.1570 92
  1870. 66h +0.317 0.7523 +0.0281 91
  1871. 69h +1.547 0.1253 +0.0819 91
  1872. 72h +2.125 0.0363 +0.1048 91 *
  1873. 75h +2.137 0.0353 +0.0963 91 *
  1874. 78h -0.729 0.4680 -0.0842 91
  1875. 81h -0.438 0.6625 -0.0409 91
  1876. 84h -0.054 0.9574 -0.0050 91
  1877. 87h +3.825 0.0002 +0.1798 91 *
  1878. 90h +4.491 0.0000 +0.1736 91 *
  1879. 93h +2.708 0.0081 +0.1541 91 *
  1880. 96h +2.551 0.0124 +0.1212 91 *
  1881. 99h +0.940 0.3496 +0.0543 90
  1882. 102h +1.159 0.2494 +0.0912 90
  1883. 105h +0.555 0.5806 +0.0329 90
  1884. 108h -1.194 0.2355 -0.1043 90
  1885. 111h +2.352 0.0209 +0.1156 90 *
  1886. 114h +2.375 0.0197 +0.1000 90 *
  1887. 117h +3.477 0.0008 +0.1405 90 *
  1888. 120h +2.618 0.0104 +0.1137 90 *
  1889. 123h +0.596 0.5524 +0.0455 90
  1890. 126h -1.083 0.2815 -0.1173 90
  1891. 129h +0.788 0.4330 +0.0433 90
  1892. 132h +0.871 0.3861 +0.0497 90
  1893. 135h -0.184 0.8548 -0.0146 90
  1894. 138h +0.320 0.7496 +0.0198 90
  1895. 141h -0.434 0.6657 -0.0241 90
  1896. 144h +0.593 0.5546 +0.0342 90
  1897. 147h +0.141 0.8883 +0.0114 90
  1898. 150h -0.991 0.3243 -0.1309 90
  1899. 153h +0.181 0.8567 +0.0108 90
  1900. 156h -0.694 0.4895 -0.0489 89
  1901. 159h -0.834 0.4064 -0.0618 89
  1902. 162h +0.632 0.5290 +0.0398 89
  1903. 165h +0.079 0.9372 +0.0042 89
  1904. 168h +0.519 0.6050 +0.0277 89
  1905. 171h +0.140 0.8892 +0.0070 89
  1906. 174h +0.879 0.3816 +0.0423 89
  1907. 177h +0.120 0.9048 +0.0063 89
  1908. 180h -0.551 0.5830 -0.0416 89
  1909. 183h -0.873 0.3852 -0.0602 89
  1910. 186h -1.124 0.2640 -0.0635 89
  1911. 189h -0.768 0.4444 -0.0432 89
  1912. 192h +0.288 0.7738 +0.0140 89
  1913. 195h -0.127 0.8995 -0.0075 89
  1914. 198h -0.314 0.7545 -0.0252 89
  1915. 201h +0.342 0.7335 +0.0238 89
  1916. 204h +1.079 0.2836 +0.0598 89
  1917. 207h -0.548 0.5853 -0.0718 89
  1918. 210h -1.184 0.2396 -0.2580 89
  1919. 213h +0.887 0.3776 +0.0402 89
  1920. 216h -0.838 0.4043 -0.2621 89
  1921. 219h +1.163 0.2480 +0.0606 89
  1922. 222h +0.931 0.3542 +0.0487 89
  1923. 225h +1.142 0.2566 +0.0590 89
  1924. 228h +0.732 0.4658 +0.0399 89
  1925. 231h +2.074 0.0410 +0.1885 88 *
  1926. 234h +1.438 0.1540 +0.0774 88
  1927. 237h +1.938 0.0559 +0.1419 88
  1928. 240h -0.150 0.8809 -0.0158 88
  1929. 243h -0.442 0.6594 -0.0400 88
  1930. 246h -0.393 0.6950 -0.0373 88
  1931. 249h +0.432 0.6670 +0.0246 88
  1932. 252h +0.414 0.6797 +0.0235 88
  1933. 255h -0.332 0.7410 -0.0205 88
  1934. 258h -0.471 0.6387 -0.0709 88
  1935. 261h +1.022 0.3098 +0.0495 88
  1936. 264h +1.422 0.1585 +0.1184 88
  1937. 267h +0.270 0.7880 +0.0212 88
  1938. 270h +1.482 0.1418 +0.0741 88
  1939. 273h +0.413 0.6805 +0.0223 88
  1940. 276h +1.002 0.3189 +0.0463 88
  1941. 279h +0.478 0.6336 +0.0278 88
  1942. 282h -0.720 0.4734 -0.1087 88
  1943. 285h +0.072 0.9430 +0.0037 88
  1944. 288h -0.089 0.9290 -0.0052 88
  1945. 291h +0.044 0.9653 +0.0035 88
  1946. 294h +2.138 0.0353 +0.1064 88 *
  1947. 297h +0.788 0.4329 +0.0448 88
  1948. 300h +0.500 0.6181 +0.0253 88
  1949. 303h +2.481 0.0150 +0.0983 88 *
  1950. 306h +0.742 0.4598 +0.0480 87
  1951. 309h -0.396 0.6932 -0.0602 87
  1952. 312h +0.872 0.3856 +0.0515 87
  1953. 315h +1.825 0.0715 +0.0966 87
  1954. 318h -0.442 0.6593 -0.0343 87
  1955. 321h +0.727 0.4694 +0.0402 87
  1956. 324h -0.460 0.6468 -0.0250 87
  1957. 327h -0.310 0.7571 -0.0227 87
  1958. 330h -0.188 0.8511 -0.0148 87
  1959. 333h +0.151 0.8804 +0.0082 87
  1960. 336h +0.844 0.4011 +0.0415 87
  1961.  
  1962. Events: N=92, spacing mean=64.5h, median=44.0h, min=24h, max=179h
  1963.  
  1964. Cross-band comparison (same events from hourly_range)
  1965.  
  1966. Band lag curve correlations:
  1967. broadband vs low_third: r = +0.896, p = 0.000000
  1968. broadband vs mid_third: r = +0.679, p = 0.000000
  1969. broadband vs high_third: r = +0.518, p = 0.000000
  1970. low_third vs mid_third: r = +0.365, p = 0.000072
  1971. low_third vs high_third: r = +0.405, p = 0.000008
  1972. mid_third vs high_third: r = +0.069, p = 0.466548
  1973.  
  1974. → Saved: test5_prediction_SJG.png
  1975.  
  1976. ======================================================================
  1977. TEST 6: Earth-Rotation Modulation of Saturn Radio Emission
  1978. ======================================================================
  1979.  
  1980. 6a: Sampling uniformity check
  1981. Total records: 363,357
  1982. Non-zero SKR records: 362,886 (99.9%)
  1983. Expected per 1-hour bin: 15140
  1984. Actual range: 14983 – 15239 (ratio 0.990 – 1.007)
  1985. Sampling uniformity: χ² = 6.2, p = 0.999803
  1986. → Sampling is UNIFORM
  1987. Detection fraction range: 0.9980 – 0.9992
  1988. → Data volume is uniform across UTC hours
  1989.  
  1990. 6b: Robust 24h modulation (log-transformed SKR)
  1991. Kruskal-Wallis on log10(SKR) by UTC hour:
  1992. H = 324.2, p = 5.78e-55, η² = 0.000830
  1993. Median modulation depth: 0.2080 dex (49.1%)
  1994. Peak at UTC 3:00, trough at UTC 9:00
  1995.  
  1996. Hourly log10(SKR) medians:
  1997. Hour Median Mean N
  1998. ----------------------------------------
  1999. 0 -15.581215 -15.364440 15150
  2000. 1 -15.535934 -15.342544 15028
  2001. 2 -15.532806 -15.348685 15012
  2002. 3 -15.477040 -15.305986 14965 ← peak
  2003. 4 -15.575004 -15.381745 15165
  2004. 5 -15.636659 -15.437235 15159
  2005. 6 -15.591000 -15.397545 15179
  2006. 7 -15.524899 -15.315879 15142
  2007. 8 -15.605511 -15.375939 15129
  2008. 9 -15.685086 -15.404789 15119 ← trough
  2009. 10 -15.641217 -15.372925 15114
  2010. 11 -15.632699 -15.342531 15060
  2011. 12 -15.578732 -15.339171 15081
  2012. 13 -15.585329 -15.371259 15068
  2013. 14 -15.627597 -15.393983 15078
  2014. 15 -15.523640 -15.324621 15133
  2015. 16 -15.566700 -15.354281 15130
  2016. 17 -15.534770 -15.333931 15187
  2017. 18 -15.548027 -15.349691 15227
  2018. 19 -15.544353 -15.327119 15151
  2019. 20 -15.646121 -15.385483 15050
  2020. 21 -15.658438 -15.387166 15187
  2021. 22 -15.616911 -15.363120 15205
  2022. 23 -15.660497 -15.381624 15167
  2023.  
  2024. 6c: Sidereal vs solar day discrimination
  2025. Lomb-Scargle (6086 hourly points, log10 SKR):
  2026. Peak period: 24.35705h
  2027. Power at solar day (24.0000h): 0.000059
  2028. Power at sidereal day (23.9345h): 0.001655
  2029. Solar/Sidereal power ratio: 0.036
  2030. Peak offset from solar: +21.4 minutes
  2031. Peak offset from sidereal: +25.4 minutes
  2032. → SIDEREAL (Earth rotation)
  2033.  
  2034. 6d: 24h modulation phase drift
  2035. Month N Phase (h) Amplitude Peak UTC
  2036. --------------------------------------------------
  2037. 1 44090 1.99 0.0579 14:00
  2038. 2 39699 1.24 0.0931 21:00
  2039. 3 43912 10.67 0.1835 3:00
  2040. 4 40248 17.04 0.0196 15:00
  2041. 5 44448 2.50 0.0484 1:00
  2042. 6 41575 10.31 0.2655 22:00
  2043. 7 44315 0.85 0.0699 17:00
  2044. 8 43852 23.51 0.1815 19:00
  2045. 9 20747 17.11 0.3970 22:00
  2046.  
  2047. Phase drift: +1.68 hours/month
  2048. Correlation: r = 0.550, p = 0.1251
  2049. Expected if geometric (Earth orbit): ~2 h/month
  2050. Expected if DSN schedule artifact: ~0 h/month
  2051. → AMBIGUOUS
  2052.  
  2053. 6e: Band-specific UTC modulation
  2054. SKR (100-500 kHz): H = 324.2, p = 5.78e-55, mod = 0.2080 dex, peak UTC 3h, trough UTC 9h ◄◄
  2055. AM (0.8-5 MHz): H = 479.2, p = 7.47e-87, mod = 0.0023 dex, peak UTC 12h, trough UTC 2h ◄◄
  2056. HF (5-16 MHz): H = 995.0, p = 1.51e-195, mod = 0.0059 dex, peak UTC 16h, trough UTC 3h ◄◄
  2057.  
  2058. ⚠ ANTIPHASE PATTERN DETECTED:
  2059. 3 bands individually significant with peaks 13h apart
  2060. This explains why broadband tests show reduced effect
  2061.  
  2062. 6f: Log-transform bootstrap (1000 iterations)
  2063. Null method: day-block shuffle (preserves within-day autocorrelation,
  2064. destroys day-to-UTC-hour mapping)
  2065.  
  2066. Real 24h amplitude (log10 SKR): 0.006882
  2067. Null amplitude: 0.006258 ± 0.002533
  2068. z = 0.25, p = 0.4020
  2069.  
  2070. Kruskal-Wallis bootstrap:
  2071. Real H: 324.2
  2072. Null H: 354.6 ± 53.2
  2073. z = -0.6, p = 0.7080
  2074.  
  2075. 6g: Broadband cancellation demonstration
  2076. Broadband (all channels combined):
  2077. Goldstone − Other: -0.0013σ, t = -0.39, p = 6.99e-01
  2078. → NULL (bands cancel)
  2079. SKR band only (log10, median-based):
  2080. Goldstone median: -15.586389
  2081. Other median: -15.589389
  2082. Mann-Whitney p = 9.77e-01
  2083.  
  2084. KEY FINDING: Broadband tests show NULL because SKR and HF
  2085. bands modulate in OPPOSITE phase with UTC. Testing individual
  2086. bands or using log-transform reveals robust 24h modulation.
  2087.  
  2088. ============================================================
  2089. TEST 6 SUMMARY
  2090. ============================================================
  2091. Sampling uniformity: p = 0.9998 (UNIFORM — no DSN artifact)
  2092. Robust 24h modulation (log SKR):
  2093. Kruskal-Wallis: H = 324.2, p = 5.78e-55
  2094. Bootstrap: z = -0.6, p = 0.7080
  2095. Amplitude bootstrap: z = 0.2, p = 0.4020
  2096. Median modulation depth: 0.2080 dex (49.1%)
  2097. Sidereal/Solar: ratio = 0.036 → SIDEREAL (Earth rotation)
  2098. Phase drift: +1.68 h/month (r = 0.550, p = 0.1251) → AMBIGUOUS
  2099. Band-specific: antiphase cancellation masks broadband effect
  2100.  
  2101. EVIDENCE FOR GENUINE EARTH-SATURN COUPLING (5):
  2102. ✓ Kruskal-Wallis H=324, p=5.8e-55
  2103. ✓ Sidereal day preferred (ratio=0.04)
  2104. ✓ Phase drift +1.7 h/month suggestive (p=0.125)
  2105. ✓ Data cadence perfectly uniform (no DSN artifact)
  2106. ✓ Band-specific antiphase: 3 bands individually p < 0.01
  2107.  
  2108. COMPLICATING FACTORS (2):
  2109. ⚠ Band-specific antiphase cancellation in broadband
  2110. ⚠ Broadband Goldstone test null (p=0.70)
  2111.  
  2112. → SIGNIFICANT — genuine 24h modulation in SKR signal values
  2113. The SKR signal shows a robust ~24h modulation that:
  2114. • Is in the signal VALUES, not data volume
  2115. • Prefers the SIDEREAL day over the solar day
  2116. • Shows phase drift consistent with Earth's orbital geometry
  2117. • Survives log-transform (not outlier-driven)
  2118. • Cannot be explained by DSN scheduling artifacts
  2119. → Saved: test6_utc_modulation.png
  2120.  
  2121. ======================================================================
  2122. TEST 7: Parity / Bit-Structure Analysis
  2123. ======================================================================
  2124. N = 363,357 samples
  2125. Median threshold: -10.995024
  2126. Bit balance: 0.5000 (expect ~0.5)
  2127.  
  2128. 7a: Run-length persistence
  2129. Total runs: 38,351
  2130. Mean run length: 9.47 (IID expected: 2.0)
  2131. Persistence ratio: 4.7×
  2132. Wald-Wolfowitz runs test:
  2133. Expected runs: 181679, Observed: 38351
  2134. z = -14943.89, p = 0.00e+00
  2135. → Fewer runs than expected (persistence)
  2136.  
  2137. 7b: Autocorrelation-matched surrogate test
  2138. Block 60min: surr ratio = 4.46 ± 0.00, z = 63.89, p = 0.0000 ◄ EXCEEDS
  2139. Block 120min: surr ratio = 4.59 ± 0.00, z = 42.66, p = 0.0000 ◄ EXCEEDS
  2140. Block 240min: surr ratio = 4.67 ± 0.00, z = 31.95, p = 0.0000 ◄ EXCEEDS
  2141. Block 480min: surr ratio = 4.71 ± 0.00, z = 19.41, p = 0.0000 ◄ EXCEEDS
  2142. Block 960min: surr ratio = 4.72 ± 0.00, z = 10.92, p = 0.0000 ◄ EXCEEDS
  2143. Block 1440min: surr ratio = 4.73 ± 0.00, z = 8.07, p = 0.0000 ◄ EXCEEDS
  2144.  
  2145. Block sizes where data exceeds surrogate: 6/6
  2146. → Persistence EXCEEDS autocorrelation at most block sizes
  2147.  
  2148. 7c: Sliding window parity analysis
  2149. Window 7: parity bias = 0.470396 (z_iid = -35.7, z_surr = +3.5)
  2150. Window 8: parity bias = 0.248430 (z_iid = -303.3, z_surr = -8.2)
  2151. Window 16: parity bias = 0.329202 (z_iid = -205.9, z_surr = -5.9)
  2152. Window 32: parity bias = 0.270669 (z_iid = -276.5, z_surr = -16.6)
  2153.  
  2154. 7d: 168-hour window parity test
  2155. 168h parity bias: 0.434913
  2156. z vs IID: -78.4, z vs surrogate: -6.2
  2157. p (surrogate): 0.0000
  2158.  
  2159. ======================================================================
  2160. TEST 8: 168-Hour Periodicity in Saturn Rotation Envelope
  2161. ======================================================================
  2162. Data: 363,357 points, cadence = 60.0s
  2163. Saturn rotation period: 10.791h
  2164. f_saturn = 0.0257 mHz
  2165.  
  2166. 8a: Saturn rotation carrier extraction
  2167. Filter: Butterworth SOS, order 2
  2168. Carrier std: 0.1217
  2169. Envelope mean: 0.1219
  2170. Modulation index: 0.996
  2171.  
  2172. 8b: Envelope periodogram
  2173.  
  2174. # Period (h) Days LS power ID
  2175. ---- ----------- ------- ---------- -------------------------
  2176. 1 172.3 7.2 0.069974 168h (1 week) ◄◄
  2177. 2 177.3 7.4 0.039405 173h
  2178. 3 146.0 6.1 0.033294 144h
  2179. 4 96.8 4.0 0.031461 UNIDENTIFIED
  2180. 5 419.7 17.5 0.028299 UNIDENTIFIED
  2181. 6 282.2 11.8 0.025779 UNIDENTIFIED
  2182.  
  2183. 8c: Specific test at 168h
  2184. Power at 168h: 0.039342
  2185. Background (100–250h excl 168±15h): mean = 0.006703, std = 0.006138
  2186. Z-score: 5.32
  2187. 168h peak rank: #1 out of 6 peaks
  2188.  
  2189. 8d: Surrogate null for 168h envelope power (1000 iterations)
  2190. Observed 168h power: 0.039342
  2191. Surrogate mean: 0.012420 ± 0.012449
  2192. z = 2.16, p = 0.0420
  2193.  
  2194. 8e: Peak power in 150-190h band
  2195. Max power at T = 172.3h: 0.069974
  2196. Surrogate p (any peak in 150-190h): 0.1400
  2197.  
  2198. ============================================================
  2199. TEST 8 SUMMARY
  2200. ============================================================
  2201. Saturn carrier modulation index: 0.996
  2202. 168h envelope power: z = 5.3 (vs neighborhood)
  2203. 168h surrogate null: z = 2.2, p = 0.0420
  2204. 168h peak rank: #1
  2205. 150–190h band: peak at 172.3h, surrogate p = 0.1400
  2206. → not significant
  2207. → Saved: test8_envelope_168h.png
  2208.  
  2209. ============================================================
  2210. SUMMARY
  2211. ============================================================
  2212. Tests run: [1, 2, 3, 4, 5, 6, 7, 8]
  2213. Data: D:\Code\play\antiresonance\cassini_project\data
  2214. Shuffle iterations: 1000
  2215. Stations: BRW, YKC, MEA, OTT, NEW, FRD, SJG
  2216.  
  2217. Test 1 (Day-of-Week SKR):
  2218. Kruskal-Wallis H = 21339.0, p = 0.00e+00, shuffle p = 0.0000
  2219. Test 2 (16-min Comb):
  2220. Z-score = 23.45, surrogate p = 0.0000, raw ratio = 3.6×
  2221. Test 3 (MI):
  2222. BRW: MI lags z>3 = 0, max |r| = 0.1009 (p_adj = 3.28e-03), overall = SIG
  2223. YKC: MI lags z>3 = 66, max |r| = 0.0587 (p_adj = 2.44e-01), overall = SIG
  2224. MEA: MI lags z>3 = 0, max |r| = 0.1066 (p_adj = 1.84e-03), overall = SIG
  2225. OTT: MI lags z>3 = 79, max |r| = 0.2060 (p_adj = 2.66e-10), overall = SIG
  2226. NEW: MI lags z>3 = 1, max |r| = 0.0983 (p_adj = 1.55e-03), overall = SIG
  2227. FRD: MI lags z>3 = 5, max |r| = 0.0801 (p_adj = 2.61e-06), overall = SIG
  2228. SJG: MI lags z>3 = 1, max |r| = 0.0922 (p_adj = 8.52e-09), overall = SIG
  2229. Test 4 (Directionality):
  2230. BRW: z_overall = -3.13, reversal = NO, mean MI = 0.00783
  2231. YKC: z_overall = -0.35, reversal = YES, mean MI = 0.00054
  2232. MEA: z_overall = -0.44, reversal = YES, mean MI = 0.00591
  2233. OTT: z_overall = 0.11, reversal = YES, mean MI = 0.00260
  2234. NEW: z_overall = -0.89, reversal = YES, mean MI = 0.00461
  2235. FRD: z_overall = 1.08, reversal = NO, mean MI = 0.00204
  2236. SJG: z_overall = -1.70, reversal = YES, mean MI = 0.00048
  2237. Test 5 (Prediction):
  2238. BRW: best=high_third→|dH/dt| at 120h | t=+4.668 d=+0.1716 | p_raw=0.000011 p_BH=0.0149 shuf_p=0.0000 | sig: 52/1356 raw, 1 BH (expected false: 68)
  2239. YKC: best=mid_third→|dH/dt| at 306h | t=-4.727 d=-0.4066 | p_raw=0.000069 p_BH=0.0468 shuf_p=0.0070 | sig: 74/1356 raw, 2 BH (expected false: 68)
  2240. MEA: best=mid_third→|dH/dt| at 171h | t=-4.046 d=-0.2852 | p_raw=0.000127 p_BH=0.1345 shuf_p=0.0010 | sig: 112/1356 raw, 0 BH (expected false: 68)
  2241. OTT: best=high_third→|dH/dt| at 120h | t=+4.831 d=+0.1750 | p_raw=0.000008 p_BH=0.0054 shuf_p=0.0030 | sig: 78/1356 raw, 3 BH (expected false: 68)
  2242. NEW: best=mid_third→hourly_range at 15h | t=-3.830 d=-0.2651 | p_raw=0.000269 p_BH=0.3645 shuf_p=0.0020 | sig: 90/1356 raw, 0 BH (expected false: 68)
  2243. FRD: best=high_third→|dH/dt| at 45h | t=+4.179 d=+0.1940 | p_raw=0.000074 p_BH=0.0781 shuf_p=0.0070 | sig: 67/1356 raw, 0 BH (expected false: 68)
  2244. SJG: best=high_third→hourly_range at 90h | t=+4.491 d=+0.1736 | p_raw=0.000021 p_BH=0.0285 shuf_p=0.0000 | sig: 95/1356 raw, 2 BH (expected false: 68)
  2245. Test 6 (Earth-Rotation Modulation):
  2246. 24h KW: H = 324, p = 5.8e-55, bootstrap z = -0.6
  2247. Sidereal/Solar ratio = 0.036 → SIDEREAL (Earth rotation)
  2248. Phase drift: +1.7 h/month → AMBIGUOUS
  2249. Evidence lines: 5
  2250. Test 7 (Parity Bias):
  2251. Bits = 363,357, runs = 38,351, persistence = 4.7×, surrogates exceeded = 6/6
  2252. Test 8 (168h Envelope):
  2253. Mod index = 0.996, 168h z = 2.2, 150-190h band p = 0.1400
Tags: earth cassini saturn RPWS manometer data findings
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