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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationThu, 29 Nov 2012 07:00:27 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/29/t1354190445km1pr1cy4v30p5l.htm/, Retrieved Sat, 27 Apr 2024 15:47:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=194280, Retrieved Sat, 27 Apr 2024 15:47:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [Workshop 9 - part...] [2012-11-29 12:00:27] [3353489d44052879174bf0d9e8b7362f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8.64
8.89
8.87
8.81
8.87
9.06
9.12
8.66
8.17
8.04
7.71
7.55
7.52
7.38
7.52
7.31
6.92
7.09
7.05
7.37
7.05
6.79
6.35
6.44
6.89
7.16
7.46
7.91
7.86
8.02
8.38
8.50
8.40
8.24
8.33
8.28
8.15
8.06
7.79
7.28
7.52
7.23
7.13
7.21
6.99
6.77
6.69
6.39
6.85
6.74
6.56
6.62
6.71
6.67
6.54
6.14
6.13
5.86
5.88
5.75
5.53
5.86
5.90
5.95
5.69
5.53
5.71
5.60
5.73
5.60
5.41
5.13
5.00
5.04
5.10
4.96
4.90
4.80
4.48
4.29
4.27
4.18
4.02
3.82
4.13
4.16
3.98
4.26
4.70
4.96
5.13
5.35
5.41
5.42
5.51
5.75
5.67
5.46
5.56
5.56
5.54
5.53
5.65
5.58
5.57
5.36
5.23
5.11
5.07
5.04
5.34
5.43
5.31
5.12
4.97
5.00
4.64
4.80
5.10
5.11
5.12
5.36
5.26
5.27
5.10
4.94
4.68
4.41
4.60
4.53
4.18
4.00
3.87
4.09
4.13
3.74
3.81
4.11
4.14
3.99
4.28
4.37
4.24
4.19
4.01
3.95
4.30
4.37
4.40
4.29
4.12
4.07
3.93
3.79
3.67
3.53
3.69
3.69
3.48
3.31
3.16
3.25
3.14
3.19
3.43
3.45
3.31
3.51
3.53
3.83
4.02
3.99
4.11
3.96
3.83
3.71
3.81
3.73
3.99
4.17
4.00
4.10
4.24
4.45
4.62
4.49
4.45
4.49
4.36
4.32
4.45
4.13
4.14
4.30
4.42
4.67
4.96
4.73
4.52




4.36
4.15
3.92
3.88
4.20
3.95
3.78
3.69




3.77
3.66
3.53
3.50
3.14
3.42
3.30
2.81
3.15
3.37
4.05
4.00
4.20
4.21
4.24
4.24
4.17
4.12
4.35
3.98
3.62
4.39
5.01
4.07
3.70
3.59
3.44
3.33
2.98
3.14
2.55
2.49
2.53
2.43

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194280&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194280&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194280&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.1248761.93460.02711
2-0.085431-1.32350.093466
30.0830191.28610.099819
40.056860.88090.189635
50.0415370.64350.260262
6-0.04286-0.6640.253671
70.0202640.31390.376922
80.0191580.29680.383437
9-0.113151-1.75290.040446
10-0.016801-0.26030.397434
11-0.028791-0.4460.327992
12-0.032971-0.51080.304984
130.0171970.26640.395075
14-0.075665-1.17220.121141
15-0.144095-2.23230.013259
16-0.039505-0.6120.270556
17-0.090422-1.40080.081281
18-0.097465-1.50990.06619
19-0.026649-0.41280.340043
20-0.11848-1.83550.033836
21-0.013209-0.20460.419015
220.0277590.430.333776
230.0910771.4110.079776

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.124876 & 1.9346 & 0.02711 \tabularnewline
2 & -0.085431 & -1.3235 & 0.093466 \tabularnewline
3 & 0.083019 & 1.2861 & 0.099819 \tabularnewline
4 & 0.05686 & 0.8809 & 0.189635 \tabularnewline
5 & 0.041537 & 0.6435 & 0.260262 \tabularnewline
6 & -0.04286 & -0.664 & 0.253671 \tabularnewline
7 & 0.020264 & 0.3139 & 0.376922 \tabularnewline
8 & 0.019158 & 0.2968 & 0.383437 \tabularnewline
9 & -0.113151 & -1.7529 & 0.040446 \tabularnewline
10 & -0.016801 & -0.2603 & 0.397434 \tabularnewline
11 & -0.028791 & -0.446 & 0.327992 \tabularnewline
12 & -0.032971 & -0.5108 & 0.304984 \tabularnewline
13 & 0.017197 & 0.2664 & 0.395075 \tabularnewline
14 & -0.075665 & -1.1722 & 0.121141 \tabularnewline
15 & -0.144095 & -2.2323 & 0.013259 \tabularnewline
16 & -0.039505 & -0.612 & 0.270556 \tabularnewline
17 & -0.090422 & -1.4008 & 0.081281 \tabularnewline
18 & -0.097465 & -1.5099 & 0.06619 \tabularnewline
19 & -0.026649 & -0.4128 & 0.340043 \tabularnewline
20 & -0.11848 & -1.8355 & 0.033836 \tabularnewline
21 & -0.013209 & -0.2046 & 0.419015 \tabularnewline
22 & 0.027759 & 0.43 & 0.333776 \tabularnewline
23 & 0.091077 & 1.411 & 0.079776 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194280&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.124876[/C][C]1.9346[/C][C]0.02711[/C][/ROW]
[ROW][C]2[/C][C]-0.085431[/C][C]-1.3235[/C][C]0.093466[/C][/ROW]
[ROW][C]3[/C][C]0.083019[/C][C]1.2861[/C][C]0.099819[/C][/ROW]
[ROW][C]4[/C][C]0.05686[/C][C]0.8809[/C][C]0.189635[/C][/ROW]
[ROW][C]5[/C][C]0.041537[/C][C]0.6435[/C][C]0.260262[/C][/ROW]
[ROW][C]6[/C][C]-0.04286[/C][C]-0.664[/C][C]0.253671[/C][/ROW]
[ROW][C]7[/C][C]0.020264[/C][C]0.3139[/C][C]0.376922[/C][/ROW]
[ROW][C]8[/C][C]0.019158[/C][C]0.2968[/C][C]0.383437[/C][/ROW]
[ROW][C]9[/C][C]-0.113151[/C][C]-1.7529[/C][C]0.040446[/C][/ROW]
[ROW][C]10[/C][C]-0.016801[/C][C]-0.2603[/C][C]0.397434[/C][/ROW]
[ROW][C]11[/C][C]-0.028791[/C][C]-0.446[/C][C]0.327992[/C][/ROW]
[ROW][C]12[/C][C]-0.032971[/C][C]-0.5108[/C][C]0.304984[/C][/ROW]
[ROW][C]13[/C][C]0.017197[/C][C]0.2664[/C][C]0.395075[/C][/ROW]
[ROW][C]14[/C][C]-0.075665[/C][C]-1.1722[/C][C]0.121141[/C][/ROW]
[ROW][C]15[/C][C]-0.144095[/C][C]-2.2323[/C][C]0.013259[/C][/ROW]
[ROW][C]16[/C][C]-0.039505[/C][C]-0.612[/C][C]0.270556[/C][/ROW]
[ROW][C]17[/C][C]-0.090422[/C][C]-1.4008[/C][C]0.081281[/C][/ROW]
[ROW][C]18[/C][C]-0.097465[/C][C]-1.5099[/C][C]0.06619[/C][/ROW]
[ROW][C]19[/C][C]-0.026649[/C][C]-0.4128[/C][C]0.340043[/C][/ROW]
[ROW][C]20[/C][C]-0.11848[/C][C]-1.8355[/C][C]0.033836[/C][/ROW]
[ROW][C]21[/C][C]-0.013209[/C][C]-0.2046[/C][C]0.419015[/C][/ROW]
[ROW][C]22[/C][C]0.027759[/C][C]0.43[/C][C]0.333776[/C][/ROW]
[ROW][C]23[/C][C]0.091077[/C][C]1.411[/C][C]0.079776[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194280&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194280&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:

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.1248761.93460.02711
2-0.085431-1.32350.093466
30.0830191.28610.099819
40.056860.88090.189635
50.0415370.64350.260262
6-0.04286-0.6640.253671
70.0202640.31390.376922
80.0191580.29680.383437
9-0.113151-1.75290.040446
10-0.016801-0.26030.397434
11-0.028791-0.4460.327992
12-0.032971-0.51080.304984
130.0171970.26640.395075
14-0.075665-1.17220.121141
15-0.144095-2.23230.013259
16-0.039505-0.6120.270556
17-0.090422-1.40080.081281
18-0.097465-1.50990.06619
19-0.026649-0.41280.340043
20-0.11848-1.83550.033836
21-0.013209-0.20460.419015
220.0277590.430.333776
230.0910771.4110.079776






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.1248761.93460.02711
2-0.102625-1.58990.056591
30.1104651.71130.044157
40.0214380.33210.370046
50.0512190.79350.214141
6-0.059049-0.91480.180612
70.0384170.59520.276149
8-0.010383-0.16080.436175
9-0.106917-1.65640.049478
100.0132140.20470.418985
11-0.05306-0.8220.205945
12-0.005642-0.08740.465213
130.0247110.38280.351096
14-0.071258-1.10390.135365
15-0.129921-2.01270.022631
16-0.010727-0.16620.43408
17-0.107103-1.65920.049188
18-0.068632-1.06320.144369
19-0.001207-0.01870.492548
20-0.131111-2.03120.02167
210.0237050.36720.356883
220.0249460.38650.349748
230.0992161.5370.0628

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.124876 & 1.9346 & 0.02711 \tabularnewline
2 & -0.102625 & -1.5899 & 0.056591 \tabularnewline
3 & 0.110465 & 1.7113 & 0.044157 \tabularnewline
4 & 0.021438 & 0.3321 & 0.370046 \tabularnewline
5 & 0.051219 & 0.7935 & 0.214141 \tabularnewline
6 & -0.059049 & -0.9148 & 0.180612 \tabularnewline
7 & 0.038417 & 0.5952 & 0.276149 \tabularnewline
8 & -0.010383 & -0.1608 & 0.436175 \tabularnewline
9 & -0.106917 & -1.6564 & 0.049478 \tabularnewline
10 & 0.013214 & 0.2047 & 0.418985 \tabularnewline
11 & -0.05306 & -0.822 & 0.205945 \tabularnewline
12 & -0.005642 & -0.0874 & 0.465213 \tabularnewline
13 & 0.024711 & 0.3828 & 0.351096 \tabularnewline
14 & -0.071258 & -1.1039 & 0.135365 \tabularnewline
15 & -0.129921 & -2.0127 & 0.022631 \tabularnewline
16 & -0.010727 & -0.1662 & 0.43408 \tabularnewline
17 & -0.107103 & -1.6592 & 0.049188 \tabularnewline
18 & -0.068632 & -1.0632 & 0.144369 \tabularnewline
19 & -0.001207 & -0.0187 & 0.492548 \tabularnewline
20 & -0.131111 & -2.0312 & 0.02167 \tabularnewline
21 & 0.023705 & 0.3672 & 0.356883 \tabularnewline
22 & 0.024946 & 0.3865 & 0.349748 \tabularnewline
23 & 0.099216 & 1.537 & 0.0628 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194280&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.124876[/C][C]1.9346[/C][C]0.02711[/C][/ROW]
[ROW][C]2[/C][C]-0.102625[/C][C]-1.5899[/C][C]0.056591[/C][/ROW]
[ROW][C]3[/C][C]0.110465[/C][C]1.7113[/C][C]0.044157[/C][/ROW]
[ROW][C]4[/C][C]0.021438[/C][C]0.3321[/C][C]0.370046[/C][/ROW]
[ROW][C]5[/C][C]0.051219[/C][C]0.7935[/C][C]0.214141[/C][/ROW]
[ROW][C]6[/C][C]-0.059049[/C][C]-0.9148[/C][C]0.180612[/C][/ROW]
[ROW][C]7[/C][C]0.038417[/C][C]0.5952[/C][C]0.276149[/C][/ROW]
[ROW][C]8[/C][C]-0.010383[/C][C]-0.1608[/C][C]0.436175[/C][/ROW]
[ROW][C]9[/C][C]-0.106917[/C][C]-1.6564[/C][C]0.049478[/C][/ROW]
[ROW][C]10[/C][C]0.013214[/C][C]0.2047[/C][C]0.418985[/C][/ROW]
[ROW][C]11[/C][C]-0.05306[/C][C]-0.822[/C][C]0.205945[/C][/ROW]
[ROW][C]12[/C][C]-0.005642[/C][C]-0.0874[/C][C]0.465213[/C][/ROW]
[ROW][C]13[/C][C]0.024711[/C][C]0.3828[/C][C]0.351096[/C][/ROW]
[ROW][C]14[/C][C]-0.071258[/C][C]-1.1039[/C][C]0.135365[/C][/ROW]
[ROW][C]15[/C][C]-0.129921[/C][C]-2.0127[/C][C]0.022631[/C][/ROW]
[ROW][C]16[/C][C]-0.010727[/C][C]-0.1662[/C][C]0.43408[/C][/ROW]
[ROW][C]17[/C][C]-0.107103[/C][C]-1.6592[/C][C]0.049188[/C][/ROW]
[ROW][C]18[/C][C]-0.068632[/C][C]-1.0632[/C][C]0.144369[/C][/ROW]
[ROW][C]19[/C][C]-0.001207[/C][C]-0.0187[/C][C]0.492548[/C][/ROW]
[ROW][C]20[/C][C]-0.131111[/C][C]-2.0312[/C][C]0.02167[/C][/ROW]
[ROW][C]21[/C][C]0.023705[/C][C]0.3672[/C][C]0.356883[/C][/ROW]
[ROW][C]22[/C][C]0.024946[/C][C]0.3865[/C][C]0.349748[/C][/ROW]
[ROW][C]23[/C][C]0.099216[/C][C]1.537[/C][C]0.0628[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194280&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194280&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:

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.1248761.93460.02711
2-0.102625-1.58990.056591
30.1104651.71130.044157
40.0214380.33210.370046
50.0512190.79350.214141
6-0.059049-0.91480.180612
70.0384170.59520.276149
8-0.010383-0.16080.436175
9-0.106917-1.65640.049478
100.0132140.20470.418985
11-0.05306-0.8220.205945
12-0.005642-0.08740.465213
130.0247110.38280.351096
14-0.071258-1.10390.135365
15-0.129921-2.01270.022631
16-0.010727-0.16620.43408
17-0.107103-1.65920.049188
18-0.068632-1.06320.144369
19-0.001207-0.01870.492548
20-0.131111-2.03120.02167
210.0237050.36720.356883
220.0249460.38650.349748
230.0992161.5370.0628


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;
R code (references can be found in the software module):
if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')