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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 03 Nov 2021 13:06:20 +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/2021/Nov/03/t1635941576f34idscphtmntja.htm/, Retrieved Sat, 11 May 2024 20:01:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319549, Retrieved Sat, 11 May 2024 20:01:06 +0000

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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] [Autocorrelação ...] [2021-11-03 12:06:20] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Dataseries X:

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Histogram

Boxplots

6.14
7.13
3.39
6.89
6.61
6.29
4.58
6.83
7.00
6.19
5.57
5.70
5.19
5.40
5.93
5.08
4.87
3.26
5.02
6.26
4.70
4.46
1.12
2.24
4.43
4.84
4.67
4.39

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=319549&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=319549&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319549&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	0.394433	2.0871	0.023049
2	0.17753	0.9394	0.17778
3	0.136445	0.722	0.238142
4	0.283184	1.4985	0.072601
5	0.269502	1.4261	0.082452
6	0.186571	0.9872	0.16599
7	0.121175	0.6412	0.263304
8	-0.021088	-0.1116	0.455974
9	-0.0689	-0.3646	0.359081
10	0.007281	0.0385	0.484771
11	0.013947	0.0738	0.470848
12	-0.124686	-0.6598	0.257395
13	-0.194251	-1.0279	0.156403
14	-0.239263	-1.2661	0.107962

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.394433 & 2.0871 & 0.023049 \tabularnewline
2 & 0.17753 & 0.9394 & 0.17778 \tabularnewline
3 & 0.136445 & 0.722 & 0.238142 \tabularnewline
4 & 0.283184 & 1.4985 & 0.072601 \tabularnewline
5 & 0.269502 & 1.4261 & 0.082452 \tabularnewline
6 & 0.186571 & 0.9872 & 0.16599 \tabularnewline
7 & 0.121175 & 0.6412 & 0.263304 \tabularnewline
8 & -0.021088 & -0.1116 & 0.455974 \tabularnewline
9 & -0.0689 & -0.3646 & 0.359081 \tabularnewline
10 & 0.007281 & 0.0385 & 0.484771 \tabularnewline
11 & 0.013947 & 0.0738 & 0.470848 \tabularnewline
12 & -0.124686 & -0.6598 & 0.257395 \tabularnewline
13 & -0.194251 & -1.0279 & 0.156403 \tabularnewline
14 & -0.239263 & -1.2661 & 0.107962 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319549&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]0.394433[/C][C]2.0871[/C][C]0.023049[/C][/ROW]
[ROW][C]2[/C][C]0.17753[/C][C]0.9394[/C][C]0.17778[/C][/ROW]
[ROW][C]3[/C][C]0.136445[/C][C]0.722[/C][C]0.238142[/C][/ROW]
[ROW][C]4[/C][C]0.283184[/C][C]1.4985[/C][C]0.072601[/C][/ROW]
[ROW][C]5[/C][C]0.269502[/C][C]1.4261[/C][C]0.082452[/C][/ROW]
[ROW][C]6[/C][C]0.186571[/C][C]0.9872[/C][C]0.16599[/C][/ROW]
[ROW][C]7[/C][C]0.121175[/C][C]0.6412[/C][C]0.263304[/C][/ROW]
[ROW][C]8[/C][C]-0.021088[/C][C]-0.1116[/C][C]0.455974[/C][/ROW]
[ROW][C]9[/C][C]-0.0689[/C][C]-0.3646[/C][C]0.359081[/C][/ROW]
[ROW][C]10[/C][C]0.007281[/C][C]0.0385[/C][C]0.484771[/C][/ROW]
[ROW][C]11[/C][C]0.013947[/C][C]0.0738[/C][C]0.470848[/C][/ROW]
[ROW][C]12[/C][C]-0.124686[/C][C]-0.6598[/C][C]0.257395[/C][/ROW]
[ROW][C]13[/C][C]-0.194251[/C][C]-1.0279[/C][C]0.156403[/C][/ROW]
[ROW][C]14[/C][C]-0.239263[/C][C]-1.2661[/C][C]0.107962[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319549&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319549&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	0.394433	2.0871	0.023049
2	0.17753	0.9394	0.17778
3	0.136445	0.722	0.238142
4	0.283184	1.4985	0.072601
5	0.269502	1.4261	0.082452
6	0.186571	0.9872	0.16599
7	0.121175	0.6412	0.263304
8	-0.021088	-0.1116	0.455974
9	-0.0689	-0.3646	0.359081
10	0.007281	0.0385	0.484771
11	0.013947	0.0738	0.470848
12	-0.124686	-0.6598	0.257395
13	-0.194251	-1.0279	0.156403
14	-0.239263	-1.2661	0.107962

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.394433	2.0871	0.023049
2	0.025997	0.1376	0.445785
3	0.068717	0.3636	0.359437
4	0.242866	1.2851	0.104638
5	0.094234	0.4986	0.310965
6	0.029041	0.1537	0.439486
7	0.013562	0.0718	0.47165
8	-0.171863	-0.9094	0.185447
9	-0.126507	-0.6694	0.254358
10	0.013268	0.0702	0.472264
11	-0.038811	-0.2054	0.419385
12	-0.133223	-0.7049	0.243333
13	-0.061941	-0.3278	0.372765
14	-0.133885	-0.7085	0.24226

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.394433 & 2.0871 & 0.023049 \tabularnewline
2 & 0.025997 & 0.1376 & 0.445785 \tabularnewline
3 & 0.068717 & 0.3636 & 0.359437 \tabularnewline
4 & 0.242866 & 1.2851 & 0.104638 \tabularnewline
5 & 0.094234 & 0.4986 & 0.310965 \tabularnewline
6 & 0.029041 & 0.1537 & 0.439486 \tabularnewline
7 & 0.013562 & 0.0718 & 0.47165 \tabularnewline
8 & -0.171863 & -0.9094 & 0.185447 \tabularnewline
9 & -0.126507 & -0.6694 & 0.254358 \tabularnewline
10 & 0.013268 & 0.0702 & 0.472264 \tabularnewline
11 & -0.038811 & -0.2054 & 0.419385 \tabularnewline
12 & -0.133223 & -0.7049 & 0.243333 \tabularnewline
13 & -0.061941 & -0.3278 & 0.372765 \tabularnewline
14 & -0.133885 & -0.7085 & 0.24226 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319549&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]0.394433[/C][C]2.0871[/C][C]0.023049[/C][/ROW]
[ROW][C]2[/C][C]0.025997[/C][C]0.1376[/C][C]0.445785[/C][/ROW]
[ROW][C]3[/C][C]0.068717[/C][C]0.3636[/C][C]0.359437[/C][/ROW]
[ROW][C]4[/C][C]0.242866[/C][C]1.2851[/C][C]0.104638[/C][/ROW]
[ROW][C]5[/C][C]0.094234[/C][C]0.4986[/C][C]0.310965[/C][/ROW]
[ROW][C]6[/C][C]0.029041[/C][C]0.1537[/C][C]0.439486[/C][/ROW]
[ROW][C]7[/C][C]0.013562[/C][C]0.0718[/C][C]0.47165[/C][/ROW]
[ROW][C]8[/C][C]-0.171863[/C][C]-0.9094[/C][C]0.185447[/C][/ROW]
[ROW][C]9[/C][C]-0.126507[/C][C]-0.6694[/C][C]0.254358[/C][/ROW]
[ROW][C]10[/C][C]0.013268[/C][C]0.0702[/C][C]0.472264[/C][/ROW]
[ROW][C]11[/C][C]-0.038811[/C][C]-0.2054[/C][C]0.419385[/C][/ROW]
[ROW][C]12[/C][C]-0.133223[/C][C]-0.7049[/C][C]0.243333[/C][/ROW]
[ROW][C]13[/C][C]-0.061941[/C][C]-0.3278[/C][C]0.372765[/C][/ROW]
[ROW][C]14[/C][C]-0.133885[/C][C]-0.7085[/C][C]0.24226[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319549&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319549&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	0.394433	2.0871	0.023049
2	0.025997	0.1376	0.445785
3	0.068717	0.3636	0.359437
4	0.242866	1.2851	0.104638
5	0.094234	0.4986	0.310965
6	0.029041	0.1537	0.439486
7	0.013562	0.0718	0.47165
8	-0.171863	-0.9094	0.185447
9	-0.126507	-0.6694	0.254358
10	0.013268	0.0702	0.472264
11	-0.038811	-0.2054	0.419385
12	-0.133223	-0.7049	0.243333
13	-0.061941	-0.3278	0.372765
14	-0.133885	-0.7085	0.24226

Figure 1

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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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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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Input Parameters & R Code