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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Nov 2007 03:28:04 -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/Nov/23/t1195813171ad7i3czwa1g3hro.htm/, Retrieved Sun, 28 Apr 2024 21:16:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6134, Retrieved Sun, 28 Apr 2024 21:16:54 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Q2, groep 1

Estimated Impact

210

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

-       [(Partial) Autocorrelation Function] [Q2, groep 1] [2007-11-23 10:28:04] [ce556af355e2eff84137e549c6ea8397] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6134&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]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=6134&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6134&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.9443	0
1	0.086098	0.7701	0.221758
2	-0.126652	-1.1328	0.869661
3	0.238801	2.1359	0.017873
4	-0.187975	-1.6813	0.951697
5	-0.001197	-0.0107	0.504257
6	0.400532	3.5825	0.000291
7	0.034563	0.3091	0.37901
8	-0.134997	-1.2075	0.884592
9	0.158917	1.4214	0.079544
10	-0.272763	-2.4397	0.991544
11	-0.093679	-0.8379	0.797707
12	0.448101	4.0079	6.8e-05
13	-0.044617	-0.3991	0.654547
14	-0.190526	-1.7041	0.953879
15	0.090011	0.8051	0.21158
16	-0.19989	-1.7879	0.961208
17	-0.106404	-0.9517	0.827944
18	0.265783	2.3772	0.009915

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.9443 & 0 \tabularnewline
1 & 0.086098 & 0.7701 & 0.221758 \tabularnewline
2 & -0.126652 & -1.1328 & 0.869661 \tabularnewline
3 & 0.238801 & 2.1359 & 0.017873 \tabularnewline
4 & -0.187975 & -1.6813 & 0.951697 \tabularnewline
5 & -0.001197 & -0.0107 & 0.504257 \tabularnewline
6 & 0.400532 & 3.5825 & 0.000291 \tabularnewline
7 & 0.034563 & 0.3091 & 0.37901 \tabularnewline
8 & -0.134997 & -1.2075 & 0.884592 \tabularnewline
9 & 0.158917 & 1.4214 & 0.079544 \tabularnewline
10 & -0.272763 & -2.4397 & 0.991544 \tabularnewline
11 & -0.093679 & -0.8379 & 0.797707 \tabularnewline
12 & 0.448101 & 4.0079 & 6.8e-05 \tabularnewline
13 & -0.044617 & -0.3991 & 0.654547 \tabularnewline
14 & -0.190526 & -1.7041 & 0.953879 \tabularnewline
15 & 0.090011 & 0.8051 & 0.21158 \tabularnewline
16 & -0.19989 & -1.7879 & 0.961208 \tabularnewline
17 & -0.106404 & -0.9517 & 0.827944 \tabularnewline
18 & 0.265783 & 2.3772 & 0.009915 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6134&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]8.9443[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.086098[/C][C]0.7701[/C][C]0.221758[/C][/ROW]
[ROW][C]2[/C][C]-0.126652[/C][C]-1.1328[/C][C]0.869661[/C][/ROW]
[ROW][C]3[/C][C]0.238801[/C][C]2.1359[/C][C]0.017873[/C][/ROW]
[ROW][C]4[/C][C]-0.187975[/C][C]-1.6813[/C][C]0.951697[/C][/ROW]
[ROW][C]5[/C][C]-0.001197[/C][C]-0.0107[/C][C]0.504257[/C][/ROW]
[ROW][C]6[/C][C]0.400532[/C][C]3.5825[/C][C]0.000291[/C][/ROW]
[ROW][C]7[/C][C]0.034563[/C][C]0.3091[/C][C]0.37901[/C][/ROW]
[ROW][C]8[/C][C]-0.134997[/C][C]-1.2075[/C][C]0.884592[/C][/ROW]
[ROW][C]9[/C][C]0.158917[/C][C]1.4214[/C][C]0.079544[/C][/ROW]
[ROW][C]10[/C][C]-0.272763[/C][C]-2.4397[/C][C]0.991544[/C][/ROW]
[ROW][C]11[/C][C]-0.093679[/C][C]-0.8379[/C][C]0.797707[/C][/ROW]
[ROW][C]12[/C][C]0.448101[/C][C]4.0079[/C][C]6.8e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.044617[/C][C]-0.3991[/C][C]0.654547[/C][/ROW]
[ROW][C]14[/C][C]-0.190526[/C][C]-1.7041[/C][C]0.953879[/C][/ROW]
[ROW][C]15[/C][C]0.090011[/C][C]0.8051[/C][C]0.21158[/C][/ROW]
[ROW][C]16[/C][C]-0.19989[/C][C]-1.7879[/C][C]0.961208[/C][/ROW]
[ROW][C]17[/C][C]-0.106404[/C][C]-0.9517[/C][C]0.827944[/C][/ROW]
[ROW][C]18[/C][C]0.265783[/C][C]2.3772[/C][C]0.009915[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6134&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6134&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	8.9443	0
1	0.086098	0.7701	0.221758
2	-0.126652	-1.1328	0.869661
3	0.238801	2.1359	0.017873
4	-0.187975	-1.6813	0.951697
5	-0.001197	-0.0107	0.504257
6	0.400532	3.5825	0.000291
7	0.034563	0.3091	0.37901
8	-0.134997	-1.2075	0.884592
9	0.158917	1.4214	0.079544
10	-0.272763	-2.4397	0.991544
11	-0.093679	-0.8379	0.797707
12	0.448101	4.0079	6.8e-05
13	-0.044617	-0.3991	0.654547
14	-0.190526	-1.7041	0.953879
15	0.090011	0.8051	0.21158
16	-0.19989	-1.7879	0.961208
17	-0.106404	-0.9517	0.827944
18	0.265783	2.3772	0.009915

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.086098	0.7701	0.221758
1	-0.135066	-1.2081	0.88471
2	0.26969	2.4122	0.009073
3	-0.291804	-2.61	0.994597
4	0.184898	1.6538	0.051046
5	0.263153	2.3537	0.010521
6	0.066407	0.594	0.277106
7	-0.167353	-1.4969	0.930817
8	0.113568	1.0158	0.156397
9	-0.322366	-2.8833	0.997474
10	0.160301	1.4338	0.077766
11	0.200482	1.7932	0.038363
12	-0.029437	-0.2633	0.603499
13	-0.236409	-2.1145	0.981207
14	0.026244	0.2347	0.407507
15	-0.019844	-0.1775	0.570213
16	0.069784	0.6242	0.267147
17	-0.084363	-0.7546	0.773636
18	-0.005664	-0.0507	0.520138

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.086098 & 0.7701 & 0.221758 \tabularnewline
1 & -0.135066 & -1.2081 & 0.88471 \tabularnewline
2 & 0.26969 & 2.4122 & 0.009073 \tabularnewline
3 & -0.291804 & -2.61 & 0.994597 \tabularnewline
4 & 0.184898 & 1.6538 & 0.051046 \tabularnewline
5 & 0.263153 & 2.3537 & 0.010521 \tabularnewline
6 & 0.066407 & 0.594 & 0.277106 \tabularnewline
7 & -0.167353 & -1.4969 & 0.930817 \tabularnewline
8 & 0.113568 & 1.0158 & 0.156397 \tabularnewline
9 & -0.322366 & -2.8833 & 0.997474 \tabularnewline
10 & 0.160301 & 1.4338 & 0.077766 \tabularnewline
11 & 0.200482 & 1.7932 & 0.038363 \tabularnewline
12 & -0.029437 & -0.2633 & 0.603499 \tabularnewline
13 & -0.236409 & -2.1145 & 0.981207 \tabularnewline
14 & 0.026244 & 0.2347 & 0.407507 \tabularnewline
15 & -0.019844 & -0.1775 & 0.570213 \tabularnewline
16 & 0.069784 & 0.6242 & 0.267147 \tabularnewline
17 & -0.084363 & -0.7546 & 0.773636 \tabularnewline
18 & -0.005664 & -0.0507 & 0.520138 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6134&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]0.086098[/C][C]0.7701[/C][C]0.221758[/C][/ROW]
[ROW][C]1[/C][C]-0.135066[/C][C]-1.2081[/C][C]0.88471[/C][/ROW]
[ROW][C]2[/C][C]0.26969[/C][C]2.4122[/C][C]0.009073[/C][/ROW]
[ROW][C]3[/C][C]-0.291804[/C][C]-2.61[/C][C]0.994597[/C][/ROW]
[ROW][C]4[/C][C]0.184898[/C][C]1.6538[/C][C]0.051046[/C][/ROW]
[ROW][C]5[/C][C]0.263153[/C][C]2.3537[/C][C]0.010521[/C][/ROW]
[ROW][C]6[/C][C]0.066407[/C][C]0.594[/C][C]0.277106[/C][/ROW]
[ROW][C]7[/C][C]-0.167353[/C][C]-1.4969[/C][C]0.930817[/C][/ROW]
[ROW][C]8[/C][C]0.113568[/C][C]1.0158[/C][C]0.156397[/C][/ROW]
[ROW][C]9[/C][C]-0.322366[/C][C]-2.8833[/C][C]0.997474[/C][/ROW]
[ROW][C]10[/C][C]0.160301[/C][C]1.4338[/C][C]0.077766[/C][/ROW]
[ROW][C]11[/C][C]0.200482[/C][C]1.7932[/C][C]0.038363[/C][/ROW]
[ROW][C]12[/C][C]-0.029437[/C][C]-0.2633[/C][C]0.603499[/C][/ROW]
[ROW][C]13[/C][C]-0.236409[/C][C]-2.1145[/C][C]0.981207[/C][/ROW]
[ROW][C]14[/C][C]0.026244[/C][C]0.2347[/C][C]0.407507[/C][/ROW]
[ROW][C]15[/C][C]-0.019844[/C][C]-0.1775[/C][C]0.570213[/C][/ROW]
[ROW][C]16[/C][C]0.069784[/C][C]0.6242[/C][C]0.267147[/C][/ROW]
[ROW][C]17[/C][C]-0.084363[/C][C]-0.7546[/C][C]0.773636[/C][/ROW]
[ROW][C]18[/C][C]-0.005664[/C][C]-0.0507[/C][C]0.520138[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6134&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6134&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	0.086098	0.7701	0.221758
1	-0.135066	-1.2081	0.88471
2	0.26969	2.4122	0.009073
3	-0.291804	-2.61	0.994597
4	0.184898	1.6538	0.051046
5	0.263153	2.3537	0.010521
6	0.066407	0.594	0.277106
7	-0.167353	-1.4969	0.930817
8	0.113568	1.0158	0.156397
9	-0.322366	-2.8833	0.997474
10	0.160301	1.4338	0.077766
11	0.200482	1.7932	0.038363
12	-0.029437	-0.2633	0.603499
13	-0.236409	-2.1145	0.981207
14	0.026244	0.2347	0.407507
15	-0.019844	-0.1775	0.570213
16	0.069784	0.6242	0.267147
17	-0.084363	-0.7546	0.773636
18	-0.005664	-0.0507	0.520138

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 = 0 ; par5 = 12 ;

Parameters (R input):

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