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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Oct 2014 19:12:25 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/19/t1413742383n8bsihdzbhva5p1.htm/, Retrieved Sun, 12 May 2024 04:49:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243722, Retrieved Sun, 12 May 2024 04:49:35 +0000

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Original text written by user:

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User-defined keywords

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [] [2014-10-19 18:12:25] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Boxplots

0,52
0,53
0,53
0,53
0,53
0,51
0,5
0,49
0,49
0,5
0,5
0,51
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0,52
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0,52
0,51
0,51
0,47
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0,44
0,47
0,49
0,48
0,52
0,51
0,52
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0,51
0,5
0,51
0,47
0,49
0,48
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0,52
0,52
0,51
0,52
0,52
0,5
0,45
0,42
0,43
0,47
0,48
0,5
0,52
0,5
0,51
0,5
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0,47
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0,46
0,49
0,5
0,53
0,5
0,51
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0,5
0,49
0,5
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0,5
0,47
0,49
0,49

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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=243722&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=243722&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243722&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.724051	6.1438	0
2	0.407177	3.455	0.000463
3	0.036922	0.3133	0.377483
4	-0.195136	-1.6558	0.051059
5	-0.370848	-3.1468	0.001201
6	-0.414294	-3.5154	0.000382
7	-0.361655	-3.0687	0.001515
8	-0.202254	-1.7162	0.045214
9	-0.057681	-0.4894	0.313009
10	0.152728	1.2959	0.099567
11	0.361358	3.0662	0.001526
12	0.477461	4.0514	6.4e-05
13	0.397835	3.3757	0.000595
14	0.159846	1.3563	0.089615
15	-0.126186	-1.0707	0.143934
16	-0.319692	-2.7127	0.004172
17	-0.408808	-3.4688	0.000443
18	-0.439798	-3.7318	0.000188

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.724051 & 6.1438 & 0 \tabularnewline
2 & 0.407177 & 3.455 & 0.000463 \tabularnewline
3 & 0.036922 & 0.3133 & 0.377483 \tabularnewline
4 & -0.195136 & -1.6558 & 0.051059 \tabularnewline
5 & -0.370848 & -3.1468 & 0.001201 \tabularnewline
6 & -0.414294 & -3.5154 & 0.000382 \tabularnewline
7 & -0.361655 & -3.0687 & 0.001515 \tabularnewline
8 & -0.202254 & -1.7162 & 0.045214 \tabularnewline
9 & -0.057681 & -0.4894 & 0.313009 \tabularnewline
10 & 0.152728 & 1.2959 & 0.099567 \tabularnewline
11 & 0.361358 & 3.0662 & 0.001526 \tabularnewline
12 & 0.477461 & 4.0514 & 6.4e-05 \tabularnewline
13 & 0.397835 & 3.3757 & 0.000595 \tabularnewline
14 & 0.159846 & 1.3563 & 0.089615 \tabularnewline
15 & -0.126186 & -1.0707 & 0.143934 \tabularnewline
16 & -0.319692 & -2.7127 & 0.004172 \tabularnewline
17 & -0.408808 & -3.4688 & 0.000443 \tabularnewline
18 & -0.439798 & -3.7318 & 0.000188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243722&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]0.724051[/C][C]6.1438[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.407177[/C][C]3.455[/C][C]0.000463[/C][/ROW]
[ROW][C]3[/C][C]0.036922[/C][C]0.3133[/C][C]0.377483[/C][/ROW]
[ROW][C]4[/C][C]-0.195136[/C][C]-1.6558[/C][C]0.051059[/C][/ROW]
[ROW][C]5[/C][C]-0.370848[/C][C]-3.1468[/C][C]0.001201[/C][/ROW]
[ROW][C]6[/C][C]-0.414294[/C][C]-3.5154[/C][C]0.000382[/C][/ROW]
[ROW][C]7[/C][C]-0.361655[/C][C]-3.0687[/C][C]0.001515[/C][/ROW]
[ROW][C]8[/C][C]-0.202254[/C][C]-1.7162[/C][C]0.045214[/C][/ROW]
[ROW][C]9[/C][C]-0.057681[/C][C]-0.4894[/C][C]0.313009[/C][/ROW]
[ROW][C]10[/C][C]0.152728[/C][C]1.2959[/C][C]0.099567[/C][/ROW]
[ROW][C]11[/C][C]0.361358[/C][C]3.0662[/C][C]0.001526[/C][/ROW]
[ROW][C]12[/C][C]0.477461[/C][C]4.0514[/C][C]6.4e-05[/C][/ROW]
[ROW][C]13[/C][C]0.397835[/C][C]3.3757[/C][C]0.000595[/C][/ROW]
[ROW][C]14[/C][C]0.159846[/C][C]1.3563[/C][C]0.089615[/C][/ROW]
[ROW][C]15[/C][C]-0.126186[/C][C]-1.0707[/C][C]0.143934[/C][/ROW]
[ROW][C]16[/C][C]-0.319692[/C][C]-2.7127[/C][C]0.004172[/C][/ROW]
[ROW][C]17[/C][C]-0.408808[/C][C]-3.4688[/C][C]0.000443[/C][/ROW]
[ROW][C]18[/C][C]-0.439798[/C][C]-3.7318[/C][C]0.000188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243722&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243722&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 k	ACF(k)	T-STAT	P-value
1	0.724051	6.1438	0
2	0.407177	3.455	0.000463
3	0.036922	0.3133	0.377483
4	-0.195136	-1.6558	0.051059
5	-0.370848	-3.1468	0.001201
6	-0.414294	-3.5154	0.000382
7	-0.361655	-3.0687	0.001515
8	-0.202254	-1.7162	0.045214
9	-0.057681	-0.4894	0.313009
10	0.152728	1.2959	0.099567
11	0.361358	3.0662	0.001526
12	0.477461	4.0514	6.4e-05
13	0.397835	3.3757	0.000595
14	0.159846	1.3563	0.089615
15	-0.126186	-1.0707	0.143934
16	-0.319692	-2.7127	0.004172
17	-0.408808	-3.4688	0.000443
18	-0.439798	-3.7318	0.000188

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.724051	6.1438	0
2	-0.246081	-2.0881	0.020165
3	-0.340691	-2.8909	0.002538
4	-0.0092	-0.0781	0.468995
5	-0.181579	-1.5408	0.063881
6	-0.066706	-0.566	0.286571
7	0.00612	0.0519	0.479364
8	0.057218	0.4855	0.314394
9	-0.062892	-0.5337	0.297613
10	0.208308	1.7676	0.040686
11	0.248135	2.1055	0.019368
12	0.008498	0.0721	0.471359
13	-0.143671	-1.2191	0.113394
14	-0.190441	-1.6159	0.05524
15	-0.133481	-1.1326	0.130565
16	0.038097	0.3233	0.373716
17	0.049075	0.4164	0.339174
18	-0.195517	-1.659	0.050731

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.724051 & 6.1438 & 0 \tabularnewline
2 & -0.246081 & -2.0881 & 0.020165 \tabularnewline
3 & -0.340691 & -2.8909 & 0.002538 \tabularnewline
4 & -0.0092 & -0.0781 & 0.468995 \tabularnewline
5 & -0.181579 & -1.5408 & 0.063881 \tabularnewline
6 & -0.066706 & -0.566 & 0.286571 \tabularnewline
7 & 0.00612 & 0.0519 & 0.479364 \tabularnewline
8 & 0.057218 & 0.4855 & 0.314394 \tabularnewline
9 & -0.062892 & -0.5337 & 0.297613 \tabularnewline
10 & 0.208308 & 1.7676 & 0.040686 \tabularnewline
11 & 0.248135 & 2.1055 & 0.019368 \tabularnewline
12 & 0.008498 & 0.0721 & 0.471359 \tabularnewline
13 & -0.143671 & -1.2191 & 0.113394 \tabularnewline
14 & -0.190441 & -1.6159 & 0.05524 \tabularnewline
15 & -0.133481 & -1.1326 & 0.130565 \tabularnewline
16 & 0.038097 & 0.3233 & 0.373716 \tabularnewline
17 & 0.049075 & 0.4164 & 0.339174 \tabularnewline
18 & -0.195517 & -1.659 & 0.050731 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243722&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]0.724051[/C][C]6.1438[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.246081[/C][C]-2.0881[/C][C]0.020165[/C][/ROW]
[ROW][C]3[/C][C]-0.340691[/C][C]-2.8909[/C][C]0.002538[/C][/ROW]
[ROW][C]4[/C][C]-0.0092[/C][C]-0.0781[/C][C]0.468995[/C][/ROW]
[ROW][C]5[/C][C]-0.181579[/C][C]-1.5408[/C][C]0.063881[/C][/ROW]
[ROW][C]6[/C][C]-0.066706[/C][C]-0.566[/C][C]0.286571[/C][/ROW]
[ROW][C]7[/C][C]0.00612[/C][C]0.0519[/C][C]0.479364[/C][/ROW]
[ROW][C]8[/C][C]0.057218[/C][C]0.4855[/C][C]0.314394[/C][/ROW]
[ROW][C]9[/C][C]-0.062892[/C][C]-0.5337[/C][C]0.297613[/C][/ROW]
[ROW][C]10[/C][C]0.208308[/C][C]1.7676[/C][C]0.040686[/C][/ROW]
[ROW][C]11[/C][C]0.248135[/C][C]2.1055[/C][C]0.019368[/C][/ROW]
[ROW][C]12[/C][C]0.008498[/C][C]0.0721[/C][C]0.471359[/C][/ROW]
[ROW][C]13[/C][C]-0.143671[/C][C]-1.2191[/C][C]0.113394[/C][/ROW]
[ROW][C]14[/C][C]-0.190441[/C][C]-1.6159[/C][C]0.05524[/C][/ROW]
[ROW][C]15[/C][C]-0.133481[/C][C]-1.1326[/C][C]0.130565[/C][/ROW]
[ROW][C]16[/C][C]0.038097[/C][C]0.3233[/C][C]0.373716[/C][/ROW]
[ROW][C]17[/C][C]0.049075[/C][C]0.4164[/C][C]0.339174[/C][/ROW]
[ROW][C]18[/C][C]-0.195517[/C][C]-1.659[/C][C]0.050731[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243722&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243722&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 k	PACF(k)	T-STAT	P-value
1	0.724051	6.1438	0
2	-0.246081	-2.0881	0.020165
3	-0.340691	-2.8909	0.002538
4	-0.0092	-0.0781	0.468995
5	-0.181579	-1.5408	0.063881
6	-0.066706	-0.566	0.286571
7	0.00612	0.0519	0.479364
8	0.057218	0.4855	0.314394
9	-0.062892	-0.5337	0.297613
10	0.208308	1.7676	0.040686
11	0.248135	2.1055	0.019368
12	0.008498	0.0721	0.471359
13	-0.143671	-1.2191	0.113394
14	-0.190441	-1.6159	0.05524
15	-0.133481	-1.1326	0.130565
16	0.038097	0.3233	0.373716
17	0.049075	0.4164	0.339174
18	-0.195517	-1.659	0.050731

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code