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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 11:55:45 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/17/t1481972255z1i6m5say2mgpsu.htm/, Retrieved Fri, 01 Nov 2024 03:29:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300684, Retrieved Fri, 01 Nov 2024 03:29:57 +0000

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Estimated Impact

106

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

-       [(Partial) Autocorrelation Function] [ACF(2) voorbeeld] [2016-12-17 10:55:45] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300684&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300684&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300684&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.139686	0.8723	0.194181
2	-0.690188	-4.3102	5.4e-05
3	-0.026743	-0.167	0.434114
4	0.718642	4.4879	3.1e-05
5	-0.003437	-0.0215	0.491493
6	-0.742682	-4.638	1.9e-05
7	-0.125648	-0.7847	0.218694
8	0.588867	3.6775	0.000354
9	-0.021963	-0.1372	0.445806
10	-0.659607	-4.1192	9.6e-05
11	-0.121769	-0.7604	0.22578
12	0.523908	3.2718	0.00112
13	0.031414	0.1962	0.422743
14	-0.460896	-2.8783	0.003228
15	0.011482	0.0717	0.471603
16	0.520515	3.2506	0.001188

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.139686 & 0.8723 & 0.194181 \tabularnewline
2 & -0.690188 & -4.3102 & 5.4e-05 \tabularnewline
3 & -0.026743 & -0.167 & 0.434114 \tabularnewline
4 & 0.718642 & 4.4879 & 3.1e-05 \tabularnewline
5 & -0.003437 & -0.0215 & 0.491493 \tabularnewline
6 & -0.742682 & -4.638 & 1.9e-05 \tabularnewline
7 & -0.125648 & -0.7847 & 0.218694 \tabularnewline
8 & 0.588867 & 3.6775 & 0.000354 \tabularnewline
9 & -0.021963 & -0.1372 & 0.445806 \tabularnewline
10 & -0.659607 & -4.1192 & 9.6e-05 \tabularnewline
11 & -0.121769 & -0.7604 & 0.22578 \tabularnewline
12 & 0.523908 & 3.2718 & 0.00112 \tabularnewline
13 & 0.031414 & 0.1962 & 0.422743 \tabularnewline
14 & -0.460896 & -2.8783 & 0.003228 \tabularnewline
15 & 0.011482 & 0.0717 & 0.471603 \tabularnewline
16 & 0.520515 & 3.2506 & 0.001188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300684&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]0.139686[/C][C]0.8723[/C][C]0.194181[/C][/ROW]
[ROW][C]2[/C][C]-0.690188[/C][C]-4.3102[/C][C]5.4e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.026743[/C][C]-0.167[/C][C]0.434114[/C][/ROW]
[ROW][C]4[/C][C]0.718642[/C][C]4.4879[/C][C]3.1e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.003437[/C][C]-0.0215[/C][C]0.491493[/C][/ROW]
[ROW][C]6[/C][C]-0.742682[/C][C]-4.638[/C][C]1.9e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.125648[/C][C]-0.7847[/C][C]0.218694[/C][/ROW]
[ROW][C]8[/C][C]0.588867[/C][C]3.6775[/C][C]0.000354[/C][/ROW]
[ROW][C]9[/C][C]-0.021963[/C][C]-0.1372[/C][C]0.445806[/C][/ROW]
[ROW][C]10[/C][C]-0.659607[/C][C]-4.1192[/C][C]9.6e-05[/C][/ROW]
[ROW][C]11[/C][C]-0.121769[/C][C]-0.7604[/C][C]0.22578[/C][/ROW]
[ROW][C]12[/C][C]0.523908[/C][C]3.2718[/C][C]0.00112[/C][/ROW]
[ROW][C]13[/C][C]0.031414[/C][C]0.1962[/C][C]0.422743[/C][/ROW]
[ROW][C]14[/C][C]-0.460896[/C][C]-2.8783[/C][C]0.003228[/C][/ROW]
[ROW][C]15[/C][C]0.011482[/C][C]0.0717[/C][C]0.471603[/C][/ROW]
[ROW][C]16[/C][C]0.520515[/C][C]3.2506[/C][C]0.001188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300684&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300684&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	0.139686	0.8723	0.194181
2	-0.690188	-4.3102	5.4e-05
3	-0.026743	-0.167	0.434114
4	0.718642	4.4879	3.1e-05
5	-0.003437	-0.0215	0.491493
6	-0.742682	-4.638	1.9e-05
7	-0.125648	-0.7847	0.218694
8	0.588867	3.6775	0.000354
9	-0.021963	-0.1372	0.445806
10	-0.659607	-4.1192	9.6e-05
11	-0.121769	-0.7604	0.22578
12	0.523908	3.2718	0.00112
13	0.031414	0.1962	0.422743
14	-0.460896	-2.8783	0.003228
15	0.011482	0.0717	0.471603
16	0.520515	3.2506	0.001188

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.139686	0.8723	0.194181
2	-0.723824	-4.5203	2.8e-05
3	0.515348	3.2183	0.001298
4	0.227081	1.4181	0.082048
5	-0.461993	-2.8851	0.003171
6	-0.050174	-0.3133	0.377848
7	-0.126437	-0.7896	0.217267
8	-0.069241	-0.4324	0.333912
9	-0.19637	-1.2263	0.113714
10	0.007306	0.0456	0.48192
11	-0.283222	-1.7687	0.042381
12	-0.090641	-0.5661	0.287301
13	-0.120198	-0.7506	0.228688
14	0.159898	0.9986	0.162081
15	-0.102234	-0.6384	0.263457
16	0.030544	0.1907	0.424857

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.139686 & 0.8723 & 0.194181 \tabularnewline
2 & -0.723824 & -4.5203 & 2.8e-05 \tabularnewline
3 & 0.515348 & 3.2183 & 0.001298 \tabularnewline
4 & 0.227081 & 1.4181 & 0.082048 \tabularnewline
5 & -0.461993 & -2.8851 & 0.003171 \tabularnewline
6 & -0.050174 & -0.3133 & 0.377848 \tabularnewline
7 & -0.126437 & -0.7896 & 0.217267 \tabularnewline
8 & -0.069241 & -0.4324 & 0.333912 \tabularnewline
9 & -0.19637 & -1.2263 & 0.113714 \tabularnewline
10 & 0.007306 & 0.0456 & 0.48192 \tabularnewline
11 & -0.283222 & -1.7687 & 0.042381 \tabularnewline
12 & -0.090641 & -0.5661 & 0.287301 \tabularnewline
13 & -0.120198 & -0.7506 & 0.228688 \tabularnewline
14 & 0.159898 & 0.9986 & 0.162081 \tabularnewline
15 & -0.102234 & -0.6384 & 0.263457 \tabularnewline
16 & 0.030544 & 0.1907 & 0.424857 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300684&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]0.139686[/C][C]0.8723[/C][C]0.194181[/C][/ROW]
[ROW][C]2[/C][C]-0.723824[/C][C]-4.5203[/C][C]2.8e-05[/C][/ROW]
[ROW][C]3[/C][C]0.515348[/C][C]3.2183[/C][C]0.001298[/C][/ROW]
[ROW][C]4[/C][C]0.227081[/C][C]1.4181[/C][C]0.082048[/C][/ROW]
[ROW][C]5[/C][C]-0.461993[/C][C]-2.8851[/C][C]0.003171[/C][/ROW]
[ROW][C]6[/C][C]-0.050174[/C][C]-0.3133[/C][C]0.377848[/C][/ROW]
[ROW][C]7[/C][C]-0.126437[/C][C]-0.7896[/C][C]0.217267[/C][/ROW]
[ROW][C]8[/C][C]-0.069241[/C][C]-0.4324[/C][C]0.333912[/C][/ROW]
[ROW][C]9[/C][C]-0.19637[/C][C]-1.2263[/C][C]0.113714[/C][/ROW]
[ROW][C]10[/C][C]0.007306[/C][C]0.0456[/C][C]0.48192[/C][/ROW]
[ROW][C]11[/C][C]-0.283222[/C][C]-1.7687[/C][C]0.042381[/C][/ROW]
[ROW][C]12[/C][C]-0.090641[/C][C]-0.5661[/C][C]0.287301[/C][/ROW]
[ROW][C]13[/C][C]-0.120198[/C][C]-0.7506[/C][C]0.228688[/C][/ROW]
[ROW][C]14[/C][C]0.159898[/C][C]0.9986[/C][C]0.162081[/C][/ROW]
[ROW][C]15[/C][C]-0.102234[/C][C]-0.6384[/C][C]0.263457[/C][/ROW]
[ROW][C]16[/C][C]0.030544[/C][C]0.1907[/C][C]0.424857[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300684&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300684&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	0.139686	0.8723	0.194181
2	-0.723824	-4.5203	2.8e-05
3	0.515348	3.2183	0.001298
4	0.227081	1.4181	0.082048
5	-0.461993	-2.8851	0.003171
6	-0.050174	-0.3133	0.377848
7	-0.126437	-0.7896	0.217267
8	-0.069241	-0.4324	0.333912
9	-0.19637	-1.2263	0.113714
10	0.007306	0.0456	0.48192
11	-0.283222	-1.7687	0.042381
12	-0.090641	-0.5661	0.287301
13	-0.120198	-0.7506	0.228688
14	0.159898	0.9986	0.162081
15	-0.102234	-0.6384	0.263457
16	0.030544	0.1907	0.424857

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 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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)
x <- na.omit(x)
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,'ACF(k)',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,'PACF(k)',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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Dataset

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Input Parameters & R Code