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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 14 Dec 2016 14:42:44 +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/14/t14817229891c714gwu7q2kjrr.htm/, Retrieved Fri, 03 May 2024 17:12:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299430, Retrieved Fri, 03 May 2024 17:12:58 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-14 13:42:44] [2802fcbee976b89d2ab84425d3d65dcf] [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=299430&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=299430&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299430&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	0.053222	0.3801	0.352731
2	0.100868	0.7203	0.237302
3	0.11006	0.786	0.217757
4	-0.281924	-2.0133	0.024685
5	-0.002498	-0.0178	0.492919
6	0.005956	0.0425	0.483118
7	-0.156209	-1.1156	0.134921
8	-0.037211	-0.2657	0.395754
9	-0.061045	-0.4359	0.332358
10	-0.147975	-1.0568	0.147802
11	0.034332	0.2452	0.403651
12	0.303004	2.1639	0.017591
13	-0.062692	-0.4477	0.32813
14	0.036312	0.2593	0.398217
15	-0.010027	-0.0716	0.471597
16	-0.099775	-0.7125	0.23969
17	0.07013	0.5008	0.309324

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.053222 & 0.3801 & 0.352731 \tabularnewline
2 & 0.100868 & 0.7203 & 0.237302 \tabularnewline
3 & 0.11006 & 0.786 & 0.217757 \tabularnewline
4 & -0.281924 & -2.0133 & 0.024685 \tabularnewline
5 & -0.002498 & -0.0178 & 0.492919 \tabularnewline
6 & 0.005956 & 0.0425 & 0.483118 \tabularnewline
7 & -0.156209 & -1.1156 & 0.134921 \tabularnewline
8 & -0.037211 & -0.2657 & 0.395754 \tabularnewline
9 & -0.061045 & -0.4359 & 0.332358 \tabularnewline
10 & -0.147975 & -1.0568 & 0.147802 \tabularnewline
11 & 0.034332 & 0.2452 & 0.403651 \tabularnewline
12 & 0.303004 & 2.1639 & 0.017591 \tabularnewline
13 & -0.062692 & -0.4477 & 0.32813 \tabularnewline
14 & 0.036312 & 0.2593 & 0.398217 \tabularnewline
15 & -0.010027 & -0.0716 & 0.471597 \tabularnewline
16 & -0.099775 & -0.7125 & 0.23969 \tabularnewline
17 & 0.07013 & 0.5008 & 0.309324 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299430&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]0.053222[/C][C]0.3801[/C][C]0.352731[/C][/ROW]
[ROW][C]2[/C][C]0.100868[/C][C]0.7203[/C][C]0.237302[/C][/ROW]
[ROW][C]3[/C][C]0.11006[/C][C]0.786[/C][C]0.217757[/C][/ROW]
[ROW][C]4[/C][C]-0.281924[/C][C]-2.0133[/C][C]0.024685[/C][/ROW]
[ROW][C]5[/C][C]-0.002498[/C][C]-0.0178[/C][C]0.492919[/C][/ROW]
[ROW][C]6[/C][C]0.005956[/C][C]0.0425[/C][C]0.483118[/C][/ROW]
[ROW][C]7[/C][C]-0.156209[/C][C]-1.1156[/C][C]0.134921[/C][/ROW]
[ROW][C]8[/C][C]-0.037211[/C][C]-0.2657[/C][C]0.395754[/C][/ROW]
[ROW][C]9[/C][C]-0.061045[/C][C]-0.4359[/C][C]0.332358[/C][/ROW]
[ROW][C]10[/C][C]-0.147975[/C][C]-1.0568[/C][C]0.147802[/C][/ROW]
[ROW][C]11[/C][C]0.034332[/C][C]0.2452[/C][C]0.403651[/C][/ROW]
[ROW][C]12[/C][C]0.303004[/C][C]2.1639[/C][C]0.017591[/C][/ROW]
[ROW][C]13[/C][C]-0.062692[/C][C]-0.4477[/C][C]0.32813[/C][/ROW]
[ROW][C]14[/C][C]0.036312[/C][C]0.2593[/C][C]0.398217[/C][/ROW]
[ROW][C]15[/C][C]-0.010027[/C][C]-0.0716[/C][C]0.471597[/C][/ROW]
[ROW][C]16[/C][C]-0.099775[/C][C]-0.7125[/C][C]0.23969[/C][/ROW]
[ROW][C]17[/C][C]0.07013[/C][C]0.5008[/C][C]0.309324[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299430&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299430&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	0.053222	0.3801	0.352731
2	0.100868	0.7203	0.237302
3	0.11006	0.786	0.217757
4	-0.281924	-2.0133	0.024685
5	-0.002498	-0.0178	0.492919
6	0.005956	0.0425	0.483118
7	-0.156209	-1.1156	0.134921
8	-0.037211	-0.2657	0.395754
9	-0.061045	-0.4359	0.332358
10	-0.147975	-1.0568	0.147802
11	0.034332	0.2452	0.403651
12	0.303004	2.1639	0.017591
13	-0.062692	-0.4477	0.32813
14	0.036312	0.2593	0.398217
15	-0.010027	-0.0716	0.471597
16	-0.099775	-0.7125	0.23969
17	0.07013	0.5008	0.309324

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.053222	0.3801	0.352731
2	0.098314	0.7021	0.242905
3	0.101249	0.7231	0.236472
4	-0.307882	-2.1987	0.01623
5	0.009668	0.069	0.472613
6	0.066232	0.473	0.319118
7	-0.109029	-0.7786	0.2199
8	-0.132735	-0.9479	0.173821
9	-0.024665	-0.1761	0.430441
10	-0.085686	-0.6119	0.271654
11	-0.00472	-0.0337	0.486622
12	0.346151	2.472	0.008406
13	-0.130925	-0.935	0.1771
14	-0.173122	-1.2363	0.110999
15	-0.026027	-0.1859	0.426641
16	0.169162	1.2081	0.116298
17	-0.02507	-0.179	0.429309

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.053222 & 0.3801 & 0.352731 \tabularnewline
2 & 0.098314 & 0.7021 & 0.242905 \tabularnewline
3 & 0.101249 & 0.7231 & 0.236472 \tabularnewline
4 & -0.307882 & -2.1987 & 0.01623 \tabularnewline
5 & 0.009668 & 0.069 & 0.472613 \tabularnewline
6 & 0.066232 & 0.473 & 0.319118 \tabularnewline
7 & -0.109029 & -0.7786 & 0.2199 \tabularnewline
8 & -0.132735 & -0.9479 & 0.173821 \tabularnewline
9 & -0.024665 & -0.1761 & 0.430441 \tabularnewline
10 & -0.085686 & -0.6119 & 0.271654 \tabularnewline
11 & -0.00472 & -0.0337 & 0.486622 \tabularnewline
12 & 0.346151 & 2.472 & 0.008406 \tabularnewline
13 & -0.130925 & -0.935 & 0.1771 \tabularnewline
14 & -0.173122 & -1.2363 & 0.110999 \tabularnewline
15 & -0.026027 & -0.1859 & 0.426641 \tabularnewline
16 & 0.169162 & 1.2081 & 0.116298 \tabularnewline
17 & -0.02507 & -0.179 & 0.429309 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299430&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]0.053222[/C][C]0.3801[/C][C]0.352731[/C][/ROW]
[ROW][C]2[/C][C]0.098314[/C][C]0.7021[/C][C]0.242905[/C][/ROW]
[ROW][C]3[/C][C]0.101249[/C][C]0.7231[/C][C]0.236472[/C][/ROW]
[ROW][C]4[/C][C]-0.307882[/C][C]-2.1987[/C][C]0.01623[/C][/ROW]
[ROW][C]5[/C][C]0.009668[/C][C]0.069[/C][C]0.472613[/C][/ROW]
[ROW][C]6[/C][C]0.066232[/C][C]0.473[/C][C]0.319118[/C][/ROW]
[ROW][C]7[/C][C]-0.109029[/C][C]-0.7786[/C][C]0.2199[/C][/ROW]
[ROW][C]8[/C][C]-0.132735[/C][C]-0.9479[/C][C]0.173821[/C][/ROW]
[ROW][C]9[/C][C]-0.024665[/C][C]-0.1761[/C][C]0.430441[/C][/ROW]
[ROW][C]10[/C][C]-0.085686[/C][C]-0.6119[/C][C]0.271654[/C][/ROW]
[ROW][C]11[/C][C]-0.00472[/C][C]-0.0337[/C][C]0.486622[/C][/ROW]
[ROW][C]12[/C][C]0.346151[/C][C]2.472[/C][C]0.008406[/C][/ROW]
[ROW][C]13[/C][C]-0.130925[/C][C]-0.935[/C][C]0.1771[/C][/ROW]
[ROW][C]14[/C][C]-0.173122[/C][C]-1.2363[/C][C]0.110999[/C][/ROW]
[ROW][C]15[/C][C]-0.026027[/C][C]-0.1859[/C][C]0.426641[/C][/ROW]
[ROW][C]16[/C][C]0.169162[/C][C]1.2081[/C][C]0.116298[/C][/ROW]
[ROW][C]17[/C][C]-0.02507[/C][C]-0.179[/C][C]0.429309[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299430&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299430&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	0.053222	0.3801	0.352731
2	0.098314	0.7021	0.242905
3	0.101249	0.7231	0.236472
4	-0.307882	-2.1987	0.01623
5	0.009668	0.069	0.472613
6	0.066232	0.473	0.319118
7	-0.109029	-0.7786	0.2199
8	-0.132735	-0.9479	0.173821
9	-0.024665	-0.1761	0.430441
10	-0.085686	-0.6119	0.271654
11	-0.00472	-0.0337	0.486622
12	0.346151	2.472	0.008406
13	-0.130925	-0.935	0.1771
14	-0.173122	-1.2363	0.110999
15	-0.026027	-0.1859	0.426641
16	0.169162	1.2081	0.116298
17	-0.02507	-0.179	0.429309

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)
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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