Free Statistics

of Irreproducible Research!

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 06:58:51 -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/t1354190356stv346g31kevekc.htm/, Retrieved Sun, 28 Apr 2024 15:14:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=194278, Retrieved Sun, 28 Apr 2024 15:14:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92
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 11:58:51] [3353489d44052879174bf0d9e8b7362f] [Current]
Feedback Forum

Post a new message
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=194278&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=194278&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194278&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
10.97285915.10280
20.9418414.62130
30.91221814.16140
40.88125713.68080
50.85123313.21470
60.81820412.70190
70.7870412.21810
80.75849711.7750
90.73299111.37910
100.71088311.03590
110.69263710.75260
120.68014810.55870
130.66550410.33140
140.64762210.05380
150.631939.81020
160.6220039.65610
170.6140289.53230
180.6069599.42250
190.6023019.35020
200.5961019.2540
210.5939619.22080
220.593479.21310
230.594019.22150

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.972859 & 15.1028 & 0 \tabularnewline
2 & 0.94184 & 14.6213 & 0 \tabularnewline
3 & 0.912218 & 14.1614 & 0 \tabularnewline
4 & 0.881257 & 13.6808 & 0 \tabularnewline
5 & 0.851233 & 13.2147 & 0 \tabularnewline
6 & 0.818204 & 12.7019 & 0 \tabularnewline
7 & 0.78704 & 12.2181 & 0 \tabularnewline
8 & 0.758497 & 11.775 & 0 \tabularnewline
9 & 0.732991 & 11.3791 & 0 \tabularnewline
10 & 0.710883 & 11.0359 & 0 \tabularnewline
11 & 0.692637 & 10.7526 & 0 \tabularnewline
12 & 0.680148 & 10.5587 & 0 \tabularnewline
13 & 0.665504 & 10.3314 & 0 \tabularnewline
14 & 0.647622 & 10.0538 & 0 \tabularnewline
15 & 0.63193 & 9.8102 & 0 \tabularnewline
16 & 0.622003 & 9.6561 & 0 \tabularnewline
17 & 0.614028 & 9.5323 & 0 \tabularnewline
18 & 0.606959 & 9.4225 & 0 \tabularnewline
19 & 0.602301 & 9.3502 & 0 \tabularnewline
20 & 0.596101 & 9.254 & 0 \tabularnewline
21 & 0.593961 & 9.2208 & 0 \tabularnewline
22 & 0.59347 & 9.2131 & 0 \tabularnewline
23 & 0.59401 & 9.2215 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194278&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]0.972859[/C][C]15.1028[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.94184[/C][C]14.6213[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.912218[/C][C]14.1614[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.881257[/C][C]13.6808[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.851233[/C][C]13.2147[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.818204[/C][C]12.7019[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.78704[/C][C]12.2181[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.758497[/C][C]11.775[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.732991[/C][C]11.3791[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.710883[/C][C]11.0359[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.692637[/C][C]10.7526[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.680148[/C][C]10.5587[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.665504[/C][C]10.3314[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.647622[/C][C]10.0538[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.63193[/C][C]9.8102[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.622003[/C][C]9.6561[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.614028[/C][C]9.5323[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.606959[/C][C]9.4225[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.602301[/C][C]9.3502[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.596101[/C][C]9.254[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.593961[/C][C]9.2208[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.59347[/C][C]9.2131[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.59401[/C][C]9.2215[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194278&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194278&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
10.97285915.10280
20.9418414.62130
30.91221814.16140
40.88125713.68080
50.85123313.21470
60.81820412.70190
70.7870412.21810
80.75849711.7750
90.73299111.37910
100.71088311.03590
110.69263710.75260
120.68014810.55870
130.66550410.33140
140.64762210.05380
150.631939.81020
160.6220039.65610
170.6140289.53230
180.6069599.42250
190.6023019.35020
200.5961019.2540
210.5939619.22080
220.593479.21310
230.594019.22150







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.97285915.10280
2-0.086186-1.3380.091085
30.0153720.23860.405796
4-0.044806-0.69560.243685
50.0059670.09260.463136
6-0.077388-1.20140.115391
70.0278190.43190.333112
80.0212880.33050.370661
90.0411240.63840.261907
100.0389870.60520.272794
110.0578570.89820.184994
120.0858691.33310.091887
13-0.064347-0.99890.159413
14-0.063702-0.98890.161848
150.0303970.47190.318719
160.0987911.53360.063214
170.0188210.29220.385202
180.0327770.50880.305667
190.0579780.90010.184494
20-0.031005-0.48130.315359
210.0759591.17920.11974
220.023950.37180.355182
230.0351810.54620.292731

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.972859 & 15.1028 & 0 \tabularnewline
2 & -0.086186 & -1.338 & 0.091085 \tabularnewline
3 & 0.015372 & 0.2386 & 0.405796 \tabularnewline
4 & -0.044806 & -0.6956 & 0.243685 \tabularnewline
5 & 0.005967 & 0.0926 & 0.463136 \tabularnewline
6 & -0.077388 & -1.2014 & 0.115391 \tabularnewline
7 & 0.027819 & 0.4319 & 0.333112 \tabularnewline
8 & 0.021288 & 0.3305 & 0.370661 \tabularnewline
9 & 0.041124 & 0.6384 & 0.261907 \tabularnewline
10 & 0.038987 & 0.6052 & 0.272794 \tabularnewline
11 & 0.057857 & 0.8982 & 0.184994 \tabularnewline
12 & 0.085869 & 1.3331 & 0.091887 \tabularnewline
13 & -0.064347 & -0.9989 & 0.159413 \tabularnewline
14 & -0.063702 & -0.9889 & 0.161848 \tabularnewline
15 & 0.030397 & 0.4719 & 0.318719 \tabularnewline
16 & 0.098791 & 1.5336 & 0.063214 \tabularnewline
17 & 0.018821 & 0.2922 & 0.385202 \tabularnewline
18 & 0.032777 & 0.5088 & 0.305667 \tabularnewline
19 & 0.057978 & 0.9001 & 0.184494 \tabularnewline
20 & -0.031005 & -0.4813 & 0.315359 \tabularnewline
21 & 0.075959 & 1.1792 & 0.11974 \tabularnewline
22 & 0.02395 & 0.3718 & 0.355182 \tabularnewline
23 & 0.035181 & 0.5462 & 0.292731 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=194278&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]0.972859[/C][C]15.1028[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.086186[/C][C]-1.338[/C][C]0.091085[/C][/ROW]
[ROW][C]3[/C][C]0.015372[/C][C]0.2386[/C][C]0.405796[/C][/ROW]
[ROW][C]4[/C][C]-0.044806[/C][C]-0.6956[/C][C]0.243685[/C][/ROW]
[ROW][C]5[/C][C]0.005967[/C][C]0.0926[/C][C]0.463136[/C][/ROW]
[ROW][C]6[/C][C]-0.077388[/C][C]-1.2014[/C][C]0.115391[/C][/ROW]
[ROW][C]7[/C][C]0.027819[/C][C]0.4319[/C][C]0.333112[/C][/ROW]
[ROW][C]8[/C][C]0.021288[/C][C]0.3305[/C][C]0.370661[/C][/ROW]
[ROW][C]9[/C][C]0.041124[/C][C]0.6384[/C][C]0.261907[/C][/ROW]
[ROW][C]10[/C][C]0.038987[/C][C]0.6052[/C][C]0.272794[/C][/ROW]
[ROW][C]11[/C][C]0.057857[/C][C]0.8982[/C][C]0.184994[/C][/ROW]
[ROW][C]12[/C][C]0.085869[/C][C]1.3331[/C][C]0.091887[/C][/ROW]
[ROW][C]13[/C][C]-0.064347[/C][C]-0.9989[/C][C]0.159413[/C][/ROW]
[ROW][C]14[/C][C]-0.063702[/C][C]-0.9889[/C][C]0.161848[/C][/ROW]
[ROW][C]15[/C][C]0.030397[/C][C]0.4719[/C][C]0.318719[/C][/ROW]
[ROW][C]16[/C][C]0.098791[/C][C]1.5336[/C][C]0.063214[/C][/ROW]
[ROW][C]17[/C][C]0.018821[/C][C]0.2922[/C][C]0.385202[/C][/ROW]
[ROW][C]18[/C][C]0.032777[/C][C]0.5088[/C][C]0.305667[/C][/ROW]
[ROW][C]19[/C][C]0.057978[/C][C]0.9001[/C][C]0.184494[/C][/ROW]
[ROW][C]20[/C][C]-0.031005[/C][C]-0.4813[/C][C]0.315359[/C][/ROW]
[ROW][C]21[/C][C]0.075959[/C][C]1.1792[/C][C]0.11974[/C][/ROW]
[ROW][C]22[/C][C]0.02395[/C][C]0.3718[/C][C]0.355182[/C][/ROW]
[ROW][C]23[/C][C]0.035181[/C][C]0.5462[/C][C]0.292731[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=194278&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=194278&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
10.97285915.10280
2-0.086186-1.3380.091085
30.0153720.23860.405796
4-0.044806-0.69560.243685
50.0059670.09260.463136
6-0.077388-1.20140.115391
70.0278190.43190.333112
80.0212880.33050.370661
90.0411240.63840.261907
100.0389870.60520.272794
110.0578570.89820.184994
120.0858691.33310.091887
13-0.064347-0.99890.159413
14-0.063702-0.98890.161848
150.0303970.47190.318719
160.0987911.53360.063214
170.0188210.29220.385202
180.0327770.50880.305667
190.0579780.90010.184494
20-0.031005-0.48130.315359
210.0759591.17920.11974
220.023950.37180.355182
230.0351810.54620.292731



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; 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')