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. 2020 Nov 16;55(5):1561–1579. doi: 10.1007/s11135-020-01074-7

Table 4.

Asymmetric causality test

Hypothesis Fisher statistic P-value Decision
WPU+  ≠  > TA+ 1.896 0.388 WPU+  ≠  > TA+
WPU+  ≠  > TA 9.537* 0.008 WPU+ → TA
WPU  ≠  > TA 0.446 0.800 WPU  ≠  > TA
WPU  ≠  > TA+ 0.989 0.610 WPU  ≠  > TA+
TA+  ≠  > WPU+ 0.669 0.716 TA+  ≠  > WPU+
TA+  ≠  > WPU 0.483 0.785 TA+  ≠  > WPU
TA  ≠  > WPU 1.619 0.445 TA  ≠  > WPU
TA  ≠  > WPU+ 0.717 0.699 TA  ≠  > WPU+
INF+  ≠  > TA+ 0.122 0.941 INF+  ≠  > TA+
INF+  ≠  > TA 0.429 0.807 INF+  ≠  > TA
INF  ≠  > TA 3.746 0.154 INF  ≠  > TA
INF  ≠  > TA+ 3.472 0.176 INF  ≠  > TA+
TA+  ≠  > INF+ 0.485 0.785 TA+  ≠  > INF+
TA+  ≠  > INF 5.086*** 0.079 TA+  → INF
TA  ≠  > INF 1.675 0.433 TA  ≠  > INF
TA  ≠  > INF+ 1.200 0.549 TA  ≠  > INF+
IP+  ≠  > TA+ 3.217 0.200 IP+  ≠  > TA+
IP+  ≠  > TA 0.341 0.843 IP+  ≠  > TA
IP  ≠  > TA 0.079 0.961 IP  ≠  > TA
IP  ≠  > TA+ 5.265*** 0.072 IP  → TA+
TA+  ≠  > IP+ 1.574 0.455 TA+  ≠  > IP+
TA+  ≠  > IP 0.757 0.685 TA+  ≠  > IP
TA  ≠  > IP 0.508 0.776 TA  ≠  > IP
TA  ≠  > IP+ 3.187 0.168 TA−−  ≠  > IP+
CCI+  ≠  > TA+ 0.375 0.829 CCI+  ≠  > TA+
CCI+  ≠  > TA 10.244*** 0.006 CCI+  → TA
CCI  ≠  > TA 1.382 0.501 CCI  ≠  > TA
CCI  ≠  > TA+ 2.092 0.351 CCI  ≠  > TA+
TA+  ≠  > CCI+ 0.371 0.831 TA+  ≠  > CCI+
TA+  ≠  > CCI 0.991 0.609 TA+  ≠  > CCI
TA  ≠  > CCI 8.254*** 0.016 TA  → CCI
TA  ≠  > CCI+ 1.431 0.489 TA  ≠  > CCI+

The symbols “ ≠  > and → ” denote the non-Granger causality and unidirectional Granger causality relationship for the selected variables

**,***Indicate the 0.05 and 0.10 significance level. The optimal lag is selected as 3 by using Hatemi-J Criterion (HJC)