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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 04 Dec 2009 10:43:26 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t1259948657g8upbrzskhh5vp1.htm/, Retrieved Sun, 28 Apr 2024 11:51:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63966, Retrieved Sun, 28 Apr 2024 11:51:43 +0000

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-       [(Partial) Autocorrelation Function] [] [2009-12-04 17:43:26] [99bf2a1e962091d45abf4c2600a412f9] [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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63966&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63966&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63966&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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.527377	-3.12	0.001806
2	0.124242	0.735	0.23361
3	-0.229307	-1.3566	0.091798
4	0.325972	1.9285	0.030969
5	-0.226635	-1.3408	0.094313
6	0.04687	0.2773	0.391596
7	0.068486	0.4052	0.34391
8	-0.164557	-0.9735	0.168484
9	0.089495	0.5295	0.299916
10	-0.064964	-0.3843	0.351528
11	0.281182	1.6635	0.052572
12	-0.334859	-1.9811	0.027743
13	0.030362	0.1796	0.429242
14	0.085624	0.5066	0.307821
15	0.12263	0.7255	0.236488
16	-0.146006	-0.8638	0.196793
17	0.011798	0.0698	0.472375

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.527377 & -3.12 & 0.001806 \tabularnewline
2 & 0.124242 & 0.735 & 0.23361 \tabularnewline
3 & -0.229307 & -1.3566 & 0.091798 \tabularnewline
4 & 0.325972 & 1.9285 & 0.030969 \tabularnewline
5 & -0.226635 & -1.3408 & 0.094313 \tabularnewline
6 & 0.04687 & 0.2773 & 0.391596 \tabularnewline
7 & 0.068486 & 0.4052 & 0.34391 \tabularnewline
8 & -0.164557 & -0.9735 & 0.168484 \tabularnewline
9 & 0.089495 & 0.5295 & 0.299916 \tabularnewline
10 & -0.064964 & -0.3843 & 0.351528 \tabularnewline
11 & 0.281182 & 1.6635 & 0.052572 \tabularnewline
12 & -0.334859 & -1.9811 & 0.027743 \tabularnewline
13 & 0.030362 & 0.1796 & 0.429242 \tabularnewline
14 & 0.085624 & 0.5066 & 0.307821 \tabularnewline
15 & 0.12263 & 0.7255 & 0.236488 \tabularnewline
16 & -0.146006 & -0.8638 & 0.196793 \tabularnewline
17 & 0.011798 & 0.0698 & 0.472375 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63966&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]-0.527377[/C][C]-3.12[/C][C]0.001806[/C][/ROW]
[ROW][C]2[/C][C]0.124242[/C][C]0.735[/C][C]0.23361[/C][/ROW]
[ROW][C]3[/C][C]-0.229307[/C][C]-1.3566[/C][C]0.091798[/C][/ROW]
[ROW][C]4[/C][C]0.325972[/C][C]1.9285[/C][C]0.030969[/C][/ROW]
[ROW][C]5[/C][C]-0.226635[/C][C]-1.3408[/C][C]0.094313[/C][/ROW]
[ROW][C]6[/C][C]0.04687[/C][C]0.2773[/C][C]0.391596[/C][/ROW]
[ROW][C]7[/C][C]0.068486[/C][C]0.4052[/C][C]0.34391[/C][/ROW]
[ROW][C]8[/C][C]-0.164557[/C][C]-0.9735[/C][C]0.168484[/C][/ROW]
[ROW][C]9[/C][C]0.089495[/C][C]0.5295[/C][C]0.299916[/C][/ROW]
[ROW][C]10[/C][C]-0.064964[/C][C]-0.3843[/C][C]0.351528[/C][/ROW]
[ROW][C]11[/C][C]0.281182[/C][C]1.6635[/C][C]0.052572[/C][/ROW]
[ROW][C]12[/C][C]-0.334859[/C][C]-1.9811[/C][C]0.027743[/C][/ROW]
[ROW][C]13[/C][C]0.030362[/C][C]0.1796[/C][C]0.429242[/C][/ROW]
[ROW][C]14[/C][C]0.085624[/C][C]0.5066[/C][C]0.307821[/C][/ROW]
[ROW][C]15[/C][C]0.12263[/C][C]0.7255[/C][C]0.236488[/C][/ROW]
[ROW][C]16[/C][C]-0.146006[/C][C]-0.8638[/C][C]0.196793[/C][/ROW]
[ROW][C]17[/C][C]0.011798[/C][C]0.0698[/C][C]0.472375[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63966&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63966&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	-0.527377	-3.12	0.001806
2	0.124242	0.735	0.23361
3	-0.229307	-1.3566	0.091798
4	0.325972	1.9285	0.030969
5	-0.226635	-1.3408	0.094313
6	0.04687	0.2773	0.391596
7	0.068486	0.4052	0.34391
8	-0.164557	-0.9735	0.168484
9	0.089495	0.5295	0.299916
10	-0.064964	-0.3843	0.351528
11	0.281182	1.6635	0.052572
12	-0.334859	-1.9811	0.027743
13	0.030362	0.1796	0.429242
14	0.085624	0.5066	0.307821
15	0.12263	0.7255	0.236488
16	-0.146006	-0.8638	0.196793
17	0.011798	0.0698	0.472375

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.527377	-3.12	0.001806
2	-0.213172	-1.2611	0.107799
3	-0.380569	-2.2515	0.015368
4	0.028327	0.1676	0.433937
5	-0.063201	-0.3739	0.355367
6	-0.139648	-0.8262	0.207153
7	0.117956	0.6978	0.244945
8	-0.245851	-1.4545	0.077363
9	-0.126731	-0.7498	0.229207
10	-0.136628	-0.8083	0.212189
11	0.170256	1.0072	0.160365
12	0.012239	0.0724	0.471345
13	-0.302317	-1.7885	0.041175
14	-0.035676	-0.2111	0.41703
15	0.035078	0.2075	0.418403
16	0.032577	0.1927	0.424143
17	0.067395	0.3987	0.346263

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.527377 & -3.12 & 0.001806 \tabularnewline
2 & -0.213172 & -1.2611 & 0.107799 \tabularnewline
3 & -0.380569 & -2.2515 & 0.015368 \tabularnewline
4 & 0.028327 & 0.1676 & 0.433937 \tabularnewline
5 & -0.063201 & -0.3739 & 0.355367 \tabularnewline
6 & -0.139648 & -0.8262 & 0.207153 \tabularnewline
7 & 0.117956 & 0.6978 & 0.244945 \tabularnewline
8 & -0.245851 & -1.4545 & 0.077363 \tabularnewline
9 & -0.126731 & -0.7498 & 0.229207 \tabularnewline
10 & -0.136628 & -0.8083 & 0.212189 \tabularnewline
11 & 0.170256 & 1.0072 & 0.160365 \tabularnewline
12 & 0.012239 & 0.0724 & 0.471345 \tabularnewline
13 & -0.302317 & -1.7885 & 0.041175 \tabularnewline
14 & -0.035676 & -0.2111 & 0.41703 \tabularnewline
15 & 0.035078 & 0.2075 & 0.418403 \tabularnewline
16 & 0.032577 & 0.1927 & 0.424143 \tabularnewline
17 & 0.067395 & 0.3987 & 0.346263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63966&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]-0.527377[/C][C]-3.12[/C][C]0.001806[/C][/ROW]
[ROW][C]2[/C][C]-0.213172[/C][C]-1.2611[/C][C]0.107799[/C][/ROW]
[ROW][C]3[/C][C]-0.380569[/C][C]-2.2515[/C][C]0.015368[/C][/ROW]
[ROW][C]4[/C][C]0.028327[/C][C]0.1676[/C][C]0.433937[/C][/ROW]
[ROW][C]5[/C][C]-0.063201[/C][C]-0.3739[/C][C]0.355367[/C][/ROW]
[ROW][C]6[/C][C]-0.139648[/C][C]-0.8262[/C][C]0.207153[/C][/ROW]
[ROW][C]7[/C][C]0.117956[/C][C]0.6978[/C][C]0.244945[/C][/ROW]
[ROW][C]8[/C][C]-0.245851[/C][C]-1.4545[/C][C]0.077363[/C][/ROW]
[ROW][C]9[/C][C]-0.126731[/C][C]-0.7498[/C][C]0.229207[/C][/ROW]
[ROW][C]10[/C][C]-0.136628[/C][C]-0.8083[/C][C]0.212189[/C][/ROW]
[ROW][C]11[/C][C]0.170256[/C][C]1.0072[/C][C]0.160365[/C][/ROW]
[ROW][C]12[/C][C]0.012239[/C][C]0.0724[/C][C]0.471345[/C][/ROW]
[ROW][C]13[/C][C]-0.302317[/C][C]-1.7885[/C][C]0.041175[/C][/ROW]
[ROW][C]14[/C][C]-0.035676[/C][C]-0.2111[/C][C]0.41703[/C][/ROW]
[ROW][C]15[/C][C]0.035078[/C][C]0.2075[/C][C]0.418403[/C][/ROW]
[ROW][C]16[/C][C]0.032577[/C][C]0.1927[/C][C]0.424143[/C][/ROW]
[ROW][C]17[/C][C]0.067395[/C][C]0.3987[/C][C]0.346263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63966&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63966&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	-0.527377	-3.12	0.001806
2	-0.213172	-1.2611	0.107799
3	-0.380569	-2.2515	0.015368
4	0.028327	0.1676	0.433937
5	-0.063201	-0.3739	0.355367
6	-0.139648	-0.8262	0.207153
7	0.117956	0.6978	0.244945
8	-0.245851	-1.4545	0.077363
9	-0.126731	-0.7498	0.229207
10	-0.136628	-0.8083	0.212189
11	0.170256	1.0072	0.160365
12	0.012239	0.0724	0.471345
13	-0.302317	-1.7885	0.041175
14	-0.035676	-0.2111	0.41703
15	0.035078	0.2075	0.418403
16	0.032577	0.1927	0.424143
17	0.067395	0.3987	0.346263

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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