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Table. 2 Comparison between uGCA methods and conventional GCA under different data length

From: Robust unified Granger causality analysis: a normalized maximum likelihood form

   uGCA-TP (%) uGCA-MIX (%) uGCA-NML (%) GCA (\(\alpha =0.05\)) (%) GCA (\(\alpha =0.01\)) (%)
\(L=150\)    
 TPR 89.933 83.433 86.178 93.810 86.200
 TNR 99.048 99.710 99.624 95.743 98.705
 Ground-truth rate 31 17.5 22 24.4 18.5
\(L=200\)    
 TPR 95.378 91.411 92.967 97.200 93.289
 TNR 99.181 99.748 99.705 95.610 98.610
 Ground-truth rate 56.4 41.1 48.2 29.3 40.8
\(L=300\)    
 TPR 99.567 98.022 99.133 99.620 98.878
 TNR 99.433 99.857 99.820 98.878 98.890
 Ground-truth rate 85.5 83.0 88.9 38.3 72.1
\(L=500\)    
 TPR 99.989 99.033 99.989 100 100
 TNR 99.324 99.824 99.786 95.186 98.571
 Ground-truth rate 86.3 91.3 95.6 34.2 72.9
  1. The data length ranges from 150 to 500, the results (\(L=1000\)) were present in Table 1, and L is the data length
  2. Bold values indicate more indicative of the method's performance