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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 22 Dec 2012 17:28:50 -0500

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/Dec/22/t135621536363jod0ie1th7jl6.htm/, Retrieved Thu, 31 Oct 2024 22:48:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204628, Retrieved Thu, 31 Oct 2024 22:48:02 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

190

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

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP     [(Partial) Autocorrelation Function] [] [2012-12-22 22:28:50] [f2337e058d7973ced5b4608d8602e1f8] [Current]
- R P       [(Partial) Autocorrelation Function] [] [2012-12-22 22:30:35] [7ba0816b78c58edd3dfdcc950c417269] 
- RMP       [Spectral Analysis] [] [2012-12-22 22:32:58] [7ba0816b78c58edd3dfdcc950c417269] 
-   P       [(Partial) Autocorrelation Function] [] [2012-12-22 22:34:39] [7ba0816b78c58edd3dfdcc950c417269] 
- R P         [(Partial) Autocorrelation Function] [] [2012-12-22 22:36:02] [7ba0816b78c58edd3dfdcc950c417269] 
- RMP         [Standard Deviation-Mean Plot] [] [2012-12-22 22:41:49] [7ba0816b78c58edd3dfdcc950c417269] 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204628&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204628&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204628&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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.580323	4.9242	3e-06
2	0.169292	1.4365	0.077597
3	-0.022645	-0.1921	0.424084
4	-0.334884	-2.8416	0.002917
5	-0.557729	-4.7325	5e-06
6	-0.653629	-5.5462	0
7	-0.526616	-4.4685	1.4e-05
8	-0.269955	-2.2906	0.012457
9	0.004388	0.0372	0.4852
10	0.170259	1.4447	0.076441
11	0.505958	4.2932	2.7e-05
12	0.823558	6.9881	0
13	0.491206	4.168	4.2e-05
14	0.149716	1.2704	0.104019
15	-0.009742	-0.0827	0.467173
16	-0.271984	-2.3079	0.011942
17	-0.452441	-3.8391	0.000131
18	-0.533287	-4.5251	1.2e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.580323 & 4.9242 & 3e-06 \tabularnewline
2 & 0.169292 & 1.4365 & 0.077597 \tabularnewline
3 & -0.022645 & -0.1921 & 0.424084 \tabularnewline
4 & -0.334884 & -2.8416 & 0.002917 \tabularnewline
5 & -0.557729 & -4.7325 & 5e-06 \tabularnewline
6 & -0.653629 & -5.5462 & 0 \tabularnewline
7 & -0.526616 & -4.4685 & 1.4e-05 \tabularnewline
8 & -0.269955 & -2.2906 & 0.012457 \tabularnewline
9 & 0.004388 & 0.0372 & 0.4852 \tabularnewline
10 & 0.170259 & 1.4447 & 0.076441 \tabularnewline
11 & 0.505958 & 4.2932 & 2.7e-05 \tabularnewline
12 & 0.823558 & 6.9881 & 0 \tabularnewline
13 & 0.491206 & 4.168 & 4.2e-05 \tabularnewline
14 & 0.149716 & 1.2704 & 0.104019 \tabularnewline
15 & -0.009742 & -0.0827 & 0.467173 \tabularnewline
16 & -0.271984 & -2.3079 & 0.011942 \tabularnewline
17 & -0.452441 & -3.8391 & 0.000131 \tabularnewline
18 & -0.533287 & -4.5251 & 1.2e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204628&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]0.580323[/C][C]4.9242[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]0.169292[/C][C]1.4365[/C][C]0.077597[/C][/ROW]
[ROW][C]3[/C][C]-0.022645[/C][C]-0.1921[/C][C]0.424084[/C][/ROW]
[ROW][C]4[/C][C]-0.334884[/C][C]-2.8416[/C][C]0.002917[/C][/ROW]
[ROW][C]5[/C][C]-0.557729[/C][C]-4.7325[/C][C]5e-06[/C][/ROW]
[ROW][C]6[/C][C]-0.653629[/C][C]-5.5462[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.526616[/C][C]-4.4685[/C][C]1.4e-05[/C][/ROW]
[ROW][C]8[/C][C]-0.269955[/C][C]-2.2906[/C][C]0.012457[/C][/ROW]
[ROW][C]9[/C][C]0.004388[/C][C]0.0372[/C][C]0.4852[/C][/ROW]
[ROW][C]10[/C][C]0.170259[/C][C]1.4447[/C][C]0.076441[/C][/ROW]
[ROW][C]11[/C][C]0.505958[/C][C]4.2932[/C][C]2.7e-05[/C][/ROW]
[ROW][C]12[/C][C]0.823558[/C][C]6.9881[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.491206[/C][C]4.168[/C][C]4.2e-05[/C][/ROW]
[ROW][C]14[/C][C]0.149716[/C][C]1.2704[/C][C]0.104019[/C][/ROW]
[ROW][C]15[/C][C]-0.009742[/C][C]-0.0827[/C][C]0.467173[/C][/ROW]
[ROW][C]16[/C][C]-0.271984[/C][C]-2.3079[/C][C]0.011942[/C][/ROW]
[ROW][C]17[/C][C]-0.452441[/C][C]-3.8391[/C][C]0.000131[/C][/ROW]
[ROW][C]18[/C][C]-0.533287[/C][C]-4.5251[/C][C]1.2e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204628&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204628&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	0.580323	4.9242	3e-06
2	0.169292	1.4365	0.077597
3	-0.022645	-0.1921	0.424084
4	-0.334884	-2.8416	0.002917
5	-0.557729	-4.7325	5e-06
6	-0.653629	-5.5462	0
7	-0.526616	-4.4685	1.4e-05
8	-0.269955	-2.2906	0.012457
9	0.004388	0.0372	0.4852
10	0.170259	1.4447	0.076441
11	0.505958	4.2932	2.7e-05
12	0.823558	6.9881	0
13	0.491206	4.168	4.2e-05
14	0.149716	1.2704	0.104019
15	-0.009742	-0.0827	0.467173
16	-0.271984	-2.3079	0.011942
17	-0.452441	-3.8391	0.000131
18	-0.533287	-4.5251	1.2e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.580323	4.9242	3e-06
2	-0.252529	-2.1428	0.017756
3	0.00137	0.0116	0.49538
4	-0.444964	-3.7756	0.000163
5	-0.239114	-2.0289	0.023081
6	-0.455135	-3.8619	0.000122
7	-0.155908	-1.3229	0.095024
8	-0.296482	-2.5157	0.007055
9	-0.137955	-1.1706	0.122813
10	-0.570015	-4.8367	4e-06
11	0.242591	2.0585	0.021583
12	0.244486	2.0745	0.020803
13	-0.384684	-3.2642	0.000841
14	-0.140458	-1.1918	0.118622
15	-0.111465	-0.9458	0.173704
16	-0.001189	-0.0101	0.49599
17	0.001882	0.016	0.493652
18	0.013329	0.1131	0.455132

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.580323 & 4.9242 & 3e-06 \tabularnewline
2 & -0.252529 & -2.1428 & 0.017756 \tabularnewline
3 & 0.00137 & 0.0116 & 0.49538 \tabularnewline
4 & -0.444964 & -3.7756 & 0.000163 \tabularnewline
5 & -0.239114 & -2.0289 & 0.023081 \tabularnewline
6 & -0.455135 & -3.8619 & 0.000122 \tabularnewline
7 & -0.155908 & -1.3229 & 0.095024 \tabularnewline
8 & -0.296482 & -2.5157 & 0.007055 \tabularnewline
9 & -0.137955 & -1.1706 & 0.122813 \tabularnewline
10 & -0.570015 & -4.8367 & 4e-06 \tabularnewline
11 & 0.242591 & 2.0585 & 0.021583 \tabularnewline
12 & 0.244486 & 2.0745 & 0.020803 \tabularnewline
13 & -0.384684 & -3.2642 & 0.000841 \tabularnewline
14 & -0.140458 & -1.1918 & 0.118622 \tabularnewline
15 & -0.111465 & -0.9458 & 0.173704 \tabularnewline
16 & -0.001189 & -0.0101 & 0.49599 \tabularnewline
17 & 0.001882 & 0.016 & 0.493652 \tabularnewline
18 & 0.013329 & 0.1131 & 0.455132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204628&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]0.580323[/C][C]4.9242[/C][C]3e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.252529[/C][C]-2.1428[/C][C]0.017756[/C][/ROW]
[ROW][C]3[/C][C]0.00137[/C][C]0.0116[/C][C]0.49538[/C][/ROW]
[ROW][C]4[/C][C]-0.444964[/C][C]-3.7756[/C][C]0.000163[/C][/ROW]
[ROW][C]5[/C][C]-0.239114[/C][C]-2.0289[/C][C]0.023081[/C][/ROW]
[ROW][C]6[/C][C]-0.455135[/C][C]-3.8619[/C][C]0.000122[/C][/ROW]
[ROW][C]7[/C][C]-0.155908[/C][C]-1.3229[/C][C]0.095024[/C][/ROW]
[ROW][C]8[/C][C]-0.296482[/C][C]-2.5157[/C][C]0.007055[/C][/ROW]
[ROW][C]9[/C][C]-0.137955[/C][C]-1.1706[/C][C]0.122813[/C][/ROW]
[ROW][C]10[/C][C]-0.570015[/C][C]-4.8367[/C][C]4e-06[/C][/ROW]
[ROW][C]11[/C][C]0.242591[/C][C]2.0585[/C][C]0.021583[/C][/ROW]
[ROW][C]12[/C][C]0.244486[/C][C]2.0745[/C][C]0.020803[/C][/ROW]
[ROW][C]13[/C][C]-0.384684[/C][C]-3.2642[/C][C]0.000841[/C][/ROW]
[ROW][C]14[/C][C]-0.140458[/C][C]-1.1918[/C][C]0.118622[/C][/ROW]
[ROW][C]15[/C][C]-0.111465[/C][C]-0.9458[/C][C]0.173704[/C][/ROW]
[ROW][C]16[/C][C]-0.001189[/C][C]-0.0101[/C][C]0.49599[/C][/ROW]
[ROW][C]17[/C][C]0.001882[/C][C]0.016[/C][C]0.493652[/C][/ROW]
[ROW][C]18[/C][C]0.013329[/C][C]0.1131[/C][C]0.455132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204628&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204628&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	0.580323	4.9242	3e-06
2	-0.252529	-2.1428	0.017756
3	0.00137	0.0116	0.49538
4	-0.444964	-3.7756	0.000163
5	-0.239114	-2.0289	0.023081
6	-0.455135	-3.8619	0.000122
7	-0.155908	-1.3229	0.095024
8	-0.296482	-2.5157	0.007055
9	-0.137955	-1.1706	0.122813
10	-0.570015	-4.8367	4e-06
11	0.242591	2.0585	0.021583
12	0.244486	2.0745	0.020803
13	-0.384684	-3.2642	0.000841
14	-0.140458	-1.1918	0.118622
15	-0.111465	-0.9458	0.173704
16	-0.001189	-0.0101	0.49599
17	0.001882	0.016	0.493652
18	0.013329	0.1131	0.455132

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