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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 16 Dec 2009 09:17:43 -0700

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/2009/Dec/16/t1260980339md7ym8c4woi5n1v.htm/, Retrieved Tue, 30 Apr 2024 15:53:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68455, Retrieved Tue, 30 Apr 2024 15:53:04 +0000

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Estimated Impact

109

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-       [(Partial) Autocorrelation Function] [] [2009-12-16 16:17:43] [df67ec12d4744494b58d8461e1971283] [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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68455&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68455&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68455&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.637359	-4.3695	3.4e-05
2	0.077239	0.5295	0.299466
3	0.321147	2.2017	0.016316
4	-0.326927	-2.2413	0.014884
5	0.085354	0.5852	0.28062
6	0.173699	1.1908	0.119851
7	-0.29586	-2.0283	0.024108
8	0.236982	1.6247	0.055461
9	-0.12252	-0.84	0.202592
10	-0.050625	-0.3471	0.365046
11	0.199809	1.3698	0.088626
12	-0.200078	-1.3717	0.08834
13	0.065096	0.4463	0.328724
14	0.023679	0.1623	0.435869
15	0.016306	0.1118	0.455735
16	-0.094427	-0.6474	0.260274
17	0.107527	0.7372	0.232341

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.637359 & -4.3695 & 3.4e-05 \tabularnewline
2 & 0.077239 & 0.5295 & 0.299466 \tabularnewline
3 & 0.321147 & 2.2017 & 0.016316 \tabularnewline
4 & -0.326927 & -2.2413 & 0.014884 \tabularnewline
5 & 0.085354 & 0.5852 & 0.28062 \tabularnewline
6 & 0.173699 & 1.1908 & 0.119851 \tabularnewline
7 & -0.29586 & -2.0283 & 0.024108 \tabularnewline
8 & 0.236982 & 1.6247 & 0.055461 \tabularnewline
9 & -0.12252 & -0.84 & 0.202592 \tabularnewline
10 & -0.050625 & -0.3471 & 0.365046 \tabularnewline
11 & 0.199809 & 1.3698 & 0.088626 \tabularnewline
12 & -0.200078 & -1.3717 & 0.08834 \tabularnewline
13 & 0.065096 & 0.4463 & 0.328724 \tabularnewline
14 & 0.023679 & 0.1623 & 0.435869 \tabularnewline
15 & 0.016306 & 0.1118 & 0.455735 \tabularnewline
16 & -0.094427 & -0.6474 & 0.260274 \tabularnewline
17 & 0.107527 & 0.7372 & 0.232341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68455&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]-0.637359[/C][C]-4.3695[/C][C]3.4e-05[/C][/ROW]
[ROW][C]2[/C][C]0.077239[/C][C]0.5295[/C][C]0.299466[/C][/ROW]
[ROW][C]3[/C][C]0.321147[/C][C]2.2017[/C][C]0.016316[/C][/ROW]
[ROW][C]4[/C][C]-0.326927[/C][C]-2.2413[/C][C]0.014884[/C][/ROW]
[ROW][C]5[/C][C]0.085354[/C][C]0.5852[/C][C]0.28062[/C][/ROW]
[ROW][C]6[/C][C]0.173699[/C][C]1.1908[/C][C]0.119851[/C][/ROW]
[ROW][C]7[/C][C]-0.29586[/C][C]-2.0283[/C][C]0.024108[/C][/ROW]
[ROW][C]8[/C][C]0.236982[/C][C]1.6247[/C][C]0.055461[/C][/ROW]
[ROW][C]9[/C][C]-0.12252[/C][C]-0.84[/C][C]0.202592[/C][/ROW]
[ROW][C]10[/C][C]-0.050625[/C][C]-0.3471[/C][C]0.365046[/C][/ROW]
[ROW][C]11[/C][C]0.199809[/C][C]1.3698[/C][C]0.088626[/C][/ROW]
[ROW][C]12[/C][C]-0.200078[/C][C]-1.3717[/C][C]0.08834[/C][/ROW]
[ROW][C]13[/C][C]0.065096[/C][C]0.4463[/C][C]0.328724[/C][/ROW]
[ROW][C]14[/C][C]0.023679[/C][C]0.1623[/C][C]0.435869[/C][/ROW]
[ROW][C]15[/C][C]0.016306[/C][C]0.1118[/C][C]0.455735[/C][/ROW]
[ROW][C]16[/C][C]-0.094427[/C][C]-0.6474[/C][C]0.260274[/C][/ROW]
[ROW][C]17[/C][C]0.107527[/C][C]0.7372[/C][C]0.232341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68455&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68455&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	-0.637359	-4.3695	3.4e-05
2	0.077239	0.5295	0.299466
3	0.321147	2.2017	0.016316
4	-0.326927	-2.2413	0.014884
5	0.085354	0.5852	0.28062
6	0.173699	1.1908	0.119851
7	-0.29586	-2.0283	0.024108
8	0.236982	1.6247	0.055461
9	-0.12252	-0.84	0.202592
10	-0.050625	-0.3471	0.365046
11	0.199809	1.3698	0.088626
12	-0.200078	-1.3717	0.08834
13	0.065096	0.4463	0.328724
14	0.023679	0.1623	0.435869
15	0.016306	0.1118	0.455735
16	-0.094427	-0.6474	0.260274
17	0.107527	0.7372	0.232341

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.637359	-4.3695	3.4e-05
2	-0.554062	-3.7985	0.000209
3	0.108181	0.7416	0.230995
4	0.185376	1.2709	0.105014
5	-0.03065	-0.2101	0.417238
6	0.050935	0.3492	0.364253
7	-0.107914	-0.7398	0.231543
8	0.018136	0.1243	0.450792
9	-0.124234	-0.8517	0.199349
10	-0.163329	-1.1197	0.13426
11	0.106494	0.7301	0.234481
12	0.12345	0.8463	0.200829
13	0.022474	0.1541	0.439105
14	-0.243542	-1.6696	0.05082
15	0.104368	0.7155	0.238917
16	0.054236	0.3718	0.355849
17	-0.04093	-0.2806	0.390124

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.637359 & -4.3695 & 3.4e-05 \tabularnewline
2 & -0.554062 & -3.7985 & 0.000209 \tabularnewline
3 & 0.108181 & 0.7416 & 0.230995 \tabularnewline
4 & 0.185376 & 1.2709 & 0.105014 \tabularnewline
5 & -0.03065 & -0.2101 & 0.417238 \tabularnewline
6 & 0.050935 & 0.3492 & 0.364253 \tabularnewline
7 & -0.107914 & -0.7398 & 0.231543 \tabularnewline
8 & 0.018136 & 0.1243 & 0.450792 \tabularnewline
9 & -0.124234 & -0.8517 & 0.199349 \tabularnewline
10 & -0.163329 & -1.1197 & 0.13426 \tabularnewline
11 & 0.106494 & 0.7301 & 0.234481 \tabularnewline
12 & 0.12345 & 0.8463 & 0.200829 \tabularnewline
13 & 0.022474 & 0.1541 & 0.439105 \tabularnewline
14 & -0.243542 & -1.6696 & 0.05082 \tabularnewline
15 & 0.104368 & 0.7155 & 0.238917 \tabularnewline
16 & 0.054236 & 0.3718 & 0.355849 \tabularnewline
17 & -0.04093 & -0.2806 & 0.390124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68455&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]-0.637359[/C][C]-4.3695[/C][C]3.4e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.554062[/C][C]-3.7985[/C][C]0.000209[/C][/ROW]
[ROW][C]3[/C][C]0.108181[/C][C]0.7416[/C][C]0.230995[/C][/ROW]
[ROW][C]4[/C][C]0.185376[/C][C]1.2709[/C][C]0.105014[/C][/ROW]
[ROW][C]5[/C][C]-0.03065[/C][C]-0.2101[/C][C]0.417238[/C][/ROW]
[ROW][C]6[/C][C]0.050935[/C][C]0.3492[/C][C]0.364253[/C][/ROW]
[ROW][C]7[/C][C]-0.107914[/C][C]-0.7398[/C][C]0.231543[/C][/ROW]
[ROW][C]8[/C][C]0.018136[/C][C]0.1243[/C][C]0.450792[/C][/ROW]
[ROW][C]9[/C][C]-0.124234[/C][C]-0.8517[/C][C]0.199349[/C][/ROW]
[ROW][C]10[/C][C]-0.163329[/C][C]-1.1197[/C][C]0.13426[/C][/ROW]
[ROW][C]11[/C][C]0.106494[/C][C]0.7301[/C][C]0.234481[/C][/ROW]
[ROW][C]12[/C][C]0.12345[/C][C]0.8463[/C][C]0.200829[/C][/ROW]
[ROW][C]13[/C][C]0.022474[/C][C]0.1541[/C][C]0.439105[/C][/ROW]
[ROW][C]14[/C][C]-0.243542[/C][C]-1.6696[/C][C]0.05082[/C][/ROW]
[ROW][C]15[/C][C]0.104368[/C][C]0.7155[/C][C]0.238917[/C][/ROW]
[ROW][C]16[/C][C]0.054236[/C][C]0.3718[/C][C]0.355849[/C][/ROW]
[ROW][C]17[/C][C]-0.04093[/C][C]-0.2806[/C][C]0.390124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68455&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68455&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	-0.637359	-4.3695	3.4e-05
2	-0.554062	-3.7985	0.000209
3	0.108181	0.7416	0.230995
4	0.185376	1.2709	0.105014
5	-0.03065	-0.2101	0.417238
6	0.050935	0.3492	0.364253
7	-0.107914	-0.7398	0.231543
8	0.018136	0.1243	0.450792
9	-0.124234	-0.8517	0.199349
10	-0.163329	-1.1197	0.13426
11	0.106494	0.7301	0.234481
12	0.12345	0.8463	0.200829
13	0.022474	0.1541	0.439105
14	-0.243542	-1.6696	0.05082
15	0.104368	0.7155	0.238917
16	0.054236	0.3718	0.355849
17	-0.04093	-0.2806	0.390124

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code