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Table 2

Statistical trends, sub-trends, and measures of persistence in synthetic series

S. no.Synthetic data being analyzedCommon trends tests applied to the entire data
The new trend test applied to sub-trends
Parameter H of the entire data
MKSMRPart 1Part 2Part 3
Figure 2 (Case 1) − 0.01 0.04 − 0.07 NA NA 0.502 
Figure 2 (Case 2) 5.46*** 5.81*** 4.94*** NA NA 0.885 
Figure 2 (Case 3) 5.08*** 5.47*** 4.68*** NA NA 0.871 
Figure 2 (Case 4) 0.14 0.13 3.63*** 3.63*** NA 0.856 
Figure 2 (Case 5) − 0.14 − 0.13 3.63*** 3.63*** NA 0.856 
Figure 2 (Case 6) 5.35*** 5.31*** − 0.69 −0.12 NA 0.892 
Figure 2 (Case 7) 5.07*** 5.22*** − 0.60 −0.60 NA 0.876 
Figure 2 (Case 8) 4.59*** 4.94*** − 0.28 3.65*** NA 0.888 
Figure 2 (Case 9) 4.49*** 4.80*** 3.65*** 0.28 NA 0.887 
10 Figure 3 (Case 1) − 1.33 − 1.26 3.63*** 3.63*** 3.63*** 0.864 
11 Figure 3 (Case 2) 6.85*** 6.87 4.93*** 3.72*** 3.63*** 0.938 
12 Figure 3 (Case 3) 2.92*** 3.25*** 4.68*** 2.32** 3.63*** 0.939 
13 Figure 3 (Case 4) 7.30*** 8.37*** − 0.15 −0.71 1.00 0.969 
14 Figure 3 (Case 5) 8.84*** 9.91*** 2.41** 3.59*** −0.14 0.977 
15 Figure 3 (Case 6) 0.14 − 0.26 3.59*** −0.14 −0.14 0.948 
16 Figure 3 (Case 7) 0.30 0.21 4.94*** 4.94*** 3.53*** 0.962 
S. no.Synthetic data being analyzedCommon trends tests applied to the entire data
The new trend test applied to sub-trends
Parameter H of the entire data
MKSMRPart 1Part 2Part 3
Figure 2 (Case 1) − 0.01 0.04 − 0.07 NA NA 0.502 
Figure 2 (Case 2) 5.46*** 5.81*** 4.94*** NA NA 0.885 
Figure 2 (Case 3) 5.08*** 5.47*** 4.68*** NA NA 0.871 
Figure 2 (Case 4) 0.14 0.13 3.63*** 3.63*** NA 0.856 
Figure 2 (Case 5) − 0.14 − 0.13 3.63*** 3.63*** NA 0.856 
Figure 2 (Case 6) 5.35*** 5.31*** − 0.69 −0.12 NA 0.892 
Figure 2 (Case 7) 5.07*** 5.22*** − 0.60 −0.60 NA 0.876 
Figure 2 (Case 8) 4.59*** 4.94*** − 0.28 3.65*** NA 0.888 
Figure 2 (Case 9) 4.49*** 4.80*** 3.65*** 0.28 NA 0.887 
10 Figure 3 (Case 1) − 1.33 − 1.26 3.63*** 3.63*** 3.63*** 0.864 
11 Figure 3 (Case 2) 6.85*** 6.87 4.93*** 3.72*** 3.63*** 0.938 
12 Figure 3 (Case 3) 2.92*** 3.25*** 4.68*** 2.32** 3.63*** 0.939 
13 Figure 3 (Case 4) 7.30*** 8.37*** − 0.15 −0.71 1.00 0.969 
14 Figure 3 (Case 5) 8.84*** 9.91*** 2.41** 3.59*** −0.14 0.977 
15 Figure 3 (Case 6) 0.14 − 0.26 3.59*** −0.14 −0.14 0.948 
16 Figure 3 (Case 7) 0.30 0.21 4.94*** 4.94*** 3.53*** 0.962 

Bold values indicate that the H0 (no trend) was rejected for p < 0.01 (**), and p < 0.001 (***). ‘NA’ = No other sub-trend(s).

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