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Table 2 Granger causality between global risk aversion (GRA) and spillover measures

From: Impact of the COVID-19 outbreak on the US equity sectors: Evidence from quantile return spillovers

  GRA \(\to\) SOI SOI \(\to\) GRA Overall conclusion
Linear Taylor ANN Linear Taylor ANN
Overall 87.77*** 2.364 1.231 11.711*** 45.626*** 133.91*** GRA \(\leftrightarrow\) SOI
  [0.000] [0.124] [0.351] [0.000] [0.000] [0.000]  
From sector TO all others
EN 2.076 0.823 3.139 4.355** 79.747*** 34.592*** GRA \(\leftarrow\) SOI
  [0.125] [0.438] [0.581] [0.012] [0.000] [0.000]  
FIN 21.390*** 3.995** 26.091*** 15.435*** 434.47*** 155.09*** GRA \(\leftrightarrow\) SOI
  [0.000] [0.018] [0.000] [0.000] [0.000] [0.000]  
IND 17.650*** 5.801*** 30.112*** 0.429 1.265 1.680 GRA \(\to\) SOI
  [0.000] [0.003] [0.000] [0.651] [0.201] [0.169]  
UTL 125.17*** 3.101** 3.827*** 0.176 10.025*** 7.273*** GRA \(\leftrightarrow\) SOI
  [0.000] [0.045] [0.009] [0.838] [0.000] [0.000]  
CS 133.64*** 5.376*** 74.733*** 12.293*** 19.744*** 31.343*** GRA \(\leftrightarrow\) SOI
  [0.000] [0.004] [0.000] [0.000] [0.000] [0.000]  
HC 7.528*** 12.153*** 98.338*** 7.995*** 81.907*** 62.312*** GRA \(\leftrightarrow\) SOI
  [0.000] [0.000] [0.000] [0.000] [0.000] [0.000]  
IT 10.216*** 1.490 91.605*** 1.751 8.827*** 47.025*** GRA \(\leftrightarrow\) SOI
  [0.000] [0.225] [0.000] [0.173] [0.000] [0.000]  
MAT 0.304 0.145 0.304 3.310** 75.410*** 26.225*** GRA \(\leftarrow\) SOI
  [0.737] [0.864] [0.732] [0.036] [0.000] [0.000]  
CD 10.296*** 1.507 29.234*** 13.886*** 347.07*** 115.74*** GRA \(\leftrightarrow\) SOI
  [0.000] [0.221] [0.000] [0.000] [0.000] [0.000]  
RE 7.096*** 1.410 12.557*** 4.538** 70.977*** 33.143*** GRA \(\leftrightarrow\) SOI
  [0.000] [0.244] [0.000] [0.011] [0.000] [0.000]  
  1. The above table displays the results of the linear, Tor-based and ANN-based nonlinear causality tests