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Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationFri, 27 May 2016 13:24:25 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/May/27/t14643519122xopbrlykjra22h.htm/, Retrieved Thu, 02 May 2024 00:25:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295617, Retrieved Thu, 02 May 2024 00:25:44 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [] [2016-05-27 12:24:25] [1af9caed13b550360754d0d82088541b] [Current]
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Dataseries X:
103,71
103,07
103,93
102,9
101,54
102,13
101,08
101,33
101,24
100,58
99,87
99,1
98,98
98,77
98,05
97,94
97,65
97,2
97,39
97,35
98,01
97,81
97,56
98,05
97,82
99,05
98,86
97,64
97,77
98,07
98,36
100
99,52
98,82
98,98
98,6
98,8
99,62
99,35
99,87
99,53
99,88
99,26
99,51
100,64
100,85
101,44
101,26
101,67
102,93
103,81
106,19
106,94
108,51
108,41
108,97
109,25
109,97
108,92
109,01
108,86
107,36
107,99
107,94
108,54
108,37
108,77
107,15
108,61
109,02
109,16
109,55




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

\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
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295617&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295617&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295617&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







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.0165260.13930.444823
20.2431812.04910.022076
30.1665361.40330.08245
4-0.025161-0.2120.416354
50.1814191.52870.065396
60.2402322.02420.023355
70.0594160.50070.309083
8-0.005145-0.04340.482771
9-0.015916-0.13410.446847
10-0.141932-1.19590.117849
110.0245410.20680.418385
12-0.028161-0.23730.406559
130.1376541.15990.124989
14-0.054575-0.45990.323512
150.00630.05310.478908
16-0.02621-0.22080.412923
17-0.104294-0.87880.191238
180.1054980.88890.188519

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.016526 & 0.1393 & 0.444823 \tabularnewline
2 & 0.243181 & 2.0491 & 0.022076 \tabularnewline
3 & 0.166536 & 1.4033 & 0.08245 \tabularnewline
4 & -0.025161 & -0.212 & 0.416354 \tabularnewline
5 & 0.181419 & 1.5287 & 0.065396 \tabularnewline
6 & 0.240232 & 2.0242 & 0.023355 \tabularnewline
7 & 0.059416 & 0.5007 & 0.309083 \tabularnewline
8 & -0.005145 & -0.0434 & 0.482771 \tabularnewline
9 & -0.015916 & -0.1341 & 0.446847 \tabularnewline
10 & -0.141932 & -1.1959 & 0.117849 \tabularnewline
11 & 0.024541 & 0.2068 & 0.418385 \tabularnewline
12 & -0.028161 & -0.2373 & 0.406559 \tabularnewline
13 & 0.137654 & 1.1599 & 0.124989 \tabularnewline
14 & -0.054575 & -0.4599 & 0.323512 \tabularnewline
15 & 0.0063 & 0.0531 & 0.478908 \tabularnewline
16 & -0.02621 & -0.2208 & 0.412923 \tabularnewline
17 & -0.104294 & -0.8788 & 0.191238 \tabularnewline
18 & 0.105498 & 0.8889 & 0.188519 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295617&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]0.016526[/C][C]0.1393[/C][C]0.444823[/C][/ROW]
[ROW][C]2[/C][C]0.243181[/C][C]2.0491[/C][C]0.022076[/C][/ROW]
[ROW][C]3[/C][C]0.166536[/C][C]1.4033[/C][C]0.08245[/C][/ROW]
[ROW][C]4[/C][C]-0.025161[/C][C]-0.212[/C][C]0.416354[/C][/ROW]
[ROW][C]5[/C][C]0.181419[/C][C]1.5287[/C][C]0.065396[/C][/ROW]
[ROW][C]6[/C][C]0.240232[/C][C]2.0242[/C][C]0.023355[/C][/ROW]
[ROW][C]7[/C][C]0.059416[/C][C]0.5007[/C][C]0.309083[/C][/ROW]
[ROW][C]8[/C][C]-0.005145[/C][C]-0.0434[/C][C]0.482771[/C][/ROW]
[ROW][C]9[/C][C]-0.015916[/C][C]-0.1341[/C][C]0.446847[/C][/ROW]
[ROW][C]10[/C][C]-0.141932[/C][C]-1.1959[/C][C]0.117849[/C][/ROW]
[ROW][C]11[/C][C]0.024541[/C][C]0.2068[/C][C]0.418385[/C][/ROW]
[ROW][C]12[/C][C]-0.028161[/C][C]-0.2373[/C][C]0.406559[/C][/ROW]
[ROW][C]13[/C][C]0.137654[/C][C]1.1599[/C][C]0.124989[/C][/ROW]
[ROW][C]14[/C][C]-0.054575[/C][C]-0.4599[/C][C]0.323512[/C][/ROW]
[ROW][C]15[/C][C]0.0063[/C][C]0.0531[/C][C]0.478908[/C][/ROW]
[ROW][C]16[/C][C]-0.02621[/C][C]-0.2208[/C][C]0.412923[/C][/ROW]
[ROW][C]17[/C][C]-0.104294[/C][C]-0.8788[/C][C]0.191238[/C][/ROW]
[ROW][C]18[/C][C]0.105498[/C][C]0.8889[/C][C]0.188519[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295617&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295617&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
10.0165260.13930.444823
20.2431812.04910.022076
30.1665361.40330.08245
4-0.025161-0.2120.416354
50.1814191.52870.065396
60.2402322.02420.023355
70.0594160.50070.309083
8-0.005145-0.04340.482771
9-0.015916-0.13410.446847
10-0.141932-1.19590.117849
110.0245410.20680.418385
12-0.028161-0.23730.406559
130.1376541.15990.124989
14-0.054575-0.45990.323512
150.00630.05310.478908
16-0.02621-0.22080.412923
17-0.104294-0.87880.191238
180.1054980.88890.188519







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.0165260.13930.444823
20.2429742.04730.022163
30.169531.42850.078769
4-0.089482-0.7540.226675
50.1084070.91350.182047
60.2719822.29180.012444
70.0191720.16150.436062
8-0.209306-1.76360.041047
9-0.103324-0.87060.193447
10-0.093069-0.78420.217762
110.0031110.02620.489579
12-0.052638-0.44350.329365
130.2048021.72570.044376
140.0276350.23290.408271
150.0046310.0390.484493
160.00640.05390.478574
17-0.077722-0.65490.257326
180.0354760.29890.382934

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.016526 & 0.1393 & 0.444823 \tabularnewline
2 & 0.242974 & 2.0473 & 0.022163 \tabularnewline
3 & 0.16953 & 1.4285 & 0.078769 \tabularnewline
4 & -0.089482 & -0.754 & 0.226675 \tabularnewline
5 & 0.108407 & 0.9135 & 0.182047 \tabularnewline
6 & 0.271982 & 2.2918 & 0.012444 \tabularnewline
7 & 0.019172 & 0.1615 & 0.436062 \tabularnewline
8 & -0.209306 & -1.7636 & 0.041047 \tabularnewline
9 & -0.103324 & -0.8706 & 0.193447 \tabularnewline
10 & -0.093069 & -0.7842 & 0.217762 \tabularnewline
11 & 0.003111 & 0.0262 & 0.489579 \tabularnewline
12 & -0.052638 & -0.4435 & 0.329365 \tabularnewline
13 & 0.204802 & 1.7257 & 0.044376 \tabularnewline
14 & 0.027635 & 0.2329 & 0.408271 \tabularnewline
15 & 0.004631 & 0.039 & 0.484493 \tabularnewline
16 & 0.0064 & 0.0539 & 0.478574 \tabularnewline
17 & -0.077722 & -0.6549 & 0.257326 \tabularnewline
18 & 0.035476 & 0.2989 & 0.382934 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295617&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]0.016526[/C][C]0.1393[/C][C]0.444823[/C][/ROW]
[ROW][C]2[/C][C]0.242974[/C][C]2.0473[/C][C]0.022163[/C][/ROW]
[ROW][C]3[/C][C]0.16953[/C][C]1.4285[/C][C]0.078769[/C][/ROW]
[ROW][C]4[/C][C]-0.089482[/C][C]-0.754[/C][C]0.226675[/C][/ROW]
[ROW][C]5[/C][C]0.108407[/C][C]0.9135[/C][C]0.182047[/C][/ROW]
[ROW][C]6[/C][C]0.271982[/C][C]2.2918[/C][C]0.012444[/C][/ROW]
[ROW][C]7[/C][C]0.019172[/C][C]0.1615[/C][C]0.436062[/C][/ROW]
[ROW][C]8[/C][C]-0.209306[/C][C]-1.7636[/C][C]0.041047[/C][/ROW]
[ROW][C]9[/C][C]-0.103324[/C][C]-0.8706[/C][C]0.193447[/C][/ROW]
[ROW][C]10[/C][C]-0.093069[/C][C]-0.7842[/C][C]0.217762[/C][/ROW]
[ROW][C]11[/C][C]0.003111[/C][C]0.0262[/C][C]0.489579[/C][/ROW]
[ROW][C]12[/C][C]-0.052638[/C][C]-0.4435[/C][C]0.329365[/C][/ROW]
[ROW][C]13[/C][C]0.204802[/C][C]1.7257[/C][C]0.044376[/C][/ROW]
[ROW][C]14[/C][C]0.027635[/C][C]0.2329[/C][C]0.408271[/C][/ROW]
[ROW][C]15[/C][C]0.004631[/C][C]0.039[/C][C]0.484493[/C][/ROW]
[ROW][C]16[/C][C]0.0064[/C][C]0.0539[/C][C]0.478574[/C][/ROW]
[ROW][C]17[/C][C]-0.077722[/C][C]-0.6549[/C][C]0.257326[/C][/ROW]
[ROW][C]18[/C][C]0.035476[/C][C]0.2989[/C][C]0.382934[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295617&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295617&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
10.0165260.13930.444823
20.2429742.04730.022163
30.169531.42850.078769
4-0.089482-0.7540.226675
50.1084070.91350.182047
60.2719822.29180.012444
70.0191720.16150.436062
8-0.209306-1.76360.041047
9-0.103324-0.87060.193447
10-0.093069-0.78420.217762
110.0031110.02620.489579
12-0.052638-0.44350.329365
130.2048021.72570.044376
140.0276350.23290.408271
150.0046310.0390.484493
160.00640.05390.478574
17-0.077722-0.65490.257326
180.0354760.29890.382934



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):
par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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)
x <- na.omit(x)
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')