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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 05 Dec 2011 17:31:05 -0500

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/2011/Dec/05/t13231242828h3jdi603g180f0.htm/, Retrieved Fri, 03 May 2024 12:25:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151308, Retrieved Fri, 03 May 2024 12:25:46 +0000

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110

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-     [Variance Reduction Matrix] [] [2011-12-05 22:04:45] [a1957df0bc37aec4aa3c994e6a08412c]
- RMP   [(Partial) Autocorrelation Function] [] [2011-12-05 22:23:23] [a1957df0bc37aec4aa3c994e6a08412c]
- R PD      [(Partial) Autocorrelation Function] [] [2011-12-05 22:31:05] [fdaf10f0fcbe7b8f79ecbd42ec74e6ad] [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	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151308&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151308&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151308&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	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.262492	2.2118	0.0151
2	0.053253	0.4487	0.327501
3	0.205334	1.7302	0.043972
4	0.172129	1.4504	0.075677
5	0.211511	1.7822	0.039494
6	-0.036119	-0.3043	0.380878
7	-0.037401	-0.3151	0.376788
8	0.122281	1.0304	0.153169
9	-0.022535	-0.1899	0.424973
10	-0.159034	-1.34	0.092252
11	0.092498	0.7794	0.219168
12	-0.072829	-0.6137	0.270699
13	-0.0797	-0.6716	0.25202
14	0.031929	0.269	0.394341
15	-0.064778	-0.5458	0.293446
16	0.047701	0.4019	0.344469
17	-0.204677	-1.7246	0.044472
18	-0.215756	-1.818	0.036642

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.262492 & 2.2118 & 0.0151 \tabularnewline
2 & 0.053253 & 0.4487 & 0.327501 \tabularnewline
3 & 0.205334 & 1.7302 & 0.043972 \tabularnewline
4 & 0.172129 & 1.4504 & 0.075677 \tabularnewline
5 & 0.211511 & 1.7822 & 0.039494 \tabularnewline
6 & -0.036119 & -0.3043 & 0.380878 \tabularnewline
7 & -0.037401 & -0.3151 & 0.376788 \tabularnewline
8 & 0.122281 & 1.0304 & 0.153169 \tabularnewline
9 & -0.022535 & -0.1899 & 0.424973 \tabularnewline
10 & -0.159034 & -1.34 & 0.092252 \tabularnewline
11 & 0.092498 & 0.7794 & 0.219168 \tabularnewline
12 & -0.072829 & -0.6137 & 0.270699 \tabularnewline
13 & -0.0797 & -0.6716 & 0.25202 \tabularnewline
14 & 0.031929 & 0.269 & 0.394341 \tabularnewline
15 & -0.064778 & -0.5458 & 0.293446 \tabularnewline
16 & 0.047701 & 0.4019 & 0.344469 \tabularnewline
17 & -0.204677 & -1.7246 & 0.044472 \tabularnewline
18 & -0.215756 & -1.818 & 0.036642 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151308&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]0.262492[/C][C]2.2118[/C][C]0.0151[/C][/ROW]
[ROW][C]2[/C][C]0.053253[/C][C]0.4487[/C][C]0.327501[/C][/ROW]
[ROW][C]3[/C][C]0.205334[/C][C]1.7302[/C][C]0.043972[/C][/ROW]
[ROW][C]4[/C][C]0.172129[/C][C]1.4504[/C][C]0.075677[/C][/ROW]
[ROW][C]5[/C][C]0.211511[/C][C]1.7822[/C][C]0.039494[/C][/ROW]
[ROW][C]6[/C][C]-0.036119[/C][C]-0.3043[/C][C]0.380878[/C][/ROW]
[ROW][C]7[/C][C]-0.037401[/C][C]-0.3151[/C][C]0.376788[/C][/ROW]
[ROW][C]8[/C][C]0.122281[/C][C]1.0304[/C][C]0.153169[/C][/ROW]
[ROW][C]9[/C][C]-0.022535[/C][C]-0.1899[/C][C]0.424973[/C][/ROW]
[ROW][C]10[/C][C]-0.159034[/C][C]-1.34[/C][C]0.092252[/C][/ROW]
[ROW][C]11[/C][C]0.092498[/C][C]0.7794[/C][C]0.219168[/C][/ROW]
[ROW][C]12[/C][C]-0.072829[/C][C]-0.6137[/C][C]0.270699[/C][/ROW]
[ROW][C]13[/C][C]-0.0797[/C][C]-0.6716[/C][C]0.25202[/C][/ROW]
[ROW][C]14[/C][C]0.031929[/C][C]0.269[/C][C]0.394341[/C][/ROW]
[ROW][C]15[/C][C]-0.064778[/C][C]-0.5458[/C][C]0.293446[/C][/ROW]
[ROW][C]16[/C][C]0.047701[/C][C]0.4019[/C][C]0.344469[/C][/ROW]
[ROW][C]17[/C][C]-0.204677[/C][C]-1.7246[/C][C]0.044472[/C][/ROW]
[ROW][C]18[/C][C]-0.215756[/C][C]-1.818[/C][C]0.036642[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151308&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151308&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	0.262492	2.2118	0.0151
2	0.053253	0.4487	0.327501
3	0.205334	1.7302	0.043972
4	0.172129	1.4504	0.075677
5	0.211511	1.7822	0.039494
6	-0.036119	-0.3043	0.380878
7	-0.037401	-0.3151	0.376788
8	0.122281	1.0304	0.153169
9	-0.022535	-0.1899	0.424973
10	-0.159034	-1.34	0.092252
11	0.092498	0.7794	0.219168
12	-0.072829	-0.6137	0.270699
13	-0.0797	-0.6716	0.25202
14	0.031929	0.269	0.394341
15	-0.064778	-0.5458	0.293446
16	0.047701	0.4019	0.344469
17	-0.204677	-1.7246	0.044472
18	-0.215756	-1.818	0.036642

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.262492	2.2118	0.0151
2	-0.016807	-0.1416	0.443891
3	0.210061	1.77	0.04051
4	0.073437	0.6188	0.269018
5	0.171845	1.448	0.076011
6	-0.184275	-1.5527	0.062467
7	-0.016932	-0.1427	0.443478
8	0.055221	0.4653	0.321569
9	-0.078974	-0.6654	0.253961
10	-0.152022	-1.281	0.102188
11	0.221842	1.8693	0.032855
12	-0.194869	-1.642	0.052506
13	0.027618	0.2327	0.408328
14	0.074491	0.6277	0.266117
15	-0.025871	-0.218	0.41403
16	-0.008648	-0.0729	0.471058
17	-0.20648	-1.7398	0.043111
18	-0.077294	-0.6513	0.258481

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.262492 & 2.2118 & 0.0151 \tabularnewline
2 & -0.016807 & -0.1416 & 0.443891 \tabularnewline
3 & 0.210061 & 1.77 & 0.04051 \tabularnewline
4 & 0.073437 & 0.6188 & 0.269018 \tabularnewline
5 & 0.171845 & 1.448 & 0.076011 \tabularnewline
6 & -0.184275 & -1.5527 & 0.062467 \tabularnewline
7 & -0.016932 & -0.1427 & 0.443478 \tabularnewline
8 & 0.055221 & 0.4653 & 0.321569 \tabularnewline
9 & -0.078974 & -0.6654 & 0.253961 \tabularnewline
10 & -0.152022 & -1.281 & 0.102188 \tabularnewline
11 & 0.221842 & 1.8693 & 0.032855 \tabularnewline
12 & -0.194869 & -1.642 & 0.052506 \tabularnewline
13 & 0.027618 & 0.2327 & 0.408328 \tabularnewline
14 & 0.074491 & 0.6277 & 0.266117 \tabularnewline
15 & -0.025871 & -0.218 & 0.41403 \tabularnewline
16 & -0.008648 & -0.0729 & 0.471058 \tabularnewline
17 & -0.20648 & -1.7398 & 0.043111 \tabularnewline
18 & -0.077294 & -0.6513 & 0.258481 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151308&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]0.262492[/C][C]2.2118[/C][C]0.0151[/C][/ROW]
[ROW][C]2[/C][C]-0.016807[/C][C]-0.1416[/C][C]0.443891[/C][/ROW]
[ROW][C]3[/C][C]0.210061[/C][C]1.77[/C][C]0.04051[/C][/ROW]
[ROW][C]4[/C][C]0.073437[/C][C]0.6188[/C][C]0.269018[/C][/ROW]
[ROW][C]5[/C][C]0.171845[/C][C]1.448[/C][C]0.076011[/C][/ROW]
[ROW][C]6[/C][C]-0.184275[/C][C]-1.5527[/C][C]0.062467[/C][/ROW]
[ROW][C]7[/C][C]-0.016932[/C][C]-0.1427[/C][C]0.443478[/C][/ROW]
[ROW][C]8[/C][C]0.055221[/C][C]0.4653[/C][C]0.321569[/C][/ROW]
[ROW][C]9[/C][C]-0.078974[/C][C]-0.6654[/C][C]0.253961[/C][/ROW]
[ROW][C]10[/C][C]-0.152022[/C][C]-1.281[/C][C]0.102188[/C][/ROW]
[ROW][C]11[/C][C]0.221842[/C][C]1.8693[/C][C]0.032855[/C][/ROW]
[ROW][C]12[/C][C]-0.194869[/C][C]-1.642[/C][C]0.052506[/C][/ROW]
[ROW][C]13[/C][C]0.027618[/C][C]0.2327[/C][C]0.408328[/C][/ROW]
[ROW][C]14[/C][C]0.074491[/C][C]0.6277[/C][C]0.266117[/C][/ROW]
[ROW][C]15[/C][C]-0.025871[/C][C]-0.218[/C][C]0.41403[/C][/ROW]
[ROW][C]16[/C][C]-0.008648[/C][C]-0.0729[/C][C]0.471058[/C][/ROW]
[ROW][C]17[/C][C]-0.20648[/C][C]-1.7398[/C][C]0.043111[/C][/ROW]
[ROW][C]18[/C][C]-0.077294[/C][C]-0.6513[/C][C]0.258481[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151308&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151308&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	0.262492	2.2118	0.0151
2	-0.016807	-0.1416	0.443891
3	0.210061	1.77	0.04051
4	0.073437	0.6188	0.269018
5	0.171845	1.448	0.076011
6	-0.184275	-1.5527	0.062467
7	-0.016932	-0.1427	0.443478
8	0.055221	0.4653	0.321569
9	-0.078974	-0.6654	0.253961
10	-0.152022	-1.281	0.102188
11	0.221842	1.8693	0.032855
12	-0.194869	-1.642	0.052506
13	0.027618	0.2327	0.408328
14	0.074491	0.6277	0.266117
15	-0.025871	-0.218	0.41403
16	-0.008648	-0.0729	0.471058
17	-0.20648	-1.7398	0.043111
18	-0.077294	-0.6513	0.258481

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 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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):

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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code