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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 02 Mar 2015 14:57:39 +0000

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/2015/Mar/02/t1425308288f2p12tvbd386t6q.htm/, Retrieved Fri, 17 May 2024 15:30:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=277817, Retrieved Fri, 17 May 2024 15:30:25 +0000

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User-defined keywords

Glenn Waem

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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] [] [2015-03-02 14:57:39] [3d92bf785db8aeb0f2ab1bed7b74f49c] [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	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277817&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277817&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277817&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.717086	6.5722	0
2	0.249466	2.2864	0.012374
3	-0.093095	-0.8532	0.197978
4	-0.189858	-1.7401	0.042754
5	-0.129748	-1.1892	0.118864
6	-0.07762	-0.7114	0.239403
7	-0.134761	-1.2351	0.110118
8	-0.217666	-1.9949	0.024646
9	-0.17776	-1.6292	0.053508
10	0.071116	0.6518	0.258159
11	0.439082	4.0243	6.2e-05
12	0.662316	6.0702	0
13	0.41941	3.844	0.000117
14	0.007502	0.0688	0.472674
15	-0.296774	-2.72	0.003966
16	-0.383614	-3.5159	0.000355
17	-0.328026	-3.0064	0.001743
18	-0.277999	-2.5479	0.006329
19	-0.312587	-2.8649	0.002634

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.717086 & 6.5722 & 0 \tabularnewline
2 & 0.249466 & 2.2864 & 0.012374 \tabularnewline
3 & -0.093095 & -0.8532 & 0.197978 \tabularnewline
4 & -0.189858 & -1.7401 & 0.042754 \tabularnewline
5 & -0.129748 & -1.1892 & 0.118864 \tabularnewline
6 & -0.07762 & -0.7114 & 0.239403 \tabularnewline
7 & -0.134761 & -1.2351 & 0.110118 \tabularnewline
8 & -0.217666 & -1.9949 & 0.024646 \tabularnewline
9 & -0.17776 & -1.6292 & 0.053508 \tabularnewline
10 & 0.071116 & 0.6518 & 0.258159 \tabularnewline
11 & 0.439082 & 4.0243 & 6.2e-05 \tabularnewline
12 & 0.662316 & 6.0702 & 0 \tabularnewline
13 & 0.41941 & 3.844 & 0.000117 \tabularnewline
14 & 0.007502 & 0.0688 & 0.472674 \tabularnewline
15 & -0.296774 & -2.72 & 0.003966 \tabularnewline
16 & -0.383614 & -3.5159 & 0.000355 \tabularnewline
17 & -0.328026 & -3.0064 & 0.001743 \tabularnewline
18 & -0.277999 & -2.5479 & 0.006329 \tabularnewline
19 & -0.312587 & -2.8649 & 0.002634 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277817&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]0.717086[/C][C]6.5722[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.249466[/C][C]2.2864[/C][C]0.012374[/C][/ROW]
[ROW][C]3[/C][C]-0.093095[/C][C]-0.8532[/C][C]0.197978[/C][/ROW]
[ROW][C]4[/C][C]-0.189858[/C][C]-1.7401[/C][C]0.042754[/C][/ROW]
[ROW][C]5[/C][C]-0.129748[/C][C]-1.1892[/C][C]0.118864[/C][/ROW]
[ROW][C]6[/C][C]-0.07762[/C][C]-0.7114[/C][C]0.239403[/C][/ROW]
[ROW][C]7[/C][C]-0.134761[/C][C]-1.2351[/C][C]0.110118[/C][/ROW]
[ROW][C]8[/C][C]-0.217666[/C][C]-1.9949[/C][C]0.024646[/C][/ROW]
[ROW][C]9[/C][C]-0.17776[/C][C]-1.6292[/C][C]0.053508[/C][/ROW]
[ROW][C]10[/C][C]0.071116[/C][C]0.6518[/C][C]0.258159[/C][/ROW]
[ROW][C]11[/C][C]0.439082[/C][C]4.0243[/C][C]6.2e-05[/C][/ROW]
[ROW][C]12[/C][C]0.662316[/C][C]6.0702[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.41941[/C][C]3.844[/C][C]0.000117[/C][/ROW]
[ROW][C]14[/C][C]0.007502[/C][C]0.0688[/C][C]0.472674[/C][/ROW]
[ROW][C]15[/C][C]-0.296774[/C][C]-2.72[/C][C]0.003966[/C][/ROW]
[ROW][C]16[/C][C]-0.383614[/C][C]-3.5159[/C][C]0.000355[/C][/ROW]
[ROW][C]17[/C][C]-0.328026[/C][C]-3.0064[/C][C]0.001743[/C][/ROW]
[ROW][C]18[/C][C]-0.277999[/C][C]-2.5479[/C][C]0.006329[/C][/ROW]
[ROW][C]19[/C][C]-0.312587[/C][C]-2.8649[/C][C]0.002634[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277817&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277817&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	0.717086	6.5722	0
2	0.249466	2.2864	0.012374
3	-0.093095	-0.8532	0.197978
4	-0.189858	-1.7401	0.042754
5	-0.129748	-1.1892	0.118864
6	-0.07762	-0.7114	0.239403
7	-0.134761	-1.2351	0.110118
8	-0.217666	-1.9949	0.024646
9	-0.17776	-1.6292	0.053508
10	0.071116	0.6518	0.258159
11	0.439082	4.0243	6.2e-05
12	0.662316	6.0702	0
13	0.41941	3.844	0.000117
14	0.007502	0.0688	0.472674
15	-0.296774	-2.72	0.003966
16	-0.383614	-3.5159	0.000355
17	-0.328026	-3.0064	0.001743
18	-0.277999	-2.5479	0.006329
19	-0.312587	-2.8649	0.002634

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.717086	6.5722	0
2	-0.544985	-4.9949	2e-06
3	0.062446	0.5723	0.284314
4	0.07315	0.6704	0.25221
5	-0.04138	-0.3793	0.352729
6	-0.125445	-1.1497	0.126761
7	-0.177696	-1.6286	0.05357
8	0.004544	0.0416	0.48344
9	0.137998	1.2648	0.104725
10	0.308286	2.8255	0.002948
11	0.351196	3.2188	0.000915
12	0.109248	1.0013	0.159785
13	-0.661905	-6.0665	0
14	0.209896	1.9237	0.028888
15	-0.106794	-0.9788	0.165248
16	-0.210933	-1.9332	0.028288
17	-0.136383	-1.25	0.10739
18	-0.116379	-1.0666	0.144596
19	0.003109	0.0285	0.488669

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.717086 & 6.5722 & 0 \tabularnewline
2 & -0.544985 & -4.9949 & 2e-06 \tabularnewline
3 & 0.062446 & 0.5723 & 0.284314 \tabularnewline
4 & 0.07315 & 0.6704 & 0.25221 \tabularnewline
5 & -0.04138 & -0.3793 & 0.352729 \tabularnewline
6 & -0.125445 & -1.1497 & 0.126761 \tabularnewline
7 & -0.177696 & -1.6286 & 0.05357 \tabularnewline
8 & 0.004544 & 0.0416 & 0.48344 \tabularnewline
9 & 0.137998 & 1.2648 & 0.104725 \tabularnewline
10 & 0.308286 & 2.8255 & 0.002948 \tabularnewline
11 & 0.351196 & 3.2188 & 0.000915 \tabularnewline
12 & 0.109248 & 1.0013 & 0.159785 \tabularnewline
13 & -0.661905 & -6.0665 & 0 \tabularnewline
14 & 0.209896 & 1.9237 & 0.028888 \tabularnewline
15 & -0.106794 & -0.9788 & 0.165248 \tabularnewline
16 & -0.210933 & -1.9332 & 0.028288 \tabularnewline
17 & -0.136383 & -1.25 & 0.10739 \tabularnewline
18 & -0.116379 & -1.0666 & 0.144596 \tabularnewline
19 & 0.003109 & 0.0285 & 0.488669 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=277817&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]0.717086[/C][C]6.5722[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.544985[/C][C]-4.9949[/C][C]2e-06[/C][/ROW]
[ROW][C]3[/C][C]0.062446[/C][C]0.5723[/C][C]0.284314[/C][/ROW]
[ROW][C]4[/C][C]0.07315[/C][C]0.6704[/C][C]0.25221[/C][/ROW]
[ROW][C]5[/C][C]-0.04138[/C][C]-0.3793[/C][C]0.352729[/C][/ROW]
[ROW][C]6[/C][C]-0.125445[/C][C]-1.1497[/C][C]0.126761[/C][/ROW]
[ROW][C]7[/C][C]-0.177696[/C][C]-1.6286[/C][C]0.05357[/C][/ROW]
[ROW][C]8[/C][C]0.004544[/C][C]0.0416[/C][C]0.48344[/C][/ROW]
[ROW][C]9[/C][C]0.137998[/C][C]1.2648[/C][C]0.104725[/C][/ROW]
[ROW][C]10[/C][C]0.308286[/C][C]2.8255[/C][C]0.002948[/C][/ROW]
[ROW][C]11[/C][C]0.351196[/C][C]3.2188[/C][C]0.000915[/C][/ROW]
[ROW][C]12[/C][C]0.109248[/C][C]1.0013[/C][C]0.159785[/C][/ROW]
[ROW][C]13[/C][C]-0.661905[/C][C]-6.0665[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.209896[/C][C]1.9237[/C][C]0.028888[/C][/ROW]
[ROW][C]15[/C][C]-0.106794[/C][C]-0.9788[/C][C]0.165248[/C][/ROW]
[ROW][C]16[/C][C]-0.210933[/C][C]-1.9332[/C][C]0.028288[/C][/ROW]
[ROW][C]17[/C][C]-0.136383[/C][C]-1.25[/C][C]0.10739[/C][/ROW]
[ROW][C]18[/C][C]-0.116379[/C][C]-1.0666[/C][C]0.144596[/C][/ROW]
[ROW][C]19[/C][C]0.003109[/C][C]0.0285[/C][C]0.488669[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=277817&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=277817&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	0.717086	6.5722	0
2	-0.544985	-4.9949	2e-06
3	0.062446	0.5723	0.284314
4	0.07315	0.6704	0.25221
5	-0.04138	-0.3793	0.352729
6	-0.125445	-1.1497	0.126761
7	-0.177696	-1.6286	0.05357
8	0.004544	0.0416	0.48344
9	0.137998	1.2648	0.104725
10	0.308286	2.8255	0.002948
11	0.351196	3.2188	0.000915
12	0.109248	1.0013	0.159785
13	-0.661905	-6.0665	0
14	0.209896	1.9237	0.028888
15	-0.106794	-0.9788	0.165248
16	-0.210933	-1.9332	0.028288
17	-0.136383	-1.25	0.10739
18	-0.116379	-1.0666	0.144596
19	0.003109	0.0285	0.488669

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)
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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code