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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 19 May 2011 17:10:09 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/19/t1305824752u01tql11vryhxlp.htm/, Retrieved Sun, 12 May 2024 08:57:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122154, Retrieved Sun, 12 May 2024 08:57:16 +0000

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-       [(Partial) Autocorrelation Function] [] [2011-05-19 17:10:09] [164acd287bf1b95108b808ea4c161e74] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122154&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122154&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122154&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.236566	-2.0212	0.023462
2	0.024254	0.2072	0.418207
3	-0.01274	-0.1089	0.45681
4	0.125557	1.0728	0.143456
5	0.120987	1.0337	0.152341
6	-0.278327	-2.378	0.010013
7	0.059653	0.5097	0.305909
8	0.065487	0.5595	0.288759
9	-0.084098	-0.7185	0.237362
10	-0.033777	-0.2886	0.386857
11	-0.311207	-2.659	0.004814
12	0.706639	6.0375	0
13	-0.237065	-2.0255	0.023237
14	-0.042189	-0.3605	0.359771
15	-0.086362	-0.7379	0.231478
16	0.040917	0.3496	0.363826
17	0.045464	0.3884	0.349408
18	-0.253025	-2.1618	0.016954

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.236566 & -2.0212 & 0.023462 \tabularnewline
2 & 0.024254 & 0.2072 & 0.418207 \tabularnewline
3 & -0.01274 & -0.1089 & 0.45681 \tabularnewline
4 & 0.125557 & 1.0728 & 0.143456 \tabularnewline
5 & 0.120987 & 1.0337 & 0.152341 \tabularnewline
6 & -0.278327 & -2.378 & 0.010013 \tabularnewline
7 & 0.059653 & 0.5097 & 0.305909 \tabularnewline
8 & 0.065487 & 0.5595 & 0.288759 \tabularnewline
9 & -0.084098 & -0.7185 & 0.237362 \tabularnewline
10 & -0.033777 & -0.2886 & 0.386857 \tabularnewline
11 & -0.311207 & -2.659 & 0.004814 \tabularnewline
12 & 0.706639 & 6.0375 & 0 \tabularnewline
13 & -0.237065 & -2.0255 & 0.023237 \tabularnewline
14 & -0.042189 & -0.3605 & 0.359771 \tabularnewline
15 & -0.086362 & -0.7379 & 0.231478 \tabularnewline
16 & 0.040917 & 0.3496 & 0.363826 \tabularnewline
17 & 0.045464 & 0.3884 & 0.349408 \tabularnewline
18 & -0.253025 & -2.1618 & 0.016954 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122154&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]-0.236566[/C][C]-2.0212[/C][C]0.023462[/C][/ROW]
[ROW][C]2[/C][C]0.024254[/C][C]0.2072[/C][C]0.418207[/C][/ROW]
[ROW][C]3[/C][C]-0.01274[/C][C]-0.1089[/C][C]0.45681[/C][/ROW]
[ROW][C]4[/C][C]0.125557[/C][C]1.0728[/C][C]0.143456[/C][/ROW]
[ROW][C]5[/C][C]0.120987[/C][C]1.0337[/C][C]0.152341[/C][/ROW]
[ROW][C]6[/C][C]-0.278327[/C][C]-2.378[/C][C]0.010013[/C][/ROW]
[ROW][C]7[/C][C]0.059653[/C][C]0.5097[/C][C]0.305909[/C][/ROW]
[ROW][C]8[/C][C]0.065487[/C][C]0.5595[/C][C]0.288759[/C][/ROW]
[ROW][C]9[/C][C]-0.084098[/C][C]-0.7185[/C][C]0.237362[/C][/ROW]
[ROW][C]10[/C][C]-0.033777[/C][C]-0.2886[/C][C]0.386857[/C][/ROW]
[ROW][C]11[/C][C]-0.311207[/C][C]-2.659[/C][C]0.004814[/C][/ROW]
[ROW][C]12[/C][C]0.706639[/C][C]6.0375[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.237065[/C][C]-2.0255[/C][C]0.023237[/C][/ROW]
[ROW][C]14[/C][C]-0.042189[/C][C]-0.3605[/C][C]0.359771[/C][/ROW]
[ROW][C]15[/C][C]-0.086362[/C][C]-0.7379[/C][C]0.231478[/C][/ROW]
[ROW][C]16[/C][C]0.040917[/C][C]0.3496[/C][C]0.363826[/C][/ROW]
[ROW][C]17[/C][C]0.045464[/C][C]0.3884[/C][C]0.349408[/C][/ROW]
[ROW][C]18[/C][C]-0.253025[/C][C]-2.1618[/C][C]0.016954[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122154&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122154&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	-0.236566	-2.0212	0.023462
2	0.024254	0.2072	0.418207
3	-0.01274	-0.1089	0.45681
4	0.125557	1.0728	0.143456
5	0.120987	1.0337	0.152341
6	-0.278327	-2.378	0.010013
7	0.059653	0.5097	0.305909
8	0.065487	0.5595	0.288759
9	-0.084098	-0.7185	0.237362
10	-0.033777	-0.2886	0.386857
11	-0.311207	-2.659	0.004814
12	0.706639	6.0375	0
13	-0.237065	-2.0255	0.023237
14	-0.042189	-0.3605	0.359771
15	-0.086362	-0.7379	0.231478
16	0.040917	0.3496	0.363826
17	0.045464	0.3884	0.349408
18	-0.253025	-2.1618	0.016954

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.236566	-2.0212	0.023462
2	-0.03359	-0.287	0.387465
3	-0.015648	-0.1337	0.447004
4	0.126908	1.0843	0.1409
5	0.194851	1.6648	0.050119
6	-0.223348	-1.9083	0.030143
7	-0.071361	-0.6097	0.271974
8	0.057218	0.4889	0.313199
9	-0.101889	-0.8705	0.193429
10	-0.025094	-0.2144	0.415414
11	-0.304031	-2.5976	0.005674
12	0.651184	5.5637	0
13	-0.040306	-0.3444	0.365776
14	-0.12636	-1.0796	0.141933
15	-0.190355	-1.6264	0.054088
16	-0.202539	-1.7305	0.043884
17	-0.242753	-2.0741	0.020799
18	0.025446	0.2174	0.414248

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.236566 & -2.0212 & 0.023462 \tabularnewline
2 & -0.03359 & -0.287 & 0.387465 \tabularnewline
3 & -0.015648 & -0.1337 & 0.447004 \tabularnewline
4 & 0.126908 & 1.0843 & 0.1409 \tabularnewline
5 & 0.194851 & 1.6648 & 0.050119 \tabularnewline
6 & -0.223348 & -1.9083 & 0.030143 \tabularnewline
7 & -0.071361 & -0.6097 & 0.271974 \tabularnewline
8 & 0.057218 & 0.4889 & 0.313199 \tabularnewline
9 & -0.101889 & -0.8705 & 0.193429 \tabularnewline
10 & -0.025094 & -0.2144 & 0.415414 \tabularnewline
11 & -0.304031 & -2.5976 & 0.005674 \tabularnewline
12 & 0.651184 & 5.5637 & 0 \tabularnewline
13 & -0.040306 & -0.3444 & 0.365776 \tabularnewline
14 & -0.12636 & -1.0796 & 0.141933 \tabularnewline
15 & -0.190355 & -1.6264 & 0.054088 \tabularnewline
16 & -0.202539 & -1.7305 & 0.043884 \tabularnewline
17 & -0.242753 & -2.0741 & 0.020799 \tabularnewline
18 & 0.025446 & 0.2174 & 0.414248 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122154&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]-0.236566[/C][C]-2.0212[/C][C]0.023462[/C][/ROW]
[ROW][C]2[/C][C]-0.03359[/C][C]-0.287[/C][C]0.387465[/C][/ROW]
[ROW][C]3[/C][C]-0.015648[/C][C]-0.1337[/C][C]0.447004[/C][/ROW]
[ROW][C]4[/C][C]0.126908[/C][C]1.0843[/C][C]0.1409[/C][/ROW]
[ROW][C]5[/C][C]0.194851[/C][C]1.6648[/C][C]0.050119[/C][/ROW]
[ROW][C]6[/C][C]-0.223348[/C][C]-1.9083[/C][C]0.030143[/C][/ROW]
[ROW][C]7[/C][C]-0.071361[/C][C]-0.6097[/C][C]0.271974[/C][/ROW]
[ROW][C]8[/C][C]0.057218[/C][C]0.4889[/C][C]0.313199[/C][/ROW]
[ROW][C]9[/C][C]-0.101889[/C][C]-0.8705[/C][C]0.193429[/C][/ROW]
[ROW][C]10[/C][C]-0.025094[/C][C]-0.2144[/C][C]0.415414[/C][/ROW]
[ROW][C]11[/C][C]-0.304031[/C][C]-2.5976[/C][C]0.005674[/C][/ROW]
[ROW][C]12[/C][C]0.651184[/C][C]5.5637[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.040306[/C][C]-0.3444[/C][C]0.365776[/C][/ROW]
[ROW][C]14[/C][C]-0.12636[/C][C]-1.0796[/C][C]0.141933[/C][/ROW]
[ROW][C]15[/C][C]-0.190355[/C][C]-1.6264[/C][C]0.054088[/C][/ROW]
[ROW][C]16[/C][C]-0.202539[/C][C]-1.7305[/C][C]0.043884[/C][/ROW]
[ROW][C]17[/C][C]-0.242753[/C][C]-2.0741[/C][C]0.020799[/C][/ROW]
[ROW][C]18[/C][C]0.025446[/C][C]0.2174[/C][C]0.414248[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122154&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122154&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	-0.236566	-2.0212	0.023462
2	-0.03359	-0.287	0.387465
3	-0.015648	-0.1337	0.447004
4	0.126908	1.0843	0.1409
5	0.194851	1.6648	0.050119
6	-0.223348	-1.9083	0.030143
7	-0.071361	-0.6097	0.271974
8	0.057218	0.4889	0.313199
9	-0.101889	-0.8705	0.193429
10	-0.025094	-0.2144	0.415414
11	-0.304031	-2.5976	0.005674
12	0.651184	5.5637	0
13	-0.040306	-0.3444	0.365776
14	-0.12636	-1.0796	0.141933
15	-0.190355	-1.6264	0.054088
16	-0.202539	-1.7305	0.043884
17	-0.242753	-2.0741	0.020799
18	0.025446	0.2174	0.414248

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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Input Parameters & R Code