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Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationFri, 23 Oct 2015 15:33:11 +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/2015/Oct/23/t14456108253psns6trv0sfgyh.htm/, Retrieved Tue, 14 May 2024 17:25:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282915, Retrieved Tue, 14 May 2024 17:25:04 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact81
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [] [2015-10-23 14:33:11] [e897088c3d9e15a1e92009c0481cb133] [Current]
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Dataseries X:
97,41
97,32
97,33
97,38
97,47
97,5
97,5
97,58
97,7
97,9
97,98
98,03
98,03
97,94
98,12
98,19
98,34
98,42
98,43
98,45
98,77
99,24
99,46
99,54
99,55
99,24
99,43
99,47
99,57
99,62
99,64
99,75
99,85
100,28
100,52
100,57
100,57
100,27
100,27
100,18
100,16
100,18
100,18
100,59
100,69
101,06
101,15
101,16
101,16
100,81
100,94
101,13
101,29
101,34
101,35
101,7
102,05
102,48
102,66
102,72
102,73
102,18
102,22
102,37
102,53
102,61
102,62
103
103,17
103,52
103,69
103,73
99,57
99,09
99,14
99,36
99,6
99,65
99,8
100,15
100,45
100,89
101,13
101,17
101,21
101,1
101,17
101,11
101,2
101,15
100,92
101,1
101,22
101,25
101,39
101,43




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282915&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282915&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282915&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9414199.2240
20.8687318.51180
30.7963657.80280
40.7329247.18120
50.6783796.64670
60.6298326.17110
70.5836195.71830
80.5428785.31910
90.5121435.0181e-06
100.4924884.82543e-06
110.474974.65375e-06
120.4446934.35711.7e-05
130.4044373.96277.1e-05
140.3571013.49890.000355
150.3135753.07240.001382
160.2783172.72690.0038
170.2539122.48780.007288
180.2347992.30060.011791
190.2143512.10020.019166

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.941419 & 9.224 & 0 \tabularnewline
2 & 0.868731 & 8.5118 & 0 \tabularnewline
3 & 0.796365 & 7.8028 & 0 \tabularnewline
4 & 0.732924 & 7.1812 & 0 \tabularnewline
5 & 0.678379 & 6.6467 & 0 \tabularnewline
6 & 0.629832 & 6.1711 & 0 \tabularnewline
7 & 0.583619 & 5.7183 & 0 \tabularnewline
8 & 0.542878 & 5.3191 & 0 \tabularnewline
9 & 0.512143 & 5.018 & 1e-06 \tabularnewline
10 & 0.492488 & 4.8254 & 3e-06 \tabularnewline
11 & 0.47497 & 4.6537 & 5e-06 \tabularnewline
12 & 0.444693 & 4.3571 & 1.7e-05 \tabularnewline
13 & 0.404437 & 3.9627 & 7.1e-05 \tabularnewline
14 & 0.357101 & 3.4989 & 0.000355 \tabularnewline
15 & 0.313575 & 3.0724 & 0.001382 \tabularnewline
16 & 0.278317 & 2.7269 & 0.0038 \tabularnewline
17 & 0.253912 & 2.4878 & 0.007288 \tabularnewline
18 & 0.234799 & 2.3006 & 0.011791 \tabularnewline
19 & 0.214351 & 2.1002 & 0.019166 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282915&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]0.941419[/C][C]9.224[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.868731[/C][C]8.5118[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.796365[/C][C]7.8028[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.732924[/C][C]7.1812[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.678379[/C][C]6.6467[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.629832[/C][C]6.1711[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.583619[/C][C]5.7183[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.542878[/C][C]5.3191[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.512143[/C][C]5.018[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.492488[/C][C]4.8254[/C][C]3e-06[/C][/ROW]
[ROW][C]11[/C][C]0.47497[/C][C]4.6537[/C][C]5e-06[/C][/ROW]
[ROW][C]12[/C][C]0.444693[/C][C]4.3571[/C][C]1.7e-05[/C][/ROW]
[ROW][C]13[/C][C]0.404437[/C][C]3.9627[/C][C]7.1e-05[/C][/ROW]
[ROW][C]14[/C][C]0.357101[/C][C]3.4989[/C][C]0.000355[/C][/ROW]
[ROW][C]15[/C][C]0.313575[/C][C]3.0724[/C][C]0.001382[/C][/ROW]
[ROW][C]16[/C][C]0.278317[/C][C]2.7269[/C][C]0.0038[/C][/ROW]
[ROW][C]17[/C][C]0.253912[/C][C]2.4878[/C][C]0.007288[/C][/ROW]
[ROW][C]18[/C][C]0.234799[/C][C]2.3006[/C][C]0.011791[/C][/ROW]
[ROW][C]19[/C][C]0.214351[/C][C]2.1002[/C][C]0.019166[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282915&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282915&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
10.9414199.2240
20.8687318.51180
30.7963657.80280
40.7329247.18120
50.6783796.64670
60.6298326.17110
70.5836195.71830
80.5428785.31910
90.5121435.0181e-06
100.4924884.82543e-06
110.474974.65375e-06
120.4446934.35711.7e-05
130.4044373.96277.1e-05
140.3571013.49890.000355
150.3135753.07240.001382
160.2783172.72690.0038
170.2539122.48780.007288
180.2347992.30060.011791
190.2143512.10020.019166







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9414199.2240
2-0.154216-1.5110.067036
3-0.021765-0.21330.41579
40.0376910.36930.356361
50.0252220.24710.402668
60.0053350.05230.479212
7-0.014772-0.14470.44261
80.0242630.23770.406301
90.0607520.59520.276539
100.0647470.63440.263669
11-0.008445-0.08270.467115
12-0.116338-1.13990.128588
13-0.06361-0.62330.267298
14-0.057027-0.55870.288818
150.0132710.130.448408
160.0268510.26310.396523
170.0511560.50120.308681
180.0152560.14950.440745
19-0.032215-0.31560.376479

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.941419 & 9.224 & 0 \tabularnewline
2 & -0.154216 & -1.511 & 0.067036 \tabularnewline
3 & -0.021765 & -0.2133 & 0.41579 \tabularnewline
4 & 0.037691 & 0.3693 & 0.356361 \tabularnewline
5 & 0.025222 & 0.2471 & 0.402668 \tabularnewline
6 & 0.005335 & 0.0523 & 0.479212 \tabularnewline
7 & -0.014772 & -0.1447 & 0.44261 \tabularnewline
8 & 0.024263 & 0.2377 & 0.406301 \tabularnewline
9 & 0.060752 & 0.5952 & 0.276539 \tabularnewline
10 & 0.064747 & 0.6344 & 0.263669 \tabularnewline
11 & -0.008445 & -0.0827 & 0.467115 \tabularnewline
12 & -0.116338 & -1.1399 & 0.128588 \tabularnewline
13 & -0.06361 & -0.6233 & 0.267298 \tabularnewline
14 & -0.057027 & -0.5587 & 0.288818 \tabularnewline
15 & 0.013271 & 0.13 & 0.448408 \tabularnewline
16 & 0.026851 & 0.2631 & 0.396523 \tabularnewline
17 & 0.051156 & 0.5012 & 0.308681 \tabularnewline
18 & 0.015256 & 0.1495 & 0.440745 \tabularnewline
19 & -0.032215 & -0.3156 & 0.376479 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282915&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]0.941419[/C][C]9.224[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.154216[/C][C]-1.511[/C][C]0.067036[/C][/ROW]
[ROW][C]3[/C][C]-0.021765[/C][C]-0.2133[/C][C]0.41579[/C][/ROW]
[ROW][C]4[/C][C]0.037691[/C][C]0.3693[/C][C]0.356361[/C][/ROW]
[ROW][C]5[/C][C]0.025222[/C][C]0.2471[/C][C]0.402668[/C][/ROW]
[ROW][C]6[/C][C]0.005335[/C][C]0.0523[/C][C]0.479212[/C][/ROW]
[ROW][C]7[/C][C]-0.014772[/C][C]-0.1447[/C][C]0.44261[/C][/ROW]
[ROW][C]8[/C][C]0.024263[/C][C]0.2377[/C][C]0.406301[/C][/ROW]
[ROW][C]9[/C][C]0.060752[/C][C]0.5952[/C][C]0.276539[/C][/ROW]
[ROW][C]10[/C][C]0.064747[/C][C]0.6344[/C][C]0.263669[/C][/ROW]
[ROW][C]11[/C][C]-0.008445[/C][C]-0.0827[/C][C]0.467115[/C][/ROW]
[ROW][C]12[/C][C]-0.116338[/C][C]-1.1399[/C][C]0.128588[/C][/ROW]
[ROW][C]13[/C][C]-0.06361[/C][C]-0.6233[/C][C]0.267298[/C][/ROW]
[ROW][C]14[/C][C]-0.057027[/C][C]-0.5587[/C][C]0.288818[/C][/ROW]
[ROW][C]15[/C][C]0.013271[/C][C]0.13[/C][C]0.448408[/C][/ROW]
[ROW][C]16[/C][C]0.026851[/C][C]0.2631[/C][C]0.396523[/C][/ROW]
[ROW][C]17[/C][C]0.051156[/C][C]0.5012[/C][C]0.308681[/C][/ROW]
[ROW][C]18[/C][C]0.015256[/C][C]0.1495[/C][C]0.440745[/C][/ROW]
[ROW][C]19[/C][C]-0.032215[/C][C]-0.3156[/C][C]0.376479[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282915&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282915&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
10.9414199.2240
2-0.154216-1.5110.067036
3-0.021765-0.21330.41579
40.0376910.36930.356361
50.0252220.24710.402668
60.0053350.05230.479212
7-0.014772-0.14470.44261
80.0242630.23770.406301
90.0607520.59520.276539
100.0647470.63440.263669
11-0.008445-0.08270.467115
12-0.116338-1.13990.128588
13-0.06361-0.62330.267298
14-0.057027-0.55870.288818
150.0132710.130.448408
160.0268510.26310.396523
170.0511560.50120.308681
180.0152560.14950.440745
19-0.032215-0.31560.376479



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')