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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 07:01:17 -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/t13541904973al8uri6k0lzyh2.htm/, Retrieved Sat, 27 Apr 2024 21:37:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=194282, Retrieved Sat, 27 Apr 2024 21:37:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
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 12:01:17] [3353489d44052879174bf0d9e8b7362f] [Current]
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Dataseries X:
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




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 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=194282&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]2 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=194282&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194282&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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
10.1169941.76660.039319
2-0.002933-0.04430.482355
30.2175153.28440.000591
40.0242330.36590.357385
50.1000321.51050.066156
60.0303160.45780.32378
70.0067390.10180.459517
80.0581720.87840.19033
9-0.121078-1.82820.03441
100.0126710.19130.42422
11-0.146099-2.2060.014189
12-0.462978-6.99080
13-0.032201-0.48620.313636
14-0.139818-2.11120.017922
15-0.137609-2.07780.019421
16-0.006915-0.10440.458465
17-0.133084-2.00950.02283
18-0.037155-0.5610.287662
19-0.024314-0.36710.356931
20-0.095683-1.44480.074945
21-0.019677-0.29710.383325
220.03890.58740.278764
230.1337592.01970.022292

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.116994 & 1.7666 & 0.039319 \tabularnewline
2 & -0.002933 & -0.0443 & 0.482355 \tabularnewline
3 & 0.217515 & 3.2844 & 0.000591 \tabularnewline
4 & 0.024233 & 0.3659 & 0.357385 \tabularnewline
5 & 0.100032 & 1.5105 & 0.066156 \tabularnewline
6 & 0.030316 & 0.4578 & 0.32378 \tabularnewline
7 & 0.006739 & 0.1018 & 0.459517 \tabularnewline
8 & 0.058172 & 0.8784 & 0.19033 \tabularnewline
9 & -0.121078 & -1.8282 & 0.03441 \tabularnewline
10 & 0.012671 & 0.1913 & 0.42422 \tabularnewline
11 & -0.146099 & -2.206 & 0.014189 \tabularnewline
12 & -0.462978 & -6.9908 & 0 \tabularnewline
13 & -0.032201 & -0.4862 & 0.313636 \tabularnewline
14 & -0.139818 & -2.1112 & 0.017922 \tabularnewline
15 & -0.137609 & -2.0778 & 0.019421 \tabularnewline
16 & -0.006915 & -0.1044 & 0.458465 \tabularnewline
17 & -0.133084 & -2.0095 & 0.02283 \tabularnewline
18 & -0.037155 & -0.561 & 0.287662 \tabularnewline
19 & -0.024314 & -0.3671 & 0.356931 \tabularnewline
20 & -0.095683 & -1.4448 & 0.074945 \tabularnewline
21 & -0.019677 & -0.2971 & 0.383325 \tabularnewline
22 & 0.0389 & 0.5874 & 0.278764 \tabularnewline
23 & 0.133759 & 2.0197 & 0.022292 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194282&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]0.116994[/C][C]1.7666[/C][C]0.039319[/C][/ROW]
[ROW][C]2[/C][C]-0.002933[/C][C]-0.0443[/C][C]0.482355[/C][/ROW]
[ROW][C]3[/C][C]0.217515[/C][C]3.2844[/C][C]0.000591[/C][/ROW]
[ROW][C]4[/C][C]0.024233[/C][C]0.3659[/C][C]0.357385[/C][/ROW]
[ROW][C]5[/C][C]0.100032[/C][C]1.5105[/C][C]0.066156[/C][/ROW]
[ROW][C]6[/C][C]0.030316[/C][C]0.4578[/C][C]0.32378[/C][/ROW]
[ROW][C]7[/C][C]0.006739[/C][C]0.1018[/C][C]0.459517[/C][/ROW]
[ROW][C]8[/C][C]0.058172[/C][C]0.8784[/C][C]0.19033[/C][/ROW]
[ROW][C]9[/C][C]-0.121078[/C][C]-1.8282[/C][C]0.03441[/C][/ROW]
[ROW][C]10[/C][C]0.012671[/C][C]0.1913[/C][C]0.42422[/C][/ROW]
[ROW][C]11[/C][C]-0.146099[/C][C]-2.206[/C][C]0.014189[/C][/ROW]
[ROW][C]12[/C][C]-0.462978[/C][C]-6.9908[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.032201[/C][C]-0.4862[/C][C]0.313636[/C][/ROW]
[ROW][C]14[/C][C]-0.139818[/C][C]-2.1112[/C][C]0.017922[/C][/ROW]
[ROW][C]15[/C][C]-0.137609[/C][C]-2.0778[/C][C]0.019421[/C][/ROW]
[ROW][C]16[/C][C]-0.006915[/C][C]-0.1044[/C][C]0.458465[/C][/ROW]
[ROW][C]17[/C][C]-0.133084[/C][C]-2.0095[/C][C]0.02283[/C][/ROW]
[ROW][C]18[/C][C]-0.037155[/C][C]-0.561[/C][C]0.287662[/C][/ROW]
[ROW][C]19[/C][C]-0.024314[/C][C]-0.3671[/C][C]0.356931[/C][/ROW]
[ROW][C]20[/C][C]-0.095683[/C][C]-1.4448[/C][C]0.074945[/C][/ROW]
[ROW][C]21[/C][C]-0.019677[/C][C]-0.2971[/C][C]0.383325[/C][/ROW]
[ROW][C]22[/C][C]0.0389[/C][C]0.5874[/C][C]0.278764[/C][/ROW]
[ROW][C]23[/C][C]0.133759[/C][C]2.0197[/C][C]0.022292[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194282&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194282&T=1

As an alternative you can also use a QR Code:  

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

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.1169941.76660.039319
2-0.002933-0.04430.482355
30.2175153.28440.000591
40.0242330.36590.357385
50.1000321.51050.066156
60.0303160.45780.32378
70.0067390.10180.459517
80.0581720.87840.19033
9-0.121078-1.82820.03441
100.0126710.19130.42422
11-0.146099-2.2060.014189
12-0.462978-6.99080
13-0.032201-0.48620.313636
14-0.139818-2.11120.017922
15-0.137609-2.07780.019421
16-0.006915-0.10440.458465
17-0.133084-2.00950.02283
18-0.037155-0.5610.287662
19-0.024314-0.36710.356931
20-0.095683-1.44480.074945
21-0.019677-0.29710.383325
220.03890.58740.278764
230.1337592.01970.022292







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.1169941.76660.039319
2-0.016852-0.25450.399688
30.2229493.36650.000447
4-0.030599-0.4620.322249
50.1184231.78820.037539
6-0.049538-0.7480.227615
70.0227370.34330.365839
80.0065660.09910.460555
9-0.133677-2.01850.022357
100.0392060.5920.27722
11-0.203072-3.06630.001214
12-0.407316-6.15030
130.0222870.33650.368393
14-0.141938-2.14320.016577
150.0713011.07660.141394
160.0224380.33880.367535
170.0117170.17690.429862
180.0148680.22450.411282
190.0370290.55910.288312
20-0.04466-0.67440.250384
21-0.091641-1.38370.083895
220.0905011.36650.086559
230.0066640.10060.459967

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.116994 & 1.7666 & 0.039319 \tabularnewline
2 & -0.016852 & -0.2545 & 0.399688 \tabularnewline
3 & 0.222949 & 3.3665 & 0.000447 \tabularnewline
4 & -0.030599 & -0.462 & 0.322249 \tabularnewline
5 & 0.118423 & 1.7882 & 0.037539 \tabularnewline
6 & -0.049538 & -0.748 & 0.227615 \tabularnewline
7 & 0.022737 & 0.3433 & 0.365839 \tabularnewline
8 & 0.006566 & 0.0991 & 0.460555 \tabularnewline
9 & -0.133677 & -2.0185 & 0.022357 \tabularnewline
10 & 0.039206 & 0.592 & 0.27722 \tabularnewline
11 & -0.203072 & -3.0663 & 0.001214 \tabularnewline
12 & -0.407316 & -6.1503 & 0 \tabularnewline
13 & 0.022287 & 0.3365 & 0.368393 \tabularnewline
14 & -0.141938 & -2.1432 & 0.016577 \tabularnewline
15 & 0.071301 & 1.0766 & 0.141394 \tabularnewline
16 & 0.022438 & 0.3388 & 0.367535 \tabularnewline
17 & 0.011717 & 0.1769 & 0.429862 \tabularnewline
18 & 0.014868 & 0.2245 & 0.411282 \tabularnewline
19 & 0.037029 & 0.5591 & 0.288312 \tabularnewline
20 & -0.04466 & -0.6744 & 0.250384 \tabularnewline
21 & -0.091641 & -1.3837 & 0.083895 \tabularnewline
22 & 0.090501 & 1.3665 & 0.086559 \tabularnewline
23 & 0.006664 & 0.1006 & 0.459967 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194282&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]0.116994[/C][C]1.7666[/C][C]0.039319[/C][/ROW]
[ROW][C]2[/C][C]-0.016852[/C][C]-0.2545[/C][C]0.399688[/C][/ROW]
[ROW][C]3[/C][C]0.222949[/C][C]3.3665[/C][C]0.000447[/C][/ROW]
[ROW][C]4[/C][C]-0.030599[/C][C]-0.462[/C][C]0.322249[/C][/ROW]
[ROW][C]5[/C][C]0.118423[/C][C]1.7882[/C][C]0.037539[/C][/ROW]
[ROW][C]6[/C][C]-0.049538[/C][C]-0.748[/C][C]0.227615[/C][/ROW]
[ROW][C]7[/C][C]0.022737[/C][C]0.3433[/C][C]0.365839[/C][/ROW]
[ROW][C]8[/C][C]0.006566[/C][C]0.0991[/C][C]0.460555[/C][/ROW]
[ROW][C]9[/C][C]-0.133677[/C][C]-2.0185[/C][C]0.022357[/C][/ROW]
[ROW][C]10[/C][C]0.039206[/C][C]0.592[/C][C]0.27722[/C][/ROW]
[ROW][C]11[/C][C]-0.203072[/C][C]-3.0663[/C][C]0.001214[/C][/ROW]
[ROW][C]12[/C][C]-0.407316[/C][C]-6.1503[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.022287[/C][C]0.3365[/C][C]0.368393[/C][/ROW]
[ROW][C]14[/C][C]-0.141938[/C][C]-2.1432[/C][C]0.016577[/C][/ROW]
[ROW][C]15[/C][C]0.071301[/C][C]1.0766[/C][C]0.141394[/C][/ROW]
[ROW][C]16[/C][C]0.022438[/C][C]0.3388[/C][C]0.367535[/C][/ROW]
[ROW][C]17[/C][C]0.011717[/C][C]0.1769[/C][C]0.429862[/C][/ROW]
[ROW][C]18[/C][C]0.014868[/C][C]0.2245[/C][C]0.411282[/C][/ROW]
[ROW][C]19[/C][C]0.037029[/C][C]0.5591[/C][C]0.288312[/C][/ROW]
[ROW][C]20[/C][C]-0.04466[/C][C]-0.6744[/C][C]0.250384[/C][/ROW]
[ROW][C]21[/C][C]-0.091641[/C][C]-1.3837[/C][C]0.083895[/C][/ROW]
[ROW][C]22[/C][C]0.090501[/C][C]1.3665[/C][C]0.086559[/C][/ROW]
[ROW][C]23[/C][C]0.006664[/C][C]0.1006[/C][C]0.459967[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194282&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194282&T=2

As an alternative you can also use a QR Code:  

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

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.1169941.76660.039319
2-0.016852-0.25450.399688
30.2229493.36650.000447
4-0.030599-0.4620.322249
50.1184231.78820.037539
6-0.049538-0.7480.227615
70.0227370.34330.365839
80.0065660.09910.460555
9-0.133677-2.01850.022357
100.0392060.5920.27722
11-0.203072-3.06630.001214
12-0.407316-6.15030
130.0222870.33650.368393
14-0.141938-2.14320.016577
150.0713011.07660.141394
160.0224380.33880.367535
170.0117170.17690.429862
180.0148680.22450.411282
190.0370290.55910.288312
20-0.04466-0.67440.250384
21-0.091641-1.38370.083895
220.0905011.36650.086559
230.0066640.10060.459967



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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')