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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 15:12:27 +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/2016/Dec/16/t1481897570bmlghm0wfvvdxin.htm/, Retrieved Tue, 13 May 2025 09:10:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300294, Retrieved Tue, 13 May 2025 09:10:14 +0000

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No (this computation is public)

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Estimated Impact

101

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

-     [ARIMA Backward Selection] [] [2016-12-16 13:36:55] [683f400e1b95307fc738e729f07c4fce]
- RM D    [(Partial) Autocorrelation Function] [] [2016-12-16 14:12:27] [404ac5ee4f7301873f6a96ef36861981] [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=300294&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=300294&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300294&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	0.02604	0.1647	0.435008
2	-0.344744	-2.1804	0.017587
3	-0.228944	-1.448	0.07771
4	0.007325	0.0463	0.481639
5	0.258595	1.6355	0.054896
6	0.02762	0.1747	0.431106
7	0.049803	0.315	0.377207
8	-0.063252	-0.4	0.345626
9	-0.123738	-0.7826	0.219238
10	-0.012146	-0.0768	0.469575
11	0.074633	0.472	0.319738
12	0.046072	0.2914	0.386132
13	-0.026513	-0.1677	0.43384
14	-0.092704	-0.5863	0.28048
15	-0.026367	-0.1668	0.434199
16	-0.060386	-0.3819	0.352274

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.02604 & 0.1647 & 0.435008 \tabularnewline
2 & -0.344744 & -2.1804 & 0.017587 \tabularnewline
3 & -0.228944 & -1.448 & 0.07771 \tabularnewline
4 & 0.007325 & 0.0463 & 0.481639 \tabularnewline
5 & 0.258595 & 1.6355 & 0.054896 \tabularnewline
6 & 0.02762 & 0.1747 & 0.431106 \tabularnewline
7 & 0.049803 & 0.315 & 0.377207 \tabularnewline
8 & -0.063252 & -0.4 & 0.345626 \tabularnewline
9 & -0.123738 & -0.7826 & 0.219238 \tabularnewline
10 & -0.012146 & -0.0768 & 0.469575 \tabularnewline
11 & 0.074633 & 0.472 & 0.319738 \tabularnewline
12 & 0.046072 & 0.2914 & 0.386132 \tabularnewline
13 & -0.026513 & -0.1677 & 0.43384 \tabularnewline
14 & -0.092704 & -0.5863 & 0.28048 \tabularnewline
15 & -0.026367 & -0.1668 & 0.434199 \tabularnewline
16 & -0.060386 & -0.3819 & 0.352274 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300294&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]0.02604[/C][C]0.1647[/C][C]0.435008[/C][/ROW]
[ROW][C]2[/C][C]-0.344744[/C][C]-2.1804[/C][C]0.017587[/C][/ROW]
[ROW][C]3[/C][C]-0.228944[/C][C]-1.448[/C][C]0.07771[/C][/ROW]
[ROW][C]4[/C][C]0.007325[/C][C]0.0463[/C][C]0.481639[/C][/ROW]
[ROW][C]5[/C][C]0.258595[/C][C]1.6355[/C][C]0.054896[/C][/ROW]
[ROW][C]6[/C][C]0.02762[/C][C]0.1747[/C][C]0.431106[/C][/ROW]
[ROW][C]7[/C][C]0.049803[/C][C]0.315[/C][C]0.377207[/C][/ROW]
[ROW][C]8[/C][C]-0.063252[/C][C]-0.4[/C][C]0.345626[/C][/ROW]
[ROW][C]9[/C][C]-0.123738[/C][C]-0.7826[/C][C]0.219238[/C][/ROW]
[ROW][C]10[/C][C]-0.012146[/C][C]-0.0768[/C][C]0.469575[/C][/ROW]
[ROW][C]11[/C][C]0.074633[/C][C]0.472[/C][C]0.319738[/C][/ROW]
[ROW][C]12[/C][C]0.046072[/C][C]0.2914[/C][C]0.386132[/C][/ROW]
[ROW][C]13[/C][C]-0.026513[/C][C]-0.1677[/C][C]0.43384[/C][/ROW]
[ROW][C]14[/C][C]-0.092704[/C][C]-0.5863[/C][C]0.28048[/C][/ROW]
[ROW][C]15[/C][C]-0.026367[/C][C]-0.1668[/C][C]0.434199[/C][/ROW]
[ROW][C]16[/C][C]-0.060386[/C][C]-0.3819[/C][C]0.352274[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300294&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300294&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	0.02604	0.1647	0.435008
2	-0.344744	-2.1804	0.017587
3	-0.228944	-1.448	0.07771
4	0.007325	0.0463	0.481639
5	0.258595	1.6355	0.054896
6	0.02762	0.1747	0.431106
7	0.049803	0.315	0.377207
8	-0.063252	-0.4	0.345626
9	-0.123738	-0.7826	0.219238
10	-0.012146	-0.0768	0.469575
11	0.074633	0.472	0.319738
12	0.046072	0.2914	0.386132
13	-0.026513	-0.1677	0.43384
14	-0.092704	-0.5863	0.28048
15	-0.026367	-0.1668	0.434199
16	-0.060386	-0.3819	0.352274

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.02604	0.1647	0.435008
2	-0.345657	-2.1861	0.017359
3	-0.236228	-1.494	0.071507
4	-0.136617	-0.864	0.196358
5	0.111985	0.7083	0.241446
6	-0.057143	-0.3614	0.35985
7	0.189268	1.197	0.11917
8	0.022557	0.1427	0.443636
9	-0.026221	-0.1658	0.434561
10	-0.034527	-0.2184	0.414127
11	0.025388	0.1606	0.436621
12	-0.069912	-0.4422	0.330377
13	-0.0088	-0.0557	0.477947
14	-0.082819	-0.5238	0.301657
15	-0.029879	-0.189	0.425535
16	-0.153476	-0.9707	0.168774

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.02604 & 0.1647 & 0.435008 \tabularnewline
2 & -0.345657 & -2.1861 & 0.017359 \tabularnewline
3 & -0.236228 & -1.494 & 0.071507 \tabularnewline
4 & -0.136617 & -0.864 & 0.196358 \tabularnewline
5 & 0.111985 & 0.7083 & 0.241446 \tabularnewline
6 & -0.057143 & -0.3614 & 0.35985 \tabularnewline
7 & 0.189268 & 1.197 & 0.11917 \tabularnewline
8 & 0.022557 & 0.1427 & 0.443636 \tabularnewline
9 & -0.026221 & -0.1658 & 0.434561 \tabularnewline
10 & -0.034527 & -0.2184 & 0.414127 \tabularnewline
11 & 0.025388 & 0.1606 & 0.436621 \tabularnewline
12 & -0.069912 & -0.4422 & 0.330377 \tabularnewline
13 & -0.0088 & -0.0557 & 0.477947 \tabularnewline
14 & -0.082819 & -0.5238 & 0.301657 \tabularnewline
15 & -0.029879 & -0.189 & 0.425535 \tabularnewline
16 & -0.153476 & -0.9707 & 0.168774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300294&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]0.02604[/C][C]0.1647[/C][C]0.435008[/C][/ROW]
[ROW][C]2[/C][C]-0.345657[/C][C]-2.1861[/C][C]0.017359[/C][/ROW]
[ROW][C]3[/C][C]-0.236228[/C][C]-1.494[/C][C]0.071507[/C][/ROW]
[ROW][C]4[/C][C]-0.136617[/C][C]-0.864[/C][C]0.196358[/C][/ROW]
[ROW][C]5[/C][C]0.111985[/C][C]0.7083[/C][C]0.241446[/C][/ROW]
[ROW][C]6[/C][C]-0.057143[/C][C]-0.3614[/C][C]0.35985[/C][/ROW]
[ROW][C]7[/C][C]0.189268[/C][C]1.197[/C][C]0.11917[/C][/ROW]
[ROW][C]8[/C][C]0.022557[/C][C]0.1427[/C][C]0.443636[/C][/ROW]
[ROW][C]9[/C][C]-0.026221[/C][C]-0.1658[/C][C]0.434561[/C][/ROW]
[ROW][C]10[/C][C]-0.034527[/C][C]-0.2184[/C][C]0.414127[/C][/ROW]
[ROW][C]11[/C][C]0.025388[/C][C]0.1606[/C][C]0.436621[/C][/ROW]
[ROW][C]12[/C][C]-0.069912[/C][C]-0.4422[/C][C]0.330377[/C][/ROW]
[ROW][C]13[/C][C]-0.0088[/C][C]-0.0557[/C][C]0.477947[/C][/ROW]
[ROW][C]14[/C][C]-0.082819[/C][C]-0.5238[/C][C]0.301657[/C][/ROW]
[ROW][C]15[/C][C]-0.029879[/C][C]-0.189[/C][C]0.425535[/C][/ROW]
[ROW][C]16[/C][C]-0.153476[/C][C]-0.9707[/C][C]0.168774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300294&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300294&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	0.02604	0.1647	0.435008
2	-0.345657	-2.1861	0.017359
3	-0.236228	-1.494	0.071507
4	-0.136617	-0.864	0.196358
5	0.111985	0.7083	0.241446
6	-0.057143	-0.3614	0.35985
7	0.189268	1.197	0.11917
8	0.022557	0.1427	0.443636
9	-0.026221	-0.1658	0.434561
10	-0.034527	-0.2184	0.414127
11	0.025388	0.1606	0.436621
12	-0.069912	-0.4422	0.330377
13	-0.0088	-0.0557	0.477947
14	-0.082819	-0.5238	0.301657
15	-0.029879	-0.189	0.425535
16	-0.153476	-0.9707	0.168774

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 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ;

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):

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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Figures (Output of Computation)

Input Parameters & R Code