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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 06:25:45 -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/t1195824194sfx193yxjyq436k.htm/, Retrieved Mon, 29 Apr 2024 05:14:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6163, Retrieved Mon, 29 Apr 2024 05:14:32 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

185

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

-     [(Partial) Autocorrelation Function] [Partiel Autocorre...] [2007-11-22 13:00:02] [ced1562ed3c62c3bc1f3b66b8f83b537]
-   PD    [(Partial) Autocorrelation Function] [WS 9] [2007-11-23 13:25:45] [d41d8cd98f00b204e9800998ecf8427e] [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=6163&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=6163&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6163&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	8.544	0
1	0.963683	8.2337	0
2	0.922125	7.8786	0
3	0.879399	7.5136	0
4	0.84063	7.1823	0
5	0.811384	6.9325	0
6	0.77473	6.6193	0
7	0.722275	6.1711	0
8	0.658282	5.6244	0
9	0.604299	5.1631	1e-06
10	0.556807	4.7574	5e-06
11	0.525819	4.4926	1.3e-05
12	0.489271	4.1803	4e-05
13	0.429799	3.6722	0.000228
14	0.369565	3.1576	0.001157
15	0.31317	2.6757	0.0046
16	0.265121	2.2652	0.013234
17	0.228117	1.949	0.027567

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.544 & 0 \tabularnewline
1 & 0.963683 & 8.2337 & 0 \tabularnewline
2 & 0.922125 & 7.8786 & 0 \tabularnewline
3 & 0.879399 & 7.5136 & 0 \tabularnewline
4 & 0.84063 & 7.1823 & 0 \tabularnewline
5 & 0.811384 & 6.9325 & 0 \tabularnewline
6 & 0.77473 & 6.6193 & 0 \tabularnewline
7 & 0.722275 & 6.1711 & 0 \tabularnewline
8 & 0.658282 & 5.6244 & 0 \tabularnewline
9 & 0.604299 & 5.1631 & 1e-06 \tabularnewline
10 & 0.556807 & 4.7574 & 5e-06 \tabularnewline
11 & 0.525819 & 4.4926 & 1.3e-05 \tabularnewline
12 & 0.489271 & 4.1803 & 4e-05 \tabularnewline
13 & 0.429799 & 3.6722 & 0.000228 \tabularnewline
14 & 0.369565 & 3.1576 & 0.001157 \tabularnewline
15 & 0.31317 & 2.6757 & 0.0046 \tabularnewline
16 & 0.265121 & 2.2652 & 0.013234 \tabularnewline
17 & 0.228117 & 1.949 & 0.027567 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6163&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]8.544[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.963683[/C][C]8.2337[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.922125[/C][C]7.8786[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.879399[/C][C]7.5136[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.84063[/C][C]7.1823[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.811384[/C][C]6.9325[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.77473[/C][C]6.6193[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.722275[/C][C]6.1711[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.658282[/C][C]5.6244[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.604299[/C][C]5.1631[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.556807[/C][C]4.7574[/C][C]5e-06[/C][/ROW]
[ROW][C]11[/C][C]0.525819[/C][C]4.4926[/C][C]1.3e-05[/C][/ROW]
[ROW][C]12[/C][C]0.489271[/C][C]4.1803[/C][C]4e-05[/C][/ROW]
[ROW][C]13[/C][C]0.429799[/C][C]3.6722[/C][C]0.000228[/C][/ROW]
[ROW][C]14[/C][C]0.369565[/C][C]3.1576[/C][C]0.001157[/C][/ROW]
[ROW][C]15[/C][C]0.31317[/C][C]2.6757[/C][C]0.0046[/C][/ROW]
[ROW][C]16[/C][C]0.265121[/C][C]2.2652[/C][C]0.013234[/C][/ROW]
[ROW][C]17[/C][C]0.228117[/C][C]1.949[/C][C]0.027567[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6163&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6163&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	8.544	0
1	0.963683	8.2337	0
2	0.922125	7.8786	0
3	0.879399	7.5136	0
4	0.84063	7.1823	0
5	0.811384	6.9325	0
6	0.77473	6.6193	0
7	0.722275	6.1711	0
8	0.658282	5.6244	0
9	0.604299	5.1631	1e-06
10	0.556807	4.7574	5e-06
11	0.525819	4.4926	1.3e-05
12	0.489271	4.1803	4e-05
13	0.429799	3.6722	0.000228
14	0.369565	3.1576	0.001157
15	0.31317	2.6757	0.0046
16	0.265121	2.2652	0.013234
17	0.228117	1.949	0.027567

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.963683	8.2337	0
1	-0.091994	-0.786	0.782793
2	-0.032996	-0.2819	0.610598
3	0.035175	0.3005	0.382311
4	0.106183	0.9072	0.183635
5	-0.142639	-1.2187	0.886561
6	-0.237141	-2.0261	0.976797
7	-0.160772	-1.3736	0.913121
8	0.153249	1.3094	0.097259
9	0.017204	0.147	0.441772
10	0.144641	1.2358	0.110245
11	-0.131602	-1.1244	0.867737
12	-0.290656	-2.4834	0.992344
13	0.035917	0.3069	0.379907
14	0.076997	0.6579	0.256349
15	-0.043268	-0.3697	0.643656
16	-0.024472	-0.2091	0.58252
17	-0.096553	-0.8249	0.793956

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.963683 & 8.2337 & 0 \tabularnewline
1 & -0.091994 & -0.786 & 0.782793 \tabularnewline
2 & -0.032996 & -0.2819 & 0.610598 \tabularnewline
3 & 0.035175 & 0.3005 & 0.382311 \tabularnewline
4 & 0.106183 & 0.9072 & 0.183635 \tabularnewline
5 & -0.142639 & -1.2187 & 0.886561 \tabularnewline
6 & -0.237141 & -2.0261 & 0.976797 \tabularnewline
7 & -0.160772 & -1.3736 & 0.913121 \tabularnewline
8 & 0.153249 & 1.3094 & 0.097259 \tabularnewline
9 & 0.017204 & 0.147 & 0.441772 \tabularnewline
10 & 0.144641 & 1.2358 & 0.110245 \tabularnewline
11 & -0.131602 & -1.1244 & 0.867737 \tabularnewline
12 & -0.290656 & -2.4834 & 0.992344 \tabularnewline
13 & 0.035917 & 0.3069 & 0.379907 \tabularnewline
14 & 0.076997 & 0.6579 & 0.256349 \tabularnewline
15 & -0.043268 & -0.3697 & 0.643656 \tabularnewline
16 & -0.024472 & -0.2091 & 0.58252 \tabularnewline
17 & -0.096553 & -0.8249 & 0.793956 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6163&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]0.963683[/C][C]8.2337[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.091994[/C][C]-0.786[/C][C]0.782793[/C][/ROW]
[ROW][C]2[/C][C]-0.032996[/C][C]-0.2819[/C][C]0.610598[/C][/ROW]
[ROW][C]3[/C][C]0.035175[/C][C]0.3005[/C][C]0.382311[/C][/ROW]
[ROW][C]4[/C][C]0.106183[/C][C]0.9072[/C][C]0.183635[/C][/ROW]
[ROW][C]5[/C][C]-0.142639[/C][C]-1.2187[/C][C]0.886561[/C][/ROW]
[ROW][C]6[/C][C]-0.237141[/C][C]-2.0261[/C][C]0.976797[/C][/ROW]
[ROW][C]7[/C][C]-0.160772[/C][C]-1.3736[/C][C]0.913121[/C][/ROW]
[ROW][C]8[/C][C]0.153249[/C][C]1.3094[/C][C]0.097259[/C][/ROW]
[ROW][C]9[/C][C]0.017204[/C][C]0.147[/C][C]0.441772[/C][/ROW]
[ROW][C]10[/C][C]0.144641[/C][C]1.2358[/C][C]0.110245[/C][/ROW]
[ROW][C]11[/C][C]-0.131602[/C][C]-1.1244[/C][C]0.867737[/C][/ROW]
[ROW][C]12[/C][C]-0.290656[/C][C]-2.4834[/C][C]0.992344[/C][/ROW]
[ROW][C]13[/C][C]0.035917[/C][C]0.3069[/C][C]0.379907[/C][/ROW]
[ROW][C]14[/C][C]0.076997[/C][C]0.6579[/C][C]0.256349[/C][/ROW]
[ROW][C]15[/C][C]-0.043268[/C][C]-0.3697[/C][C]0.643656[/C][/ROW]
[ROW][C]16[/C][C]-0.024472[/C][C]-0.2091[/C][C]0.58252[/C][/ROW]
[ROW][C]17[/C][C]-0.096553[/C][C]-0.8249[/C][C]0.793956[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6163&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6163&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	0.963683	8.2337	0
1	-0.091994	-0.786	0.782793
2	-0.032996	-0.2819	0.610598
3	0.035175	0.3005	0.382311
4	0.106183	0.9072	0.183635
5	-0.142639	-1.2187	0.886561
6	-0.237141	-2.0261	0.976797
7	-0.160772	-1.3736	0.913121
8	0.153249	1.3094	0.097259
9	0.017204	0.147	0.441772
10	0.144641	1.2358	0.110245
11	-0.131602	-1.1244	0.867737
12	-0.290656	-2.4834	0.992344
13	0.035917	0.3069	0.379907
14	0.076997	0.6579	0.256349
15	-0.043268	-0.3697	0.643656
16	-0.024472	-0.2091	0.58252
17	-0.096553	-0.8249	0.793956

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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