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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 23 Jan 2017 10:48:53 +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/2017/Jan/23/t14851649623f453tj35lrzi0l.htm/, Retrieved Sat, 10 May 2025 01:03:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=304661, Retrieved Sat, 10 May 2025 01:03:24 +0000

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105

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-       [(Partial) Autocorrelation Function] [examen] [2017-01-23 09:48:53] [2ea868439aa9f960cb5a0f1a9b97f873] [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=304661&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=304661&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=304661&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	0.066651	0.5163	0.303779
2	-0.306029	-2.3705	0.010497
3	-0.033184	-0.257	0.399012
4	-0.010116	-0.0784	0.468902
5	-0.076217	-0.5904	0.278578
6	-0.002803	-0.0217	0.491376
7	0.012958	0.1004	0.460192
8	-0.041669	-0.3228	0.373998
9	0.095334	0.7385	0.231559
10	0.400961	3.1058	0.001448
11	0.009846	0.0763	0.469731
12	-0.57189	-4.4298	2e-05
13	-0.031461	-0.2437	0.404149
14	0.109551	0.8486	0.199745
15	-0.082553	-0.6395	0.262481
16	0.028798	0.2231	0.412121
17	0.064823	0.5021	0.308712
18	-0.010242	-0.0793	0.468516

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.066651 & 0.5163 & 0.303779 \tabularnewline
2 & -0.306029 & -2.3705 & 0.010497 \tabularnewline
3 & -0.033184 & -0.257 & 0.399012 \tabularnewline
4 & -0.010116 & -0.0784 & 0.468902 \tabularnewline
5 & -0.076217 & -0.5904 & 0.278578 \tabularnewline
6 & -0.002803 & -0.0217 & 0.491376 \tabularnewline
7 & 0.012958 & 0.1004 & 0.460192 \tabularnewline
8 & -0.041669 & -0.3228 & 0.373998 \tabularnewline
9 & 0.095334 & 0.7385 & 0.231559 \tabularnewline
10 & 0.400961 & 3.1058 & 0.001448 \tabularnewline
11 & 0.009846 & 0.0763 & 0.469731 \tabularnewline
12 & -0.57189 & -4.4298 & 2e-05 \tabularnewline
13 & -0.031461 & -0.2437 & 0.404149 \tabularnewline
14 & 0.109551 & 0.8486 & 0.199745 \tabularnewline
15 & -0.082553 & -0.6395 & 0.262481 \tabularnewline
16 & 0.028798 & 0.2231 & 0.412121 \tabularnewline
17 & 0.064823 & 0.5021 & 0.308712 \tabularnewline
18 & -0.010242 & -0.0793 & 0.468516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=304661&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]0.066651[/C][C]0.5163[/C][C]0.303779[/C][/ROW]
[ROW][C]2[/C][C]-0.306029[/C][C]-2.3705[/C][C]0.010497[/C][/ROW]
[ROW][C]3[/C][C]-0.033184[/C][C]-0.257[/C][C]0.399012[/C][/ROW]
[ROW][C]4[/C][C]-0.010116[/C][C]-0.0784[/C][C]0.468902[/C][/ROW]
[ROW][C]5[/C][C]-0.076217[/C][C]-0.5904[/C][C]0.278578[/C][/ROW]
[ROW][C]6[/C][C]-0.002803[/C][C]-0.0217[/C][C]0.491376[/C][/ROW]
[ROW][C]7[/C][C]0.012958[/C][C]0.1004[/C][C]0.460192[/C][/ROW]
[ROW][C]8[/C][C]-0.041669[/C][C]-0.3228[/C][C]0.373998[/C][/ROW]
[ROW][C]9[/C][C]0.095334[/C][C]0.7385[/C][C]0.231559[/C][/ROW]
[ROW][C]10[/C][C]0.400961[/C][C]3.1058[/C][C]0.001448[/C][/ROW]
[ROW][C]11[/C][C]0.009846[/C][C]0.0763[/C][C]0.469731[/C][/ROW]
[ROW][C]12[/C][C]-0.57189[/C][C]-4.4298[/C][C]2e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.031461[/C][C]-0.2437[/C][C]0.404149[/C][/ROW]
[ROW][C]14[/C][C]0.109551[/C][C]0.8486[/C][C]0.199745[/C][/ROW]
[ROW][C]15[/C][C]-0.082553[/C][C]-0.6395[/C][C]0.262481[/C][/ROW]
[ROW][C]16[/C][C]0.028798[/C][C]0.2231[/C][C]0.412121[/C][/ROW]
[ROW][C]17[/C][C]0.064823[/C][C]0.5021[/C][C]0.308712[/C][/ROW]
[ROW][C]18[/C][C]-0.010242[/C][C]-0.0793[/C][C]0.468516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=304661&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=304661&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	0.066651	0.5163	0.303779
2	-0.306029	-2.3705	0.010497
3	-0.033184	-0.257	0.399012
4	-0.010116	-0.0784	0.468902
5	-0.076217	-0.5904	0.278578
6	-0.002803	-0.0217	0.491376
7	0.012958	0.1004	0.460192
8	-0.041669	-0.3228	0.373998
9	0.095334	0.7385	0.231559
10	0.400961	3.1058	0.001448
11	0.009846	0.0763	0.469731
12	-0.57189	-4.4298	2e-05
13	-0.031461	-0.2437	0.404149
14	0.109551	0.8486	0.199745
15	-0.082553	-0.6395	0.262481
16	0.028798	0.2231	0.412121
17	0.064823	0.5021	0.308712
18	-0.010242	-0.0793	0.468516

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.066651	0.5163	0.303779
2	-0.311857	-2.4156	0.009385
3	0.015978	0.1238	0.450959
4	-0.115724	-0.8964	0.186811
5	-0.080077	-0.6203	0.268714
6	-0.031392	-0.2432	0.404356
7	-0.044444	-0.3443	0.365925
8	-0.061528	-0.4766	0.317691
9	0.094844	0.7347	0.232704
10	0.396455	3.0709	0.001602
11	0.024108	0.1867	0.426246
12	-0.440689	-3.4136	0.000577
13	0.076565	0.5931	0.277681
14	-0.126158	-0.9772	0.166193
15	-0.067602	-0.5236	0.301228
16	0.00917	0.071	0.471806
17	-0.038601	-0.299	0.382986
18	-0.013623	-0.1055	0.458155

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.066651 & 0.5163 & 0.303779 \tabularnewline
2 & -0.311857 & -2.4156 & 0.009385 \tabularnewline
3 & 0.015978 & 0.1238 & 0.450959 \tabularnewline
4 & -0.115724 & -0.8964 & 0.186811 \tabularnewline
5 & -0.080077 & -0.6203 & 0.268714 \tabularnewline
6 & -0.031392 & -0.2432 & 0.404356 \tabularnewline
7 & -0.044444 & -0.3443 & 0.365925 \tabularnewline
8 & -0.061528 & -0.4766 & 0.317691 \tabularnewline
9 & 0.094844 & 0.7347 & 0.232704 \tabularnewline
10 & 0.396455 & 3.0709 & 0.001602 \tabularnewline
11 & 0.024108 & 0.1867 & 0.426246 \tabularnewline
12 & -0.440689 & -3.4136 & 0.000577 \tabularnewline
13 & 0.076565 & 0.5931 & 0.277681 \tabularnewline
14 & -0.126158 & -0.9772 & 0.166193 \tabularnewline
15 & -0.067602 & -0.5236 & 0.301228 \tabularnewline
16 & 0.00917 & 0.071 & 0.471806 \tabularnewline
17 & -0.038601 & -0.299 & 0.382986 \tabularnewline
18 & -0.013623 & -0.1055 & 0.458155 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=304661&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]0.066651[/C][C]0.5163[/C][C]0.303779[/C][/ROW]
[ROW][C]2[/C][C]-0.311857[/C][C]-2.4156[/C][C]0.009385[/C][/ROW]
[ROW][C]3[/C][C]0.015978[/C][C]0.1238[/C][C]0.450959[/C][/ROW]
[ROW][C]4[/C][C]-0.115724[/C][C]-0.8964[/C][C]0.186811[/C][/ROW]
[ROW][C]5[/C][C]-0.080077[/C][C]-0.6203[/C][C]0.268714[/C][/ROW]
[ROW][C]6[/C][C]-0.031392[/C][C]-0.2432[/C][C]0.404356[/C][/ROW]
[ROW][C]7[/C][C]-0.044444[/C][C]-0.3443[/C][C]0.365925[/C][/ROW]
[ROW][C]8[/C][C]-0.061528[/C][C]-0.4766[/C][C]0.317691[/C][/ROW]
[ROW][C]9[/C][C]0.094844[/C][C]0.7347[/C][C]0.232704[/C][/ROW]
[ROW][C]10[/C][C]0.396455[/C][C]3.0709[/C][C]0.001602[/C][/ROW]
[ROW][C]11[/C][C]0.024108[/C][C]0.1867[/C][C]0.426246[/C][/ROW]
[ROW][C]12[/C][C]-0.440689[/C][C]-3.4136[/C][C]0.000577[/C][/ROW]
[ROW][C]13[/C][C]0.076565[/C][C]0.5931[/C][C]0.277681[/C][/ROW]
[ROW][C]14[/C][C]-0.126158[/C][C]-0.9772[/C][C]0.166193[/C][/ROW]
[ROW][C]15[/C][C]-0.067602[/C][C]-0.5236[/C][C]0.301228[/C][/ROW]
[ROW][C]16[/C][C]0.00917[/C][C]0.071[/C][C]0.471806[/C][/ROW]
[ROW][C]17[/C][C]-0.038601[/C][C]-0.299[/C][C]0.382986[/C][/ROW]
[ROW][C]18[/C][C]-0.013623[/C][C]-0.1055[/C][C]0.458155[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=304661&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=304661&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	0.066651	0.5163	0.303779
2	-0.311857	-2.4156	0.009385
3	0.015978	0.1238	0.450959
4	-0.115724	-0.8964	0.186811
5	-0.080077	-0.6203	0.268714
6	-0.031392	-0.2432	0.404356
7	-0.044444	-0.3443	0.365925
8	-0.061528	-0.4766	0.317691
9	0.094844	0.7347	0.232704
10	0.396455	3.0709	0.001602
11	0.024108	0.1867	0.426246
12	-0.440689	-3.4136	0.000577
13	0.076565	0.5931	0.277681
14	-0.126158	-0.9772	0.166193
15	-0.067602	-0.5236	0.301228
16	0.00917	0.071	0.471806
17	-0.038601	-0.299	0.382986
18	-0.013623	-0.1055	0.458155

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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 <- '1'
par3 <- '1'
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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code