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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 03 Dec 2007 13:00:30 -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/2007/Dec/03/t1196711321j7ebaivs1b33mvt.htm/, Retrieved Fri, 03 May 2024 15:10:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2355, Retrieved Fri, 03 May 2024 15:10:51 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

205

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [ARMA 1] [2007-12-03 20:00:30] [640491d00f3c9cca22cbf779aa38ac16] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2355&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2355&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2355&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.2462	0
1	0.951577	7.8469	0
2	0.886749	7.3123	0
3	0.825041	6.8035	0
4	0.75303	6.2096	0
5	0.669901	5.5241	0
6	0.589816	4.8637	4e-06
7	0.510143	4.2067	3.9e-05
8	0.42587	3.5118	0.000398
9	0.352996	2.9109	0.002434
10	0.282788	2.3319	0.011337
11	0.216499	1.7853	0.039336
12	0.168516	1.3896	0.084588
13	0.144929	1.1951	0.118097
14	0.128327	1.0582	0.146853
15	0.11494	0.9478	0.173289
16	0.111042	0.9157	0.181536
17	0.104878	0.8648	0.195081
18	0.100263	0.8268	0.205625

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.2462 & 0 \tabularnewline
1 & 0.951577 & 7.8469 & 0 \tabularnewline
2 & 0.886749 & 7.3123 & 0 \tabularnewline
3 & 0.825041 & 6.8035 & 0 \tabularnewline
4 & 0.75303 & 6.2096 & 0 \tabularnewline
5 & 0.669901 & 5.5241 & 0 \tabularnewline
6 & 0.589816 & 4.8637 & 4e-06 \tabularnewline
7 & 0.510143 & 4.2067 & 3.9e-05 \tabularnewline
8 & 0.42587 & 3.5118 & 0.000398 \tabularnewline
9 & 0.352996 & 2.9109 & 0.002434 \tabularnewline
10 & 0.282788 & 2.3319 & 0.011337 \tabularnewline
11 & 0.216499 & 1.7853 & 0.039336 \tabularnewline
12 & 0.168516 & 1.3896 & 0.084588 \tabularnewline
13 & 0.144929 & 1.1951 & 0.118097 \tabularnewline
14 & 0.128327 & 1.0582 & 0.146853 \tabularnewline
15 & 0.11494 & 0.9478 & 0.173289 \tabularnewline
16 & 0.111042 & 0.9157 & 0.181536 \tabularnewline
17 & 0.104878 & 0.8648 & 0.195081 \tabularnewline
18 & 0.100263 & 0.8268 & 0.205625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2355&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]0[/C][C]1[/C][C]8.2462[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.951577[/C][C]7.8469[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.886749[/C][C]7.3123[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.825041[/C][C]6.8035[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.75303[/C][C]6.2096[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.669901[/C][C]5.5241[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.589816[/C][C]4.8637[/C][C]4e-06[/C][/ROW]
[ROW][C]7[/C][C]0.510143[/C][C]4.2067[/C][C]3.9e-05[/C][/ROW]
[ROW][C]8[/C][C]0.42587[/C][C]3.5118[/C][C]0.000398[/C][/ROW]
[ROW][C]9[/C][C]0.352996[/C][C]2.9109[/C][C]0.002434[/C][/ROW]
[ROW][C]10[/C][C]0.282788[/C][C]2.3319[/C][C]0.011337[/C][/ROW]
[ROW][C]11[/C][C]0.216499[/C][C]1.7853[/C][C]0.039336[/C][/ROW]
[ROW][C]12[/C][C]0.168516[/C][C]1.3896[/C][C]0.084588[/C][/ROW]
[ROW][C]13[/C][C]0.144929[/C][C]1.1951[/C][C]0.118097[/C][/ROW]
[ROW][C]14[/C][C]0.128327[/C][C]1.0582[/C][C]0.146853[/C][/ROW]
[ROW][C]15[/C][C]0.11494[/C][C]0.9478[/C][C]0.173289[/C][/ROW]
[ROW][C]16[/C][C]0.111042[/C][C]0.9157[/C][C]0.181536[/C][/ROW]
[ROW][C]17[/C][C]0.104878[/C][C]0.8648[/C][C]0.195081[/C][/ROW]
[ROW][C]18[/C][C]0.100263[/C][C]0.8268[/C][C]0.205625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2355&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2355&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
0	1	8.2462	0
1	0.951577	7.8469	0
2	0.886749	7.3123	0
3	0.825041	6.8035	0
4	0.75303	6.2096	0
5	0.669901	5.5241	0
6	0.589816	4.8637	4e-06
7	0.510143	4.2067	3.9e-05
8	0.42587	3.5118	0.000398
9	0.352996	2.9109	0.002434
10	0.282788	2.3319	0.011337
11	0.216499	1.7853	0.039336
12	0.168516	1.3896	0.084588
13	0.144929	1.1951	0.118097
14	0.128327	1.0582	0.146853
15	0.11494	0.9478	0.173289
16	0.111042	0.9157	0.181536
17	0.104878	0.8648	0.195081
18	0.100263	0.8268	0.205625

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.951577	7.8469	0
1	-0.198396	-1.636	0.946771
2	0.028769	0.2372	0.406594
3	-0.164098	-1.3532	0.909762
4	-0.121857	-1.0049	0.840736
5	0.003988	0.0329	0.48693
6	-0.062733	-0.5173	0.69669
7	-0.078553	-0.6478	0.740342
8	0.085549	0.7055	0.241469
9	-0.083913	-0.692	0.754341
10	0.018697	0.1542	0.438963
11	0.125214	1.0325	0.152739
12	0.152014	1.2535	0.107151
13	0.002616	0.0216	0.491427
14	-0.013082	-0.1079	0.542795
15	-0.003586	-0.0296	0.511753
16	-0.09712	-0.8009	0.787003
17	0.012263	0.1011	0.459877
18	-0.023116	-0.1906	0.575303

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.951577 & 7.8469 & 0 \tabularnewline
1 & -0.198396 & -1.636 & 0.946771 \tabularnewline
2 & 0.028769 & 0.2372 & 0.406594 \tabularnewline
3 & -0.164098 & -1.3532 & 0.909762 \tabularnewline
4 & -0.121857 & -1.0049 & 0.840736 \tabularnewline
5 & 0.003988 & 0.0329 & 0.48693 \tabularnewline
6 & -0.062733 & -0.5173 & 0.69669 \tabularnewline
7 & -0.078553 & -0.6478 & 0.740342 \tabularnewline
8 & 0.085549 & 0.7055 & 0.241469 \tabularnewline
9 & -0.083913 & -0.692 & 0.754341 \tabularnewline
10 & 0.018697 & 0.1542 & 0.438963 \tabularnewline
11 & 0.125214 & 1.0325 & 0.152739 \tabularnewline
12 & 0.152014 & 1.2535 & 0.107151 \tabularnewline
13 & 0.002616 & 0.0216 & 0.491427 \tabularnewline
14 & -0.013082 & -0.1079 & 0.542795 \tabularnewline
15 & -0.003586 & -0.0296 & 0.511753 \tabularnewline
16 & -0.09712 & -0.8009 & 0.787003 \tabularnewline
17 & 0.012263 & 0.1011 & 0.459877 \tabularnewline
18 & -0.023116 & -0.1906 & 0.575303 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2355&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]0[/C][C]0.951577[/C][C]7.8469[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.198396[/C][C]-1.636[/C][C]0.946771[/C][/ROW]
[ROW][C]2[/C][C]0.028769[/C][C]0.2372[/C][C]0.406594[/C][/ROW]
[ROW][C]3[/C][C]-0.164098[/C][C]-1.3532[/C][C]0.909762[/C][/ROW]
[ROW][C]4[/C][C]-0.121857[/C][C]-1.0049[/C][C]0.840736[/C][/ROW]
[ROW][C]5[/C][C]0.003988[/C][C]0.0329[/C][C]0.48693[/C][/ROW]
[ROW][C]6[/C][C]-0.062733[/C][C]-0.5173[/C][C]0.69669[/C][/ROW]
[ROW][C]7[/C][C]-0.078553[/C][C]-0.6478[/C][C]0.740342[/C][/ROW]
[ROW][C]8[/C][C]0.085549[/C][C]0.7055[/C][C]0.241469[/C][/ROW]
[ROW][C]9[/C][C]-0.083913[/C][C]-0.692[/C][C]0.754341[/C][/ROW]
[ROW][C]10[/C][C]0.018697[/C][C]0.1542[/C][C]0.438963[/C][/ROW]
[ROW][C]11[/C][C]0.125214[/C][C]1.0325[/C][C]0.152739[/C][/ROW]
[ROW][C]12[/C][C]0.152014[/C][C]1.2535[/C][C]0.107151[/C][/ROW]
[ROW][C]13[/C][C]0.002616[/C][C]0.0216[/C][C]0.491427[/C][/ROW]
[ROW][C]14[/C][C]-0.013082[/C][C]-0.1079[/C][C]0.542795[/C][/ROW]
[ROW][C]15[/C][C]-0.003586[/C][C]-0.0296[/C][C]0.511753[/C][/ROW]
[ROW][C]16[/C][C]-0.09712[/C][C]-0.8009[/C][C]0.787003[/C][/ROW]
[ROW][C]17[/C][C]0.012263[/C][C]0.1011[/C][C]0.459877[/C][/ROW]
[ROW][C]18[/C][C]-0.023116[/C][C]-0.1906[/C][C]0.575303[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2355&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2355&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
0	0.951577	7.8469	0
1	-0.198396	-1.636	0.946771
2	0.028769	0.2372	0.406594
3	-0.164098	-1.3532	0.909762
4	-0.121857	-1.0049	0.840736
5	0.003988	0.0329	0.48693
6	-0.062733	-0.5173	0.69669
7	-0.078553	-0.6478	0.740342
8	0.085549	0.7055	0.241469
9	-0.083913	-0.692	0.754341
10	0.018697	0.1542	0.438963
11	0.125214	1.0325	0.152739
12	0.152014	1.2535	0.107151
13	0.002616	0.0216	0.491427
14	-0.013082	-0.1079	0.542795
15	-0.003586	-0.0296	0.511753
16	-0.09712	-0.8009	0.787003
17	0.012263	0.1011	0.459877
18	-0.023116	-0.1906	0.575303

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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