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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationMon, 26 Nov 2007 12:22:00 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/26/t11961043813ixqe3on5bg8xgl.htm/, Retrieved Tue, 10 Feb 2026 13:58:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6640, Retrieved Tue, 10 Feb 2026 13:58:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordspartial correlation fucntion, groep 4, paper
Estimated Impact391

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] [partial correlati...] [2007-11-26 19:22:00] [bd7b8d7754bcf95ad80b21f541dc6b78] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
88,95
88,81
88,90
90,15
90,92
90,78
90,81
89,46
89,22
88,89
89,41
89,59
90,25
90,20
90,27
90,71
91,18
90,66
89,72
88,72
88,91
89,15
89,15
89,08
89,28
89,47
89,53
90,72
90,91
91,38
91,49
90,90
90,93
90,57
91,28
90,83
91,50
91,58
92,49
94,16
95,46
95,80
95,32
95,41
95,35
95,68
95,59
94,96
96,92
96,06
96,59
96,67
97,27
96,38
96,47
96,05
96,76
96,51
96,55
95,97
97,00
97,46
97,90
98,42
98,54
99,00
98,94
99,02
100,07
98,72
98,73
98,04
99,08
99,22
99,57
100,44
100,84
100,75
100,49
99,98
99,96
99,76
100,11
99,79
100,29
101,12
102,65
102,71
103,39
102,80
102,07
102,15
101,21
101,27
101,86
101,65
101,94
102,62
102,71
103,39
104,51
104,09
104,29
104,57
105,39
105,15
106,13
105,46
106,47
106,62
106,52
108,04
107,15
107,32
107,76
107,26
107,89

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6640&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6640&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6640&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Autocorrelation Function
Time lag kACF(k)T-STATP-value
0110.77030
1-0.084439-0.90940.817498
20.1878142.02280.022696
3-0.111488-1.20080.883855
4-0.127438-1.37250.913729
5-0.101414-1.09230.861508
6-0.105229-1.13340.870299
7-0.158469-1.70680.954729
8-0.048889-0.52660.700244
9-0.029116-0.31360.622803
100.0640090.68940.245976
110.1056071.13740.128854
120.3360683.61960.000219
13-0.028828-0.31050.621626
140.0968811.04340.149456
15-0.189853-2.04480.97843
16-0.030522-0.32870.628524
17-0.128096-1.37960.914824
180.0361750.38960.348769
19-0.23336-2.51340.993334

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 10.7703 & 0 \tabularnewline
1 & -0.084439 & -0.9094 & 0.817498 \tabularnewline
2 & 0.187814 & 2.0228 & 0.022696 \tabularnewline
3 & -0.111488 & -1.2008 & 0.883855 \tabularnewline
4 & -0.127438 & -1.3725 & 0.913729 \tabularnewline
5 & -0.101414 & -1.0923 & 0.861508 \tabularnewline
6 & -0.105229 & -1.1334 & 0.870299 \tabularnewline
7 & -0.158469 & -1.7068 & 0.954729 \tabularnewline
8 & -0.048889 & -0.5266 & 0.700244 \tabularnewline
9 & -0.029116 & -0.3136 & 0.622803 \tabularnewline
10 & 0.064009 & 0.6894 & 0.245976 \tabularnewline
11 & 0.105607 & 1.1374 & 0.128854 \tabularnewline
12 & 0.336068 & 3.6196 & 0.000219 \tabularnewline
13 & -0.028828 & -0.3105 & 0.621626 \tabularnewline
14 & 0.096881 & 1.0434 & 0.149456 \tabularnewline
15 & -0.189853 & -2.0448 & 0.97843 \tabularnewline
16 & -0.030522 & -0.3287 & 0.628524 \tabularnewline
17 & -0.128096 & -1.3796 & 0.914824 \tabularnewline
18 & 0.036175 & 0.3896 & 0.348769 \tabularnewline
19 & -0.23336 & -2.5134 & 0.993334 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6640&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]0[/C][C]1[/C][C]10.7703[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.084439[/C][C]-0.9094[/C][C]0.817498[/C][/ROW]
[ROW][C]2[/C][C]0.187814[/C][C]2.0228[/C][C]0.022696[/C][/ROW]
[ROW][C]3[/C][C]-0.111488[/C][C]-1.2008[/C][C]0.883855[/C][/ROW]
[ROW][C]4[/C][C]-0.127438[/C][C]-1.3725[/C][C]0.913729[/C][/ROW]
[ROW][C]5[/C][C]-0.101414[/C][C]-1.0923[/C][C]0.861508[/C][/ROW]
[ROW][C]6[/C][C]-0.105229[/C][C]-1.1334[/C][C]0.870299[/C][/ROW]
[ROW][C]7[/C][C]-0.158469[/C][C]-1.7068[/C][C]0.954729[/C][/ROW]
[ROW][C]8[/C][C]-0.048889[/C][C]-0.5266[/C][C]0.700244[/C][/ROW]
[ROW][C]9[/C][C]-0.029116[/C][C]-0.3136[/C][C]0.622803[/C][/ROW]
[ROW][C]10[/C][C]0.064009[/C][C]0.6894[/C][C]0.245976[/C][/ROW]
[ROW][C]11[/C][C]0.105607[/C][C]1.1374[/C][C]0.128854[/C][/ROW]
[ROW][C]12[/C][C]0.336068[/C][C]3.6196[/C][C]0.000219[/C][/ROW]
[ROW][C]13[/C][C]-0.028828[/C][C]-0.3105[/C][C]0.621626[/C][/ROW]
[ROW][C]14[/C][C]0.096881[/C][C]1.0434[/C][C]0.149456[/C][/ROW]
[ROW][C]15[/C][C]-0.189853[/C][C]-2.0448[/C][C]0.97843[/C][/ROW]
[ROW][C]16[/C][C]-0.030522[/C][C]-0.3287[/C][C]0.628524[/C][/ROW]
[ROW][C]17[/C][C]-0.128096[/C][C]-1.3796[/C][C]0.914824[/C][/ROW]
[ROW][C]18[/C][C]0.036175[/C][C]0.3896[/C][C]0.348769[/C][/ROW]
[ROW][C]19[/C][C]-0.23336[/C][C]-2.5134[/C][C]0.993334[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6640&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6640&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
0110.77030
1-0.084439-0.90940.817498
20.1878142.02280.022696
3-0.111488-1.20080.883855
4-0.127438-1.37250.913729
5-0.101414-1.09230.861508
6-0.105229-1.13340.870299
7-0.158469-1.70680.954729
8-0.048889-0.52660.700244
9-0.029116-0.31360.622803
100.0640090.68940.245976
110.1056071.13740.128854
120.3360683.61960.000219
13-0.028828-0.31050.621626
140.0968811.04340.149456
15-0.189853-2.04480.97843
16-0.030522-0.32870.628524
17-0.128096-1.37960.914824
180.0361750.38960.348769
19-0.23336-2.51340.993334






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
0-0.084439-0.90940.817498
10.1819811.960.026197
2-0.086614-0.93290.823586
3-0.182359-1.96410.974043
4-0.091548-0.9860.836909
5-0.07603-0.81890.79273
6-0.184364-1.98570.975285
7-0.101693-1.09530.862166
8-0.039481-0.42520.66427
90.0027510.02960.488205
100.0385570.41530.339356
110.3133053.37440.000503
12-0.024047-0.2590.60195
13-0.032573-0.35080.636821
14-0.117622-1.26680.896123
150.0189010.20360.419525
16-0.038606-0.41580.660837
170.1019181.09770.137306
18-0.172848-1.86160.967407
19-0.008127-0.08750.534798

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.084439 & -0.9094 & 0.817498 \tabularnewline
1 & 0.181981 & 1.96 & 0.026197 \tabularnewline
2 & -0.086614 & -0.9329 & 0.823586 \tabularnewline
3 & -0.182359 & -1.9641 & 0.974043 \tabularnewline
4 & -0.091548 & -0.986 & 0.836909 \tabularnewline
5 & -0.07603 & -0.8189 & 0.79273 \tabularnewline
6 & -0.184364 & -1.9857 & 0.975285 \tabularnewline
7 & -0.101693 & -1.0953 & 0.862166 \tabularnewline
8 & -0.039481 & -0.4252 & 0.66427 \tabularnewline
9 & 0.002751 & 0.0296 & 0.488205 \tabularnewline
10 & 0.038557 & 0.4153 & 0.339356 \tabularnewline
11 & 0.313305 & 3.3744 & 0.000503 \tabularnewline
12 & -0.024047 & -0.259 & 0.60195 \tabularnewline
13 & -0.032573 & -0.3508 & 0.636821 \tabularnewline
14 & -0.117622 & -1.2668 & 0.896123 \tabularnewline
15 & 0.018901 & 0.2036 & 0.419525 \tabularnewline
16 & -0.038606 & -0.4158 & 0.660837 \tabularnewline
17 & 0.101918 & 1.0977 & 0.137306 \tabularnewline
18 & -0.172848 & -1.8616 & 0.967407 \tabularnewline
19 & -0.008127 & -0.0875 & 0.534798 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6640&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]0[/C][C]-0.084439[/C][C]-0.9094[/C][C]0.817498[/C][/ROW]
[ROW][C]1[/C][C]0.181981[/C][C]1.96[/C][C]0.026197[/C][/ROW]
[ROW][C]2[/C][C]-0.086614[/C][C]-0.9329[/C][C]0.823586[/C][/ROW]
[ROW][C]3[/C][C]-0.182359[/C][C]-1.9641[/C][C]0.974043[/C][/ROW]
[ROW][C]4[/C][C]-0.091548[/C][C]-0.986[/C][C]0.836909[/C][/ROW]
[ROW][C]5[/C][C]-0.07603[/C][C]-0.8189[/C][C]0.79273[/C][/ROW]
[ROW][C]6[/C][C]-0.184364[/C][C]-1.9857[/C][C]0.975285[/C][/ROW]
[ROW][C]7[/C][C]-0.101693[/C][C]-1.0953[/C][C]0.862166[/C][/ROW]
[ROW][C]8[/C][C]-0.039481[/C][C]-0.4252[/C][C]0.66427[/C][/ROW]
[ROW][C]9[/C][C]0.002751[/C][C]0.0296[/C][C]0.488205[/C][/ROW]
[ROW][C]10[/C][C]0.038557[/C][C]0.4153[/C][C]0.339356[/C][/ROW]
[ROW][C]11[/C][C]0.313305[/C][C]3.3744[/C][C]0.000503[/C][/ROW]
[ROW][C]12[/C][C]-0.024047[/C][C]-0.259[/C][C]0.60195[/C][/ROW]
[ROW][C]13[/C][C]-0.032573[/C][C]-0.3508[/C][C]0.636821[/C][/ROW]
[ROW][C]14[/C][C]-0.117622[/C][C]-1.2668[/C][C]0.896123[/C][/ROW]
[ROW][C]15[/C][C]0.018901[/C][C]0.2036[/C][C]0.419525[/C][/ROW]
[ROW][C]16[/C][C]-0.038606[/C][C]-0.4158[/C][C]0.660837[/C][/ROW]
[ROW][C]17[/C][C]0.101918[/C][C]1.0977[/C][C]0.137306[/C][/ROW]
[ROW][C]18[/C][C]-0.172848[/C][C]-1.8616[/C][C]0.967407[/C][/ROW]
[ROW][C]19[/C][C]-0.008127[/C][C]-0.0875[/C][C]0.534798[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6640&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6640&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
0-0.084439-0.90940.817498
10.1819811.960.026197
2-0.086614-0.93290.823586
3-0.182359-1.96410.974043
4-0.091548-0.9860.836909
5-0.07603-0.81890.79273
6-0.184364-1.98570.975285
7-0.101693-1.09530.862166
8-0.039481-0.42520.66427
90.0027510.02960.488205
100.0385570.41530.339356
110.3133053.37440.000503
12-0.024047-0.2590.60195
13-0.032573-0.35080.636821
14-0.117622-1.26680.896123
150.0189010.20360.419525
16-0.038606-0.41580.660837
170.1019181.09770.137306
18-0.172848-1.86160.967407
19-0.008127-0.08750.534798


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;
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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')