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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_grangercausality.wasp
Title produced by softwareBivariate Granger Causality
Date of computationWed, 18 Oct 2023 10:36:19 +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/2023/Oct/18/t16976182010a5ej45evmhgxky.htm/, Retrieved Sat, 16 May 2026 00:22:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319965, Retrieved Sat, 16 May 2026 00:22:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact277

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Bivariate Granger Causality] [] [2023-10-18 08:36:19] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
543.3
563.3
605.1
638.6
685.8
743.7
815
861.7
942.5
1019.9
1073.303
1164.85
1279.11
1425.376
1545.243
1684.904
1873.412
2081.826
2351.599
2627.333
2857.307
3207.041
3343.789
3634.038
4037.613
4338.979
4579.631
4855.215
5236.438
5641.58
5963.144
6158.129
6520.327
6858.559
7287.236
7639.749
8073.122
8577.554457
9062.818202
9631.174489
10250.947997
10581.929774
10929.112955
11456.442041
12217.193198
13039.199193
13815.586948
14474.226905
14769.857911
14478.064934
15048.964444
15599.728123
16253.97223
16843.190993
17550.680174
18206.020741
18695.110842
19477.336549
20533.057312
21380.976119
21060.473613
23315.08056
25462.7
Dataseries Y:
Download CSV
Histogram 
2.91
2.85
2.85
2.91
3.00
3.01
3.10
3.12
3.18
3.32
3.39
3.60
3.60
4.75
9.35
12.21
13.10
14.40
14.95
25.10
37.42
35.75
31.83
29.08
28.75
26.92
14.44
17.75
14.87
18.33
23.19
20.20
19.25
16.75
15.66
16.75
20.46
18.64
11.91
16.56
27.39
23.00
22.81
27.69
37.66
50.04
58.30
64.20
91.48
53.48
71.21
87.04
86.46
91.17
85.60
41.85
36.34
43.97
57.77
50.01
32.25
60.84
87.40

Tables (Output of Computation)





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=319965&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=319965&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319965&T=0

As an alternative you can also use a QR Code:  
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 model59
Reduced model60-17.749934530670810.00720665297843624

\begin{tabular}{lllllllll}
\hline
Granger Causality Test: Y = f(X) \tabularnewline
Model & Res.DF & Diff. DF & F & p-value \tabularnewline
Complete model & 59 &  &  &  \tabularnewline
Reduced model & 60 & -1 & 7.74993453067081 & 0.00720665297843624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319965&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]59[/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Reduced model[/C][C]60[/C][C]-1[/C][C]7.74993453067081[/C][C]0.00720665297843624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319965&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319965&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Granger Causality Test: Y = f(X)
ModelRes.DFDiff. DFFp-value
Complete model59
Reduced model60-17.749934530670810.00720665297843624






Granger Causality Test: X = f(Y)
ModelRes.DFDiff. DFFp-value
Complete model59
Reduced model60-16.420285662116060.0139582236287501

\begin{tabular}{lllllllll}
\hline
Granger Causality Test: X = f(Y) \tabularnewline
Model & Res.DF & Diff. DF & F & p-value \tabularnewline
Complete model & 59 &  &  &  \tabularnewline
Reduced model & 60 & -1 & 6.42028566211606 & 0.0139582236287501 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319965&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]59[/C][C][/C][C][/C][C][/C][/ROW]
[ROW][C]Reduced model[/C][C]60[/C][C]-1[/C][C]6.42028566211606[/C][C]0.0139582236287501[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319965&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319965&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Granger Causality Test: X = f(Y)
ModelRes.DFDiff. DFFp-value
Complete model59
Reduced model60-16.420285662116060.0139582236287501


Figures (Output of Computation)

Input Parameters & R Code

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')