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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 28 Mar 2012 14:56:16 -0400

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/2012/Mar/28/t1332964555wtosi2g94d4whna.htm/, Retrieved Sun, 05 May 2024 16:15:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164174, Retrieved Sun, 05 May 2024 16:15:48 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

180

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

-       [(Partial) Autocorrelation Function] [] [2012-03-28 18:56:16] [26fc2906931796130cbcdf91b421d42d] [Current]

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Dataseries X:

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Histogram

Boxplots

1,44
1,45
1,45
1,47
1,49
1,5
1,5
1,5
1,5
1,5
1,5
1,51
1,52
1,51
1,51
1,51
1,52
1,52
1,52
1,52
1,52
1,53
1,53
1,53
1,53
1,54
1,54
1,55
1,56
1,55
1,56
1,56
1,56
1,56
1,57
1,56
1,57
1,58
1,58
1,58
1,6
1,61
1,61
1,61
1,6
1,59
1,56
1,57
1,55
1,59
1,62
1,63
1,62
1,56
1,56
1,54
1,54
1,52
1,56
1,59

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	'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164174&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164174&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164174&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.87856	6.8053	0
2	0.760027	5.8871	0
3	0.644611	4.9931	3e-06
4	0.569237	4.4093	2.2e-05
5	0.535012	4.1442	5.4e-05
6	0.530594	4.11	6.1e-05
7	0.560344	4.3404	2.8e-05
8	0.546305	4.2317	4e-05
9	0.519124	4.0211	8.2e-05
10	0.446641	3.4597	0.000501
11	0.376722	2.9181	0.002475
12	0.322851	2.5008	0.00757
13	0.282603	2.189	0.016248
14	0.243464	1.8859	0.032079
15	0.201762	1.5628	0.061675
16	0.157707	1.2216	0.11332
17	0.122434	0.9484	0.173374

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.87856 & 6.8053 & 0 \tabularnewline
2 & 0.760027 & 5.8871 & 0 \tabularnewline
3 & 0.644611 & 4.9931 & 3e-06 \tabularnewline
4 & 0.569237 & 4.4093 & 2.2e-05 \tabularnewline
5 & 0.535012 & 4.1442 & 5.4e-05 \tabularnewline
6 & 0.530594 & 4.11 & 6.1e-05 \tabularnewline
7 & 0.560344 & 4.3404 & 2.8e-05 \tabularnewline
8 & 0.546305 & 4.2317 & 4e-05 \tabularnewline
9 & 0.519124 & 4.0211 & 8.2e-05 \tabularnewline
10 & 0.446641 & 3.4597 & 0.000501 \tabularnewline
11 & 0.376722 & 2.9181 & 0.002475 \tabularnewline
12 & 0.322851 & 2.5008 & 0.00757 \tabularnewline
13 & 0.282603 & 2.189 & 0.016248 \tabularnewline
14 & 0.243464 & 1.8859 & 0.032079 \tabularnewline
15 & 0.201762 & 1.5628 & 0.061675 \tabularnewline
16 & 0.157707 & 1.2216 & 0.11332 \tabularnewline
17 & 0.122434 & 0.9484 & 0.173374 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164174&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]0.87856[/C][C]6.8053[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.760027[/C][C]5.8871[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.644611[/C][C]4.9931[/C][C]3e-06[/C][/ROW]
[ROW][C]4[/C][C]0.569237[/C][C]4.4093[/C][C]2.2e-05[/C][/ROW]
[ROW][C]5[/C][C]0.535012[/C][C]4.1442[/C][C]5.4e-05[/C][/ROW]
[ROW][C]6[/C][C]0.530594[/C][C]4.11[/C][C]6.1e-05[/C][/ROW]
[ROW][C]7[/C][C]0.560344[/C][C]4.3404[/C][C]2.8e-05[/C][/ROW]
[ROW][C]8[/C][C]0.546305[/C][C]4.2317[/C][C]4e-05[/C][/ROW]
[ROW][C]9[/C][C]0.519124[/C][C]4.0211[/C][C]8.2e-05[/C][/ROW]
[ROW][C]10[/C][C]0.446641[/C][C]3.4597[/C][C]0.000501[/C][/ROW]
[ROW][C]11[/C][C]0.376722[/C][C]2.9181[/C][C]0.002475[/C][/ROW]
[ROW][C]12[/C][C]0.322851[/C][C]2.5008[/C][C]0.00757[/C][/ROW]
[ROW][C]13[/C][C]0.282603[/C][C]2.189[/C][C]0.016248[/C][/ROW]
[ROW][C]14[/C][C]0.243464[/C][C]1.8859[/C][C]0.032079[/C][/ROW]
[ROW][C]15[/C][C]0.201762[/C][C]1.5628[/C][C]0.061675[/C][/ROW]
[ROW][C]16[/C][C]0.157707[/C][C]1.2216[/C][C]0.11332[/C][/ROW]
[ROW][C]17[/C][C]0.122434[/C][C]0.9484[/C][C]0.173374[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164174&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164174&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	0.87856	6.8053	0
2	0.760027	5.8871	0
3	0.644611	4.9931	3e-06
4	0.569237	4.4093	2.2e-05
5	0.535012	4.1442	5.4e-05
6	0.530594	4.11	6.1e-05
7	0.560344	4.3404	2.8e-05
8	0.546305	4.2317	4e-05
9	0.519124	4.0211	8.2e-05
10	0.446641	3.4597	0.000501
11	0.376722	2.9181	0.002475
12	0.322851	2.5008	0.00757
13	0.282603	2.189	0.016248
14	0.243464	1.8859	0.032079
15	0.201762	1.5628	0.061675
16	0.157707	1.2216	0.11332
17	0.122434	0.9484	0.173374

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.87856	6.8053	0
2	-0.051902	-0.402	0.344545
3	-0.053515	-0.4145	0.339984
4	0.106577	0.8255	0.206167
5	0.135369	1.0486	0.149292
6	0.113184	0.8767	0.192068
7	0.181343	1.4047	0.082636
8	-0.118206	-0.9156	0.181766
9	-0.001853	-0.0144	0.494298
10	-0.137327	-1.0637	0.145857
11	-0.015528	-0.1203	0.452333
12	0.015834	0.1226	0.451397
13	-0.032544	-0.2521	0.400918
14	-0.126101	-0.9768	0.166301
15	-0.061471	-0.4762	0.317847
16	-0.082923	-0.6423	0.261556
17	0.054524	0.4223	0.337143

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.87856 & 6.8053 & 0 \tabularnewline
2 & -0.051902 & -0.402 & 0.344545 \tabularnewline
3 & -0.053515 & -0.4145 & 0.339984 \tabularnewline
4 & 0.106577 & 0.8255 & 0.206167 \tabularnewline
5 & 0.135369 & 1.0486 & 0.149292 \tabularnewline
6 & 0.113184 & 0.8767 & 0.192068 \tabularnewline
7 & 0.181343 & 1.4047 & 0.082636 \tabularnewline
8 & -0.118206 & -0.9156 & 0.181766 \tabularnewline
9 & -0.001853 & -0.0144 & 0.494298 \tabularnewline
10 & -0.137327 & -1.0637 & 0.145857 \tabularnewline
11 & -0.015528 & -0.1203 & 0.452333 \tabularnewline
12 & 0.015834 & 0.1226 & 0.451397 \tabularnewline
13 & -0.032544 & -0.2521 & 0.400918 \tabularnewline
14 & -0.126101 & -0.9768 & 0.166301 \tabularnewline
15 & -0.061471 & -0.4762 & 0.317847 \tabularnewline
16 & -0.082923 & -0.6423 & 0.261556 \tabularnewline
17 & 0.054524 & 0.4223 & 0.337143 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164174&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]0.87856[/C][C]6.8053[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.051902[/C][C]-0.402[/C][C]0.344545[/C][/ROW]
[ROW][C]3[/C][C]-0.053515[/C][C]-0.4145[/C][C]0.339984[/C][/ROW]
[ROW][C]4[/C][C]0.106577[/C][C]0.8255[/C][C]0.206167[/C][/ROW]
[ROW][C]5[/C][C]0.135369[/C][C]1.0486[/C][C]0.149292[/C][/ROW]
[ROW][C]6[/C][C]0.113184[/C][C]0.8767[/C][C]0.192068[/C][/ROW]
[ROW][C]7[/C][C]0.181343[/C][C]1.4047[/C][C]0.082636[/C][/ROW]
[ROW][C]8[/C][C]-0.118206[/C][C]-0.9156[/C][C]0.181766[/C][/ROW]
[ROW][C]9[/C][C]-0.001853[/C][C]-0.0144[/C][C]0.494298[/C][/ROW]
[ROW][C]10[/C][C]-0.137327[/C][C]-1.0637[/C][C]0.145857[/C][/ROW]
[ROW][C]11[/C][C]-0.015528[/C][C]-0.1203[/C][C]0.452333[/C][/ROW]
[ROW][C]12[/C][C]0.015834[/C][C]0.1226[/C][C]0.451397[/C][/ROW]
[ROW][C]13[/C][C]-0.032544[/C][C]-0.2521[/C][C]0.400918[/C][/ROW]
[ROW][C]14[/C][C]-0.126101[/C][C]-0.9768[/C][C]0.166301[/C][/ROW]
[ROW][C]15[/C][C]-0.061471[/C][C]-0.4762[/C][C]0.317847[/C][/ROW]
[ROW][C]16[/C][C]-0.082923[/C][C]-0.6423[/C][C]0.261556[/C][/ROW]
[ROW][C]17[/C][C]0.054524[/C][C]0.4223[/C][C]0.337143[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164174&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164174&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	0.87856	6.8053	0
2	-0.051902	-0.402	0.344545
3	-0.053515	-0.4145	0.339984
4	0.106577	0.8255	0.206167
5	0.135369	1.0486	0.149292
6	0.113184	0.8767	0.192068
7	0.181343	1.4047	0.082636
8	-0.118206	-0.9156	0.181766
9	-0.001853	-0.0144	0.494298
10	-0.137327	-1.0637	0.145857
11	-0.015528	-0.1203	0.452333
12	0.015834	0.1226	0.451397
13	-0.032544	-0.2521	0.400918
14	-0.126101	-0.9768	0.166301
15	-0.061471	-0.4762	0.317847
16	-0.082923	-0.6423	0.261556
17	0.054524	0.4223	0.337143

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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code