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Author's title

Author*Unverified author*
R Software Modulerwasp_grangercausality.wasp
Title produced by softwareBivariate Granger Causality
Date of computationThu, 21 May 2020 06:28:14 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2020/May/21/t1590035398ysy3aduxrx35n77.htm/, Retrieved Wed, 21 Apr 2021 08:44:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319162, Retrieved Wed, 21 Apr 2021 08:44:50 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
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Estimated Impact33
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Bivariate Granger Causality] [Put/Call Ratio vs...] [2020-05-21 04:28:14] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
0.91
0.9
0.91
0.76
0.79
0.78
0.84
1.06
0.8
0.82
0.83
0.78
0.78
0.86
1.03
0.89
1.06
1.27
0.93
0.67
0.77
0.91
0.86
0.76
0.84
0.89
0.79
0.72
0.96
0.87
0.61
0.74
1.09
0.96
0.85
0.79
1.11
0.84
0.85
0.96
0.88
0.87
0.82
0.9
0.86
0.79
0.81
0.72
0.75
0.89
0.88
0.9
0.84
0.97
0.91
0.85
1.2
0.98
0.98
0.94
0.78
0.84
0.98
0.82
0.85
0.87
0.85
0.93
1.18
0.96
0.96
0.76
0.84
0.96
1.12
1.04
1.38
1.03
1.68
1.1
1.4
1.32
1.65
1.24
1.18
1.02
1.16
1.06
1.42
1.61
1.15
1.23
0.81
0.95
1.13
0.93
0.93
1
0.99
1.36
1.18
1.2
0.84
1.13
1.05
0.76
0.78
1.14
1
1.03
0.96
0.84
0.9
0.81
0.93
0.75
0.91
1.21
0.82
0.83
1.01
0.97
1.15
0.81
0.89
0.84
0.7
1
0.74
1.1
0.95
0.88
0.92
1.03
0.77
0.98
0.95
1.2
0.99
1.14
1.03
0.91
0.92
0.93
0.89
0.9
0.98
1.12
1.24
1.13
1.08
1.09
0.97
0.79
1.03
0.93
0.88
1.06
0.98
1.03
1.14
1.13
0.84
0.89
1.03
0.85
0.93
0.89
0.87
0.8
1
0.89
0.77
0.93
0.83
0.92
1.1
0.8
1.22
0.81
1.47
1.05
1.52
1.41
1.16
1.27
1.35
1.1
1.44
1.28
1.06
1.01
1.13
1.11
1.02
1.4
1.49
1.5
1.24
0.91
0.9
1.09
1.15
1.06
1
1.29
0.96
0.93
1.06
1.07
1.12
0.88
1.18
1.15
1.06
0.87
1.03
1.1
1.03
1.03
0.96
1.01
0.85
0.84
1.13
0.87
0.85
1.1
0.88
0.99
0.82
0.72
0.78
0.82
0.81
0.89
0.9
0.78
0.8
0.96
0.95
0.77
1.16
1.01
0.96
0.98
1.09
0.82
0.92
1.16
0.77
0.96
1.14
1.03
0.98
1.06
1.22
1.08
0.92
1.19
0.91
1.31
1.27
1.11
1.12
1.23
0.89
0.98
0.82
0.9
0.89
1.06
0.83
1.08
0.89
0.88
0.99
0.96
1.1
0.99
1.06
1.06
1.11
1.04
1.14
0.68
0.59
0.89
0.9
0.98
0.97
1.05
1.16
1.01
1.05
1.04
1.47
1.15
0.97
0.93
0.95
1.25
1.19
1.5
1.34
1.18
1.13
0.88
1.06
0.92
0.9
0.81
0.96
0.81
0.94
1.15
1.06
1.12
1.13
0.96
1.13
0.97
1.01
1.15
1.01
0.85
0.96
1.15
0.93
1.07
1.09
1.24
1.28
1.23
1.18
1.14
1.27
1.24
1.49
1.11
1.11
1.21
1.42
1.49
1
1.21
1.11
0.82
0.96
1.03
1.14
1.17
1.02
0.9
1.05
1.05
1.19
0.97
1.13
1.16
0.98
1.29
1.02
1.06
0.92
0.93
0.82
0.94
1.07
0.95
0.9
0.91
0.96
1.08
0.92
0.93
0.9
0.89
0.82
1.02
0.89
0.92
0.86
0.79
0.8
0.77
0.86
0.85
1.08
1.18
0.97
1.05
0.94
0.81
0.85
0.84
1.07
1.16
1.08
0.97
1.14
0.95
0.96
1.14
0.97
0.91
0.93
0.99
1.12
0.99
1.32
0.87
0.99
0.86
1.15
1.13
1.09
1.02
1.08
1.2
1.21
1.02
1.01
1.06
1.15
1.16
1.16
0.93
0.86
0.93
0.88
0.91
0.9
1.05
0.85
1.06
0.86
0.87
0.95
0.99
0.97
0.77
0.94
1.05
0.93
0.86
1.06
1.02
0.87
1
1.06
1.13
0.96
0.97
0.86
1.12
0.97
0.82
0.82
1
0.96
0.86
1.05
1.01
0.9
1.12
1.1
1
1.01
1.46
1.29
1.37
1.18
0.83
0.97
1.04
1.06
0.8
1.02
1.36
1.3
0.99
1.36
1.1
1.52
1.11
1.19
1.35
1.23
0.89
0.87
1.13
1.15
0.97
0.82
0.89
1.21
1.23
1.24
1.17
1.01
0.79
0.8
0.96
0.96
0.99
0.94
1.33
0.94
1.11
1.17
1.18
0.99
1.02
0.94
1.08
1.39
1.32
1.13
0.74
0.78
0.75
0.88
1
0.94
1.04
0.94
0.92
0.86
0.84
0.94
0.98
1.04
1.05
0.9
0.84
0.9
0.82
0.82
0.71
0.81
0.79
0.94
0.82
0.8
0.94
0.83
0.8
1.13
1.07
1.03
1.16
0.9
1.13
1.18
0.96
0.96
0.93
0.87
0.77
0.78
0.78
0.75
0.96
1.02
0.81
0.81
0.89
0.75
0.71
0.66
0.88
0.92
0.9
0.89
1.03
1.18
1.14
1.07
0.95
0.78
0.85
0.69
0.97
1.07
0.95
0.96
1.02
0.88
0.73
0.72
0.75
0.7
0.71
0.79
0.78
0.64
0.77
0.9
0.7
0.76
0.85
0.91
0.91
1.12
0.82
0.9
0.69
0.82
0.95
0.96
0.85
0.8
0.67
0.77
0.92
0.75
0.72
0.92
0.84
0.78
0.9
0.84
0.81
0.89
0.78
0.94
0.85
0.75
0.71
0.77
0.82
0.87
0.86
0.86
0.87
0.87
0.8
0.77
0.81
0.85
0.97
0.8
0.72
0.86
0.76
0.77
0.77
0.84
0.96
0.88
0.81
0.93
0.87
0.87
0.77
0.87
0.81
1.01
1.14
0.93
0.86
0.94
1
0.86
0.9
0.82
0.78
1.07
0.8
1.06
0.87
1.01
1.04
1.07
1.07
0.83
0.84
0.77
0.75
0.73
0.7
0.8
0.98
0.88
0.93
0.79
0.81
0.92
0.67
0.84
0.76
0.81
0.74
0.91
0.73
0.76
0.77
0.92
0.78
0.95
0.99
0.93
0.97
0.71
0.59
0.73
0.81
1.04
0.81
0.76
0.89
0.93
0.92
0.93
0.89
0.79
0.86
0.9
0.88
0.8
0.76
0.66
0.78
0.86
0.74
0.76
0.89
0.99
0.96
1
0.86
1.11
0.97
1.11
0.8
0.77
0.78
0.72
0.79
0.82
0.81
0.69
0.69
0.76
0.9
0.91
0.94
0.81
0.85
0.88
1.01
1.1
0.84
1.21
1.03
0.93
0.82
0.88
1.03
0.87
0.83
0.89
0.85
1.01
0.84
0.88
0.83
0.99
0.91
0.67
0.88
0.84
1.05
1.04
0.85
0.87
0.67
0.84
0.89
0.89
0.95
0.88
0.89
0.87
0.75
0.87
0.89
0.95
0.62
0.6
0.81
0.7
0.77
0.9
0.77
0.9
0.68
0.71
0.69
0.7
0.64
0.67
0.8
0.81
0.75
0.82
0.73
0.94
0.93
1.07
0.98
0.84
0.95
0.8
0.99
0.74
0.86
0.84
1.06
1.22
0.99
0.98
0.94
0.88
0.9
0.88
0.92
0.78
0.85
0.82
1.04
0.84
1.03
0.86
0.95
0.78
0.87
1
0.82
0.91
0.68
0.82
0.91
0.85
0.79
0.76
0.85
0.77
0.97
0.9
0.65
0.92
0.84
0.92
0.86
0.85
0.84
0.88
0.78
0.73
0.9
0.78
0.71
0.67
0.72
0.55
0.69
0.85
0.89
0.89
0.89
0.74
0.71
0.67
0.88
0.82
0.72
1.04
0.79
0.99
1.13
1.02
1.2
0.99
1.07
0.85
0.85
1.12
1.01
1
1.37
1.5
1.28
0.92
1.11
1.03
1.01
1.2
0.9
0.9
1.07
0.99
0.97
1.14
1.05
1
1.08
1.07
0.84
0.94
0.9
0.86
0.91
1.04
1.09
1.29
0.89
0.78
1.09
1.08
1.24
0.89
1.2
0.87
0.81
0.84
0.97
0.8
0.91
0.87
1.06
0.7
0.84
0.99
0.81
0.83
0.95
0.81
0.95
0.96
0.8
0.9
0.85
0.81
0.94
0.89
0.8
1
1.05
0.98
1
0.9
0.97
1.2
0.96
1.03
0.71
0.96
1
0.93
0.82
0.95
0.91
0.82
0.87
0.94
1.31
0.93
1.05
1.22
0.81
0.89
0.94
0.83
0.9
0.78
0.94
0.95
0.93
0.84
0.83
1
0.77
0.83
0.76
0.81
0.85
0.84
1.05
0.84
0.81
1.1
0.73
0.81
0.72
0.83
0.92
0.98
0.96
0.88
0.9
0.89
0.84
0.85
0.89
0.86
0.78
0.88
0.76
0.67
0.69
0.83
0.71
0.75
1
0.77
0.92
0.89
0.81
0.66
0.77
0.92
1.05
0.83
0.96
0.86
0.79
0.69
0.76
0.71
0.73
0.71
0.69
0.73
0.55
0.82
0.66
0.85
0.74
0.73
0.7
0.8
0.85
0.74
0.76
0.74
0.7
0.97
0.64
0.63
0.69
0.71
0.87
0.78
0.83
0.81
0.7
0.58
0.71
0.82
0.91
0.79
0.73
0.92
0.9
1
1.05
1
0.8
0.75
0.86
0.87
0.79
0.81
0.85
0.78
0.78
0.85
0.82
0.91
0.72
0.9
0.96
0.95
0.98
0.82
0.83
0.93
0.79
0.85
0.79
0.91
0.86
0.86
1.03
1.06
0.94
1.06
1.18
1.04
0.97
0.74
0.76
0.84
0.86
0.82
0.83
0.74
0.76
0.86
0.9
1.04
0.81
0.68
0.88
0.86
0.96
1.1
0.87
0.97
0.93
0.85
0.89
0.92
0.92
0.74
0.86
0.87
0.82
0.92
0.83
0.89
1.01
1.06
0.97
0.79
0.8
0.95
0.86
0.92
0.94
1.14
0.96
0.96
1.05
1.04
0.8
0.73
0.91
0.71
0.76
1.09
1.06
1.23
1.11
1.05
1.16
1.02
1.17
1.07
1.02
1.37
1.12
1.2
0.88
0.95
0.84
1.03
1.07
0.84
0.9
1.02
0.93
0.86
1.11
1.04
0.84
1.01
1.15
1.09
1
1.05
1.07
0.95
0.67
0.79
0.75
0.84
0.91
0.8
1.1
0.91
1.17
1.13
1.15
1.28
1.3
1.21
1.35
1.39
1.21
1.01
1.08
1.12
1.05
1.34
1.48
1.33
1.09
1.02
1.18
1.26
1.17
0.99
1.15
1.21
1.08
1.41
1.26
0.89
1.13
1.32
1.24
1.17
1.04
1.01
1.02
0.98
1.11
1.25
1.25
1.11
1
1.11
1.43
1.18
1.25
1.28
1.18
1.09
1.24
1.23
1.35
1.39
1.27
1.04
0.97
1.16
1.01
1.11
1.35
0.85
0.94
1.04
0.99
0.9
0.98
1.28
1.34
1.15
1.07
1.13
0.99
1.24
1.32
1.16
0.93
1.14
1.09
1.37
1.28
0.88
1.05
1.03
1.26
1.27
0.89
0.96
0.9
0.92
0.96
0.96
0.88
0.9
0.95
1.18
1.1
1.14
1.1
1.22
1.15
0.86
0.81
1.05
0.99
0.86
0.99
0.92
1.08
0.86
0.76
0.97
0.82
0.96
0.91
0.8
0.79
0.84
0.74
0.83
0.83
0.7
0.79
1.07
1.02
0.77
0.98
0.88
0.91
0.87
0.83
0.87
0.77
0.83
0.74
0.83
0.84
1.1
0.88
0.96
1.08
0.87
0.75
0.86
0.9
0.98
1.06
0.9
0.78
1.04
1
0.95
0.93
1.05
0.96
0.94
0.89
1.06
0.85
0.82
0.7
0.77
0.84
0.86
0.97
1.07
1.05
1.04
0.95
1.02
1.04
0.98
0.82
0.93
0.97
0.94
1.01
0.97
1.08
0.86
0.95
1
0.86
0.99
1.02
0.88
0.81
0.89
0.76
0.84
0.85
0.87
0.9
1
0.94
1.04
0.89
1.13
0.99
1.06
1.24
1.24
1.16
1.24
1.44
1.33
0.92
1
0.97
0.97
1.09
0.96
1.24
1.07
1.36
0.97
1.01
1.13
0.98
0.96
0.94
1.14
1.28
1.03
1.02
1
1.08
0.94
1.12
0.99
1.15
1
0.93
0.98
0.89
1.04
0.91
0.86
1.09
0.99
1.1
0.96
0.98
1
0.93
0.84
0.85
0.86
1
0.84
0.88
0.94
0.98
0.89
0.78
0.81
0.95
0.93
0.83
0.8
0.81
0.8
0.86
0.99
0.8
0.82
0.75
0.84
0.75
0.99
0.9
0.97
0.93
0.85
0.87
0.83
1.03
1.06
0.91
0.89
0.92
0.86
0.74
0.79
0.79
0.74
0.77
0.69
0.85
0.79
0.68
0.85
0.8
0.79
0.93
0.9
0.82
0.99
0.87
0.74
0.92
0.81
0.94
0.84
1
1
0.89
1.05
0.77
0.81
0.79
0.88
1.12
0.94
1.06
0.91
0.85
0.99
0.86
0.95
0.92
0.81
0.96
1.21
1.13
1.17
0.99
0.83
1.12
1.24
1.03
0.75
1.1
0.86
0.89
0.63
0.85
0.83
1.01
1.16
0.82
1.04
0.87
0.92
0.8
0.9
0.84
0.89
0.84
0.89
0.71
0.85
0.97
0.86
1.05
0.97
0.96
1.06
1.08
1.02
0.97
0.84
0.82
0.89
0.95
0.85
0.78
0.72
0.81
1.03
0.87
0.79
0.75
0.94
0.89
0.88
0.88
0.97
0.97
0.95
0.91
0.9
1.1
0.95
0.97
1.03
0.9
1.07
0.92
0.91
0.83
0.88
0.99
1.14
1.1
0.9
1.15
1.1
0.99
0.98
1.17
1.12
1.12
0.71
0.83
0.9
0.93
1.08
0.78
0.73
0.85
0.91
0.97
0.74
0.86
0.92
0.89
0.79
0.92
0.9
1
0.87
1.06
1.09
1
0.9
0.67
0.85
0.87
1.15
1.09
0.88
1.19
1.18
1.1
1.03
0.9
0.79
0.97
0.89
0.9
0.89
1.03
0.91
0.9
0.78
0.89
0.88
1
0.75
0.87
0.81
0.78
0.99
0.81
0.79
0.92
1.03
1.01
1.26
0.98
0.86
0.86
1.19
0.92
1.16
1.18
1.22
1.13
1.08
1.04
1.2
0.98
1.19
0.96
0.86
1.11
1.39
1.17
1.01
1.08
0.85
1.02
0.96
0.91
1.04
1.14
0.97
1.04
1.01
1.04
1.01
0.9
0.83
0.97
0.92
0.74
0.79
0.93
0.93
0.96
0.96
0.98
0.84
0.78
0.88
0.85
0.88
0.85
0.9
0.96
0.76
0.9
0.77
0.77
0.79
0.96
0.93
0.93
0.9
0.97
0.82
0.81
0.9
1.02
0.81
0.96
1.12
0.75
0.77
0.82
0.86
0.65
0.76
0.92
0.86
0.77
0.91
0.8
0.84
0.76
1.05
0.99
0.87
0.96
0.7
0.94
1.11
0.85
0.77
0.99
0.87
0.92
0.97
1.3
0.93
0.95
0.9
0.99
0.93
0.87
0.69
0.81
0.84
0.86
0.81
0.93
0.78
0.74
0.98
0.9
0.92
0.76
0.78
0.91
0.92
0.86
0.82
0.84
0.83
0.83
0.75
0.79
0.82
0.96
0.79
0.94
0.77
0.74
0.81
0.81
0.75
0.87
0.89
0.77
0.87
0.94
0.76
0.95
0.7
0.85
0.8
0.88
0.85
0.75
0.75
0.61
0.6
0.65
0.73
0.73
0.66
0.82
0.9
0.69
0.7
0.71
0.72
0.76
0.72
0.68
0.75
0.78
0.71
0.76
0.82
0.88
0.92
0.87
0.8
0.97
0.83
0.86
0.8
0.99
0.97
0.92
0.82
0.94
0.84
0.85
0.79
0.83
0.76
0.9
0.86
0.69
0.78
0.83
0.85
0.89
0.82
0.9
0.8
0.77
0.83
0.82
0.83
0.81
0.96
1.04
0.79
0.84
0.74
0.82
0.76
0.9
1
0.75
1.02
0.84
0.96
0.96
0.99
0.66
0.88
0.94
0.97
0.91
0.61
1.03
1.15
0.75
0.93
0.91
0.85
0.76
0.73
1.01
0.79
1.14
0.9
0.9
0.77
0.81
0.95
0.87
0.89
0.86
0.94
0.94
0.64
0.88
1.08
1.01
0.89
0.81
0.92
0.87
0.87
0.76
0.74
0.9
0.72
0.89
0.73
0.95
0.75
0.75
0.92
0.83
0.7
0.74
0.8
0.77
0.71
0.81
0.77
0.68
0.78
0.81
0.85
0.87
0.93
0.84
0.85
0.92
0.88
1.02
1
0.9
0.84
1.06
0.89
0.88
0.81
0.8
1
0.91
0.9
0.92
0.76
0.91
0.95
0.91
0.86
0.96
0.99
1.24
1.16
1.18
1.13
1
1.09
0.74
1.08
0.94
0.92
1.01
0.88
0.9
0.86
0.72
0.93
0.89
0.8
0.88
1.3
0.96
0.82
1
0.97
1.03
0.88
0.89
0.94
1.01
0.89
0.86
0.89
0.96
0.91
0.83
1.05
1.01
0.88
1.15
1.13
0.89
1.13
1.29
1.02
0.92
0.99
0.99
0.99
0.97
1.2
1.53
1.05
1.3
1.01
1.2
0.88
1.03
1.14
0.82
0.9
0.97
1
1.03
0.96
0.77
0.84
0.89
0.89
0.91
0.95
1.05
0.99
0.81
0.95
0.92
0.84
0.88
0.93
0.96
0.75
0.79
0.98
0.84
1.09
0.99
1.13
0.78
1.06
1.03
1.04
1.05
0.96
0.99
1.13
1.05
0.98
1.24
0.78
0.88
0.75
0.86
0.89
0.73
0.85
0.99
0.94
1.22
1.23
1.11
0.97
0.85
0.99
1.06
0.9
1.16
1.03
0.91
0.8
1.07
0.98
1.28
0.9
1.09
0.97
1.15
1.14
1.06
0.95
0.95
0.96
1.02
1.07
0.97
0.96
0.87
0.97
0.95
0.96
0.89
0.79
0.87
1
1
1.02
1.02
1.02
0.98
0.91
0.95
1.28
1.11
1.09
1.11
1.05
1.21
1.02
0.95
0.98
0.89
0.81
0.88
1.04
1.08
0.97
1.07
0.93
1.08
1.14
1.12
0.87
1
0.95
1.04
0.85
0.89
1.08
0.78
0.86
1.12
0.79
0.9
0.94
1.03
0.76
0.88
0.91
0.94
1.05
0.97
0.95
1.24
1.02
0.94
0.86
0.56
1.06
0.86
0.79
0.83
0.97
1.03
0.85
0.93
0.89
1.14
1.07
1.08
1.16
0.85
0.94
0.91
1.16
1.04
1.01
0.9
0.62
0.84
1.06
0.89
0.75
0.85
0.89
0.93
0.89
0.97
0.9
1.08
1.06
1.38
1.1
1.15
1
1.15
1.24
1.45
1.16
1.02
0.57
0.97
0.97
0.88
0.85
0.91
0.91
0.85
1.03
1.41
1.22
0.93
0.9
0.76
1.11
0.97
0.93
0.98
1.3
1.23
0.56
1.1
1.04
0.96
1.01
0.89
0.94
1.11
1.33
1.69
1.28
1.25
1.04
1.2
1.28
1.19
1.24
1.31
1.12
1.48
0.93
1.03
1.19
1.21
1.03
1.17
1.2
0.92
1.14
1
1.16
1.05
1.03
1.3
1.44
1.37
0.84
0.97
1.09
1.01
0.93
1.09
0.93
0.87
0.94
0.9
0.96
1.11
0.87
0.89
0.99
0.96
0.91
0.77
0.95
0.99
0.77
0.86
0.95
0.88
0.95
1
1.06
1.04
1.1
1
0.88
1.22
1.16
0.88
0.88
1.02
0.95
0.94
1.03
1.06
1.04
1.12
1.17
1.07
1.04
1.12
0.9
1.01
1.08
0.93
1.25
1.08
0.91
0.88
0.75
0.98
1.03
0.84
0.92
0.84
0.92
1.31
0.82
1
1.04
1.08
1
1.03
1.38
1.34
1.13
1.02
1.2
1.02
1.52
0.9
1.18
1.1
1.11
1.03
0.88
0.95
0.87
0.91
1.02
1.03
0.85
0.94
0.97
1.16
0.92
1.09
0.96
0.92
0.95
1.12
1.07
1.06
0.94
1.12
1.05
0.93
1
1.21
0.89
0.8
0.77
0.84
0.85
0.98
0.92
0.99
1.01
0.91
0.9
0.9
0.68
0.78
0.89
1.07
1.04
1.06
0.78
0.97
1.13
1.15
0.96
0.97
1.13
0.99
1.02
1
0.87
0.93
0.61
0.86
0.8
0.98
0.62
0.88
1.17
0.98
0.76
0.8
1.02
1
1.16
1.08
1.1
1.09
1.2
1.19
1.14
1.07
0.93
1.28
1.15
0.77
1.21
1.02
1.37
1.04
1.01
1.01
0.97
0.93
0.9
0.93
1.04
0.91
0.88
0.74
0.85
0.86
0.94
1.09
0.92
1.03
1.17
1.39
1.11
0.99
1.01
1.04
1.28
1.24
1.29
1.14
1.17
1.23
0.92
1.24
1.01
0.86
0.73
0.76
0.79
0.89
0.62
0.85
0.92
0.92
0.79
0.95
0.82
0.91
0.92
0.92
0.9
1.2
1.35
1.15
0.94
0.93
0.92
0.98
0.91
0.87
0.95
0.76
0.78
1.03
0.9
0.86
0.84
0.9
0.86
0.93
1.15
1.04
0.93
0.97
1.2
1.01
0.96
0.87
0.89
0.97
1.18
1
0.98
1.09
0.84
1
0.79
0.98
1
0.97
1.05
1.15
0.99
0.9
1.04
1.01
1.06
0.9
0.77
1
1.18
0.93
1.12
1.06
0.97
0.94
0.97
0.97
0.95
0.99
0.97
0.93
0.97
0.9
0.84
1.11
1.06
1.43
1.31
1.19
1.37
1.22
1.48
1.07
0.89
1.07
0.91
0.91
1.02
0.87
0.94
0.84
1
0.96
0.8
0.92
0.96
0.9
0.95
0.92
0.86
0.83
0.84
0.75
0.82
0.8
0.6
0.9
0.85
0.91
1.17
0.94
0.92
0.89
0.86
1.02
0.91
0.94
1.09
0.98
0.87
1.16
0.97
1
0.89
0.84
1.07
0.92
0.95
1.07
0.94
1
0.95
0.76
0.72
0.87
1
1.1
1.03
0.91
0.86
0.76
1.05
1.1
0.97
0.93
0.98
0.66
0.7
0.84
0.89
0.93
0.82
0.89
0.83
0.83
0.83
1.19
0.87
1.02
0.94
0.9
0.84
0.98
1.12
0.88
0.94
0.93
0.71
0.91
0.96
1.06
1.01
0.99
1.13
1.21
1.09
0.87
0.83
0.94
1.19
0.98
1.12
0.92
0.9
0.95
1.05
0.91
0.95
0.98
0.85
0.65
0.74
0.9
1.04
1.05
0.83
0.79
0.92
0.96
0.85
0.75
1.09
0.91
1
0.85
0.74
0.94
0.91
0.85
0.75
0.79
1.09
1.13
0.99
0.86
0.9
0.93
0.86
0.91
0.94
1.01
1
0.82
0.74
0.77
0.9
0.7
1.06
0.96
0.97
0.84
0.98
1.09
0.8
0.83
0.89
0.8
0.96
0.81
0.77
0.95
0.98
1.13
0.96
0.92
1.12
0.93
0.91
1.06
0.71
0.87
0.84
0.99
0.87
0.77
0.74
0.74
0.82
0.8
0.74
0.94
0.83
0.92
0.88
0.97
1.01
1
0.93
0.93
1.06
0.93
0.97
0.85
0.95
0.96
1.07
1.11
0.99
1.02
0.94
1.09
1
0.93
0.77
0.83
1.06
0.83
1.17
0.95
1.13
1.09
0.93
0.84
0.81
0.79
1.08
0.92
0.76
0.88
0.84
0.98
0.7
0.94
0.83
0.73
1.05
0.93
0.72
0.83
0.84
0.87
0.98
0.73
0.9
1.05
0.85
1.17
0.82
0.95
0.97
0.81
0.98
0.78
1.16
0.87
0.88
0.94
0.87
0.95
0.87
0.94
0.92
1.02
0.97
1.1
1.18
0.9
0.9
1.04
0.95
0.8
0.92
0.85
0.93
0.87
0.72
0.68
0.71
0.85
0.78
0.84
0.83
0.81
0.84
0.94
0.82
0.85
0.75
0.8
0.97
0.69
0.87
0.8
0.84
0.95
0.99
0.95
1.13
1.11
0.88
0.85
0.82
0.92
0.65
0.81
0.72
0.72
0.74
0.69
0.79
0.83
0.86
0.89
0.64
0.84
0.8
0.79
0.74
0.95
0.9
0.91
0.9
0.92
0.99
0.91
1.14
1.31
0.94
0.96
1.17
0.92
0.93
0.86
1.06
1.12
1.01
0.93
1.04
1.08
1.29
1.16
1
0.93
1.05
0.9
0.81
0.87
0.87
1.05
0.89
0.96
1.02
0.84
1.16
1.22
1.54
1.18
1.07
1.34
0.95
1.28
1.04
0.98
0.85
1.03
0.98
0.85
1.02
0.99
0.98
0.94
0.96
0.96
0.97
0.98
0.93
1.04
0.96
0.82
0.88
0.92
1.11
0.93
1.02
0.96
0.93
0.83
0.84
0.81
0.98
0.88
1.11
0.89
0.83
1.03
0.82
0.83
0.99
0.87
0.92
1.09
0.98
1.13
0.86
0.81
0.77
0.83
0.92
0.95
0.74
0.72
0.74
0.93
0.93
1.03
0.84
0.89
1.03
0.86
1.1
0.91
1.08
1.32
1.24
1.06
1.07
0.91
1
0.92
0.98
1.02
0.92
0.98
0.99
0.95
0.85
0.9
0.98
0.85
0.91
0.82
0.74
1.05
1.12
1
1.02
0.97
0.9
0.9
0.92
0.95
0.85
1.2
1.08
0.91
1.16
0.94
1.04
0.79
0.81
0.96
1.03
0.92
0.74
0.81
0.85
0.82
1.03
0.85
0.99
1.05
1.17
1.15
0.88
0.82
0.84
0.83
0.92
0.83
0.95
0.89
0.98
0.98
0.88
0.87
0.94
1.06
1.01
0.8
0.86
1.07
1.18
1.17
0.94
1.22
1.18
1.16
0.96
1.03
1.17
1.3
1.14
1.07
1.04
1.29
1.03
1.32
1.27
1.18
1.12
0.85
0.93
1.02
1.12
0.96
0.97
1.11
1.19
0.98
1.22
0.85
0.94
0.97
0.92
1.08
1.12
0.96
0.92
0.84
0.89
0.76
0.76
0.95
1.08
1.17
1.07
0.97
1
1.16
1.14
1.37
1.09
1.28
1.82
1.43
1.32
1.06
0.96
0.78
0.98
1.03
1.31
0.91
0.87
0.97
0.93
1.13
1.08
1.04
1.03
1.08
0.8
0.84
0.93
1.16
0.98
0.75
0.99
0.89
0.89
0.84
1.13
0.84
0.83
0.97
0.99
1.04
0.87
0.78
1.01
0.92
0.8
0.86
0.79
0.93
0.79
0.78
0.85
0.93
0.96
0.91
1
0.89
1.06
1.12
0.97
0.82
1.01
0.85
0.91
0.85
0.81
0.96
0.89
0.77
0.89
0.86
0.88
1.03
0.87
0.88
0.84
0.83
0.86
0.81
0.82
0.76
0.86
0.89
0.99
0.74
0.91
0.92
0.81
0.88
0.86
0.81
0.87
0.85
0.86
0.86
1.04
0.93
0.93
0.77
1.05
0.87
1.2
1.28
1.24
1.09
1.02
1.15
1.02
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0.85
1
0.94
1.21
0.96
1.07
1.41
1.1
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1.13
0.96
0.99
0.85
0.79
0.78
0.98
1
0.9
0.97
1
0.91
0.85
0.76
0.76
0.77
0.98
0.91
0.89
0.86
0.88
0.89
0.77
0.9
0.94
0.94
0.87
0.88
0.9
0.96
0.9
0.99
0.94
1.09
0.99
0.75
0.73
0.77
0.81
0.81
1.03
0.99
1.06
1.13
1.24
1.1
1.26
1.05
0.99
1.16
0.93
1.27
1.17
1.1
0.94
0.84
1.28
0.93
1.19
1.09
0.95
1.18
1.01
1.25
1.11
1
0.82
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1.12
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1.03
1.15
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Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319162&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319162&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319162&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Granger Causality Test: Y = f(X)
ModelRes.DFDiff. DFFp-value
Complete model3249
Reduced model3250-12.668659088720360.10243910632995

\begin{tabular}{lllllllll}
\hline
Granger Causality Test: Y = f(X) \tabularnewline
Model & Res.DF & Diff. DF & F & p-value \tabularnewline
Complete model & 3249 &  &  &  \tabularnewline
Reduced model & 3250 & -1 & 2.66865908872036 & 0.10243910632995 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319162&T=1

[TABLE]
[ROW][C]Granger Causality Test: Y = f(X)[/C][/ROW]
[ROW][C]Model[/C][C]Res.DF[/C][C]Diff. DF[/C][C]F[/C][C]p-value[/C][/ROW]
[ROW][C]Complete model[/C][C]3249[/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Reduced model[/C][C]3250[/C][C]-1[/C][C]2.66865908872036[/C][C]0.10243910632995[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319162&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319162&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Granger Causality Test: Y = f(X)
ModelRes.DFDiff. DFFp-value
Complete model3249
Reduced model3250-12.668659088720360.10243910632995







Granger Causality Test: X = f(Y)
ModelRes.DFDiff. DFFp-value
Complete model3249
Reduced model3250-13.674482528130650.055339020945339

\begin{tabular}{lllllllll}
\hline
Granger Causality Test: X = f(Y) \tabularnewline
Model & Res.DF & Diff. DF & F & p-value \tabularnewline
Complete model & 3249 &  &  &  \tabularnewline
Reduced model & 3250 & -1 & 3.67448252813065 & 0.055339020945339 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319162&T=2

[TABLE]
[ROW][C]Granger Causality Test: X = f(Y)[/C][/ROW]
[ROW][C]Model[/C][C]Res.DF[/C][C]Diff. DF[/C][C]F[/C][C]p-value[/C][/ROW]
[ROW][C]Complete model[/C][C]3249[/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Reduced model[/C][C]3250[/C][C]-1[/C][C]3.67448252813065[/C][C]0.055339020945339[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319162&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319162&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Granger Causality Test: X = f(Y)
ModelRes.DFDiff. DFFp-value
Complete model3249
Reduced model3250-13.674482528130650.055339020945339



Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 1 ; par5 = 1 ; par6 = 0 ; par7 = 0 ; par8 = 1 ;
Parameters (R input):
par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 1 ; par5 = 1 ; par6 = 0 ; par7 = 0 ; par8 = 1 ;
R code (references can be found in the software module):
library(lmtest)
par1 <- as.numeric(par1)
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
par6 <- as.numeric(par6)
par7 <- as.numeric(par7)
par8 <- as.numeric(par8)
ox <- x
oy <- y
if (par1 == 0) {
x <- log(x)
} else {
x <- (x ^ par1 - 1) / par1
}
if (par5 == 0) {
y <- log(y)
} else {
y <- (y ^ par5 - 1) / par5
}
if (par2 > 0) x <- diff(x,lag=1,difference=par2)
if (par6 > 0) y <- diff(y,lag=1,difference=par6)
if (par3 > 0) x <- diff(x,lag=par4,difference=par3)
if (par7 > 0) y <- diff(y,lag=par4,difference=par7)
print(x)
print(y)
(gyx <- grangertest(y ~ x, order=par8))
(gxy <- grangertest(x ~ y, order=par8))
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
(r <- ccf(ox,oy,main='Cross Correlation Function (raw data)',ylab='CCF',xlab='Lag (k)'))
(r <- ccf(x,y,main='Cross Correlation Function (transformed and differenced)',ylab='CCF',xlab='Lag (k)'))
par(op)
dev.off()
bitmap(file='test2.png')
op <- par(mfrow=c(2,1))
acf(ox,lag.max=round(length(x)/2),main='ACF of x (raw)')
acf(x,lag.max=round(length(x)/2),main='ACF of x (transformed and differenced)')
par(op)
dev.off()
bitmap(file='test3.png')
op <- par(mfrow=c(2,1))
acf(oy,lag.max=round(length(y)/2),main='ACF of y (raw)')
acf(y,lag.max=round(length(y)/2),main='ACF of y (transformed and differenced)')
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Granger Causality Test: Y = f(X)',5,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Model',header=TRUE)
a<-table.element(a,'Res.DF',header=TRUE)
a<-table.element(a,'Diff. DF',header=TRUE)
a<-table.element(a,'F',header=TRUE)
a<-table.element(a,'p-value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Complete model',header=TRUE)
a<-table.element(a,gyx$Res.Df[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Reduced model',header=TRUE)
a<-table.element(a,gyx$Res.Df[2])
a<-table.element(a,gyx$Df[2])
a<-table.element(a,gyx$F[2])
a<-table.element(a,gyx$Pr[2])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Granger Causality Test: X = f(Y)',5,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Model',header=TRUE)
a<-table.element(a,'Res.DF',header=TRUE)
a<-table.element(a,'Diff. DF',header=TRUE)
a<-table.element(a,'F',header=TRUE)
a<-table.element(a,'p-value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Complete model',header=TRUE)
a<-table.element(a,gxy$Res.Df[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Reduced model',header=TRUE)
a<-table.element(a,gxy$Res.Df[2])
a<-table.element(a,gxy$Df[2])
a<-table.element(a,gxy$F[2])
a<-table.element(a,gxy$Pr[2])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')