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1======================================================================2GRANGER CAUSALITY & VAR ANALYSIS3======================================================================45--- A. GRANGER CAUSALITY TESTS ---6 ATM_IV → RV : F= 62.381, p=0.0000, 100.0% sig ***7 RV → ATM_IV : F= 17.933, p=0.1501, 60.9% sig 8 Skew → RV : F= 20.792, p=0.0177, 94.2% sig **9 RV → Skew : F= 6.589, p=0.0628, 75.4% sig *10 ATM_IV → Return : F= 1.799, p=0.2688, 24.6% sig 11 Return → ATM_IV : F= 3.977, p=0.1741, 58.0% sig 12 Skew → Return : F= 1.412, p=0.3817, 13.0% sig 13 Return → Skew : F= 13.576, p=0.0133, 95.7% sig **14 PC_Ratio → Return : F= 1.010, p=0.4999, 5.8% sig 15 Return → PC_Ratio : F= 2.819, p=0.1638, 46.4% sig 16 Impl_Skew → RV : F= 1.343, p=0.3856, 17.4% sig 17 Impl_Kurt → RV : F= 5.619, p=0.0861, 75.4% sig *1819--- B. BIVARIATE VAR: IV_ATM ↔ RV (pooled) ---2021 VAR estimated for 20 tickers22 Avg R² (IV equation): 0.936323 Avg R² (RV equation): 0.39772425 Average Impulse Response Function:26 h IV→IV RV→IV IV→RV RV→RV27 0 1.0000 0.0000 0.0000 1.000028 2 0.8923 -0.0485 0.6683 0.141029 4 0.8046 -0.0417 0.5105 0.103830 6 0.7625 -0.0415 0.4224 0.059731 8 0.7212 -0.0397 0.3869 0.029532 10 0.6819 -0.0375 0.3534 0.012733 12 0.6455 -0.0354 0.3296 0.001834 14 0.6114 -0.0332 0.3088 -0.004035 16 0.5795 -0.0312 0.2907 -0.007336 18 0.5496 -0.0292 0.2747 -0.00903738--- C. FORECAST ERROR VARIANCE DECOMPOSITION ---39 Horizon % RV by IV % RV by RV40 1 0.00 100.0041 2 28.01 71.9942 3 44.32 55.6843 4 51.28 48.7244 5 56.10 43.9045 6 58.76 41.2446 7 61.24 38.7647 8 63.29 36.7148 9 64.98 35.0249 10 66.41 33.5950 11 67.61 32.3951 12 68.66 31.3452 13 69.58 30.4253 14 70.40 29.6054 15 71.12 28.8855 16 71.77 28.2356 17 72.36 27.6457 18 72.89 27.1158 19 73.37 26.6359 20 73.82 26.186061GRANGER CAUSALITY & VAR ANALYSIS COMPLETE.62