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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 05 Dec 2011 17:23:23 -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/2011/Dec/05/t1323123820ve8i0odkiey0eup.htm/, Retrieved Fri, 03 May 2024 13:12:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151303, Retrieved Fri, 03 May 2024 13:12:10 +0000

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Estimated Impact

116

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

-     [Variance Reduction Matrix] [] [2011-12-05 22:04:45] [a1957df0bc37aec4aa3c994e6a08412c]
- RMP     [(Partial) Autocorrelation Function] [] [2011-12-05 22:23:23] [fdaf10f0fcbe7b8f79ecbd42ec74e6ad] [Current]
- R PD      [(Partial) Autocorrelation Function] [] [2011-12-05 22:31:05] [a1957df0bc37aec4aa3c994e6a08412c] 

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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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151303&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151303&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151303&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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.971799	8.246	0
2	0.932283	7.9107	0
3	0.891001	7.5604	0
4	0.845964	7.1782	0
5	0.795047	6.7462	0
6	0.738132	6.2633	0
7	0.682898	5.7946	0
8	0.628462	5.3327	1e-06
9	0.569675	4.8339	4e-06
10	0.509256	4.3212	2.4e-05
11	0.45355	3.8485	0.000127
12	0.393533	3.3392	0.000667
13	0.33568	2.8483	0.002862
14	0.278615	2.3641	0.010386
15	0.217707	1.8473	0.034405
16	0.157538	1.3368	0.092756
17	0.095606	0.8112	0.209949
18	0.039284	0.3333	0.369923

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.971799 & 8.246 & 0 \tabularnewline
2 & 0.932283 & 7.9107 & 0 \tabularnewline
3 & 0.891001 & 7.5604 & 0 \tabularnewline
4 & 0.845964 & 7.1782 & 0 \tabularnewline
5 & 0.795047 & 6.7462 & 0 \tabularnewline
6 & 0.738132 & 6.2633 & 0 \tabularnewline
7 & 0.682898 & 5.7946 & 0 \tabularnewline
8 & 0.628462 & 5.3327 & 1e-06 \tabularnewline
9 & 0.569675 & 4.8339 & 4e-06 \tabularnewline
10 & 0.509256 & 4.3212 & 2.4e-05 \tabularnewline
11 & 0.45355 & 3.8485 & 0.000127 \tabularnewline
12 & 0.393533 & 3.3392 & 0.000667 \tabularnewline
13 & 0.33568 & 2.8483 & 0.002862 \tabularnewline
14 & 0.278615 & 2.3641 & 0.010386 \tabularnewline
15 & 0.217707 & 1.8473 & 0.034405 \tabularnewline
16 & 0.157538 & 1.3368 & 0.092756 \tabularnewline
17 & 0.095606 & 0.8112 & 0.209949 \tabularnewline
18 & 0.039284 & 0.3333 & 0.369923 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151303&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]0.971799[/C][C]8.246[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.932283[/C][C]7.9107[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.891001[/C][C]7.5604[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.845964[/C][C]7.1782[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.795047[/C][C]6.7462[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.738132[/C][C]6.2633[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.682898[/C][C]5.7946[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.628462[/C][C]5.3327[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]0.569675[/C][C]4.8339[/C][C]4e-06[/C][/ROW]
[ROW][C]10[/C][C]0.509256[/C][C]4.3212[/C][C]2.4e-05[/C][/ROW]
[ROW][C]11[/C][C]0.45355[/C][C]3.8485[/C][C]0.000127[/C][/ROW]
[ROW][C]12[/C][C]0.393533[/C][C]3.3392[/C][C]0.000667[/C][/ROW]
[ROW][C]13[/C][C]0.33568[/C][C]2.8483[/C][C]0.002862[/C][/ROW]
[ROW][C]14[/C][C]0.278615[/C][C]2.3641[/C][C]0.010386[/C][/ROW]
[ROW][C]15[/C][C]0.217707[/C][C]1.8473[/C][C]0.034405[/C][/ROW]
[ROW][C]16[/C][C]0.157538[/C][C]1.3368[/C][C]0.092756[/C][/ROW]
[ROW][C]17[/C][C]0.095606[/C][C]0.8112[/C][C]0.209949[/C][/ROW]
[ROW][C]18[/C][C]0.039284[/C][C]0.3333[/C][C]0.369923[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151303&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151303&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	0.971799	8.246	0
2	0.932283	7.9107	0
3	0.891001	7.5604	0
4	0.845964	7.1782	0
5	0.795047	6.7462	0
6	0.738132	6.2633	0
7	0.682898	5.7946	0
8	0.628462	5.3327	1e-06
9	0.569675	4.8339	4e-06
10	0.509256	4.3212	2.4e-05
11	0.45355	3.8485	0.000127
12	0.393533	3.3392	0.000667
13	0.33568	2.8483	0.002862
14	0.278615	2.3641	0.010386
15	0.217707	1.8473	0.034405
16	0.157538	1.3368	0.092756
17	0.095606	0.8112	0.209949
18	0.039284	0.3333	0.369923

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.971799	8.246	0
2	-0.217766	-1.8478	0.034369
3	-0.012443	-0.1056	0.458102
4	-0.088177	-0.7482	0.228386
5	-0.109892	-0.9325	0.177107
6	-0.106379	-0.9027	0.18486
7	0.036885	0.313	0.3776
8	-0.028647	-0.2431	0.404318
9	-0.105142	-0.8922	0.187641
10	-0.031351	-0.266	0.395491
11	0.054334	0.461	0.32308
12	-0.164755	-1.398	0.083204
13	0.051994	0.4412	0.330202
14	-0.044351	-0.3763	0.353888
15	-0.138658	-1.1766	0.121625
16	-0.016335	-0.1386	0.445073
17	-0.072007	-0.611	0.271562
18	0.051643	0.4382	0.331274

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.971799 & 8.246 & 0 \tabularnewline
2 & -0.217766 & -1.8478 & 0.034369 \tabularnewline
3 & -0.012443 & -0.1056 & 0.458102 \tabularnewline
4 & -0.088177 & -0.7482 & 0.228386 \tabularnewline
5 & -0.109892 & -0.9325 & 0.177107 \tabularnewline
6 & -0.106379 & -0.9027 & 0.18486 \tabularnewline
7 & 0.036885 & 0.313 & 0.3776 \tabularnewline
8 & -0.028647 & -0.2431 & 0.404318 \tabularnewline
9 & -0.105142 & -0.8922 & 0.187641 \tabularnewline
10 & -0.031351 & -0.266 & 0.395491 \tabularnewline
11 & 0.054334 & 0.461 & 0.32308 \tabularnewline
12 & -0.164755 & -1.398 & 0.083204 \tabularnewline
13 & 0.051994 & 0.4412 & 0.330202 \tabularnewline
14 & -0.044351 & -0.3763 & 0.353888 \tabularnewline
15 & -0.138658 & -1.1766 & 0.121625 \tabularnewline
16 & -0.016335 & -0.1386 & 0.445073 \tabularnewline
17 & -0.072007 & -0.611 & 0.271562 \tabularnewline
18 & 0.051643 & 0.4382 & 0.331274 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151303&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]0.971799[/C][C]8.246[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.217766[/C][C]-1.8478[/C][C]0.034369[/C][/ROW]
[ROW][C]3[/C][C]-0.012443[/C][C]-0.1056[/C][C]0.458102[/C][/ROW]
[ROW][C]4[/C][C]-0.088177[/C][C]-0.7482[/C][C]0.228386[/C][/ROW]
[ROW][C]5[/C][C]-0.109892[/C][C]-0.9325[/C][C]0.177107[/C][/ROW]
[ROW][C]6[/C][C]-0.106379[/C][C]-0.9027[/C][C]0.18486[/C][/ROW]
[ROW][C]7[/C][C]0.036885[/C][C]0.313[/C][C]0.3776[/C][/ROW]
[ROW][C]8[/C][C]-0.028647[/C][C]-0.2431[/C][C]0.404318[/C][/ROW]
[ROW][C]9[/C][C]-0.105142[/C][C]-0.8922[/C][C]0.187641[/C][/ROW]
[ROW][C]10[/C][C]-0.031351[/C][C]-0.266[/C][C]0.395491[/C][/ROW]
[ROW][C]11[/C][C]0.054334[/C][C]0.461[/C][C]0.32308[/C][/ROW]
[ROW][C]12[/C][C]-0.164755[/C][C]-1.398[/C][C]0.083204[/C][/ROW]
[ROW][C]13[/C][C]0.051994[/C][C]0.4412[/C][C]0.330202[/C][/ROW]
[ROW][C]14[/C][C]-0.044351[/C][C]-0.3763[/C][C]0.353888[/C][/ROW]
[ROW][C]15[/C][C]-0.138658[/C][C]-1.1766[/C][C]0.121625[/C][/ROW]
[ROW][C]16[/C][C]-0.016335[/C][C]-0.1386[/C][C]0.445073[/C][/ROW]
[ROW][C]17[/C][C]-0.072007[/C][C]-0.611[/C][C]0.271562[/C][/ROW]
[ROW][C]18[/C][C]0.051643[/C][C]0.4382[/C][C]0.331274[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151303&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151303&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	0.971799	8.246	0
2	-0.217766	-1.8478	0.034369
3	-0.012443	-0.1056	0.458102
4	-0.088177	-0.7482	0.228386
5	-0.109892	-0.9325	0.177107
6	-0.106379	-0.9027	0.18486
7	0.036885	0.313	0.3776
8	-0.028647	-0.2431	0.404318
9	-0.105142	-0.8922	0.187641
10	-0.031351	-0.266	0.395491
11	0.054334	0.461	0.32308
12	-0.164755	-1.398	0.083204
13	0.051994	0.4412	0.330202
14	-0.044351	-0.3763	0.353888
15	-0.138658	-1.1766	0.121625
16	-0.016335	-0.1386	0.445073
17	-0.072007	-0.611	0.271562
18	0.051643	0.4382	0.331274

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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Input Parameters & R Code