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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Nov 2007 09:34:26 -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/t1195835250a09ysx9qiwufxqc.htm/, Retrieved Sun, 28 Apr 2024 21:25:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6224, Retrieved Sun, 28 Apr 2024 21:25:29 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

174

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

-       [(Partial) Autocorrelation Function] [autocorrelatie in...] [2007-11-23 16:34:26] [bd02e85be52eb1cb060a2c60779eb820] [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=6224&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=6224&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6224&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	7.746	0
1	0.143189	1.1091	0.135898
2	0.085576	0.6629	0.254975
3	0.263337	2.0398	0.02289
4	-0.023449	-0.1816	0.57176
5	0.087077	0.6745	0.251293
6	0.191357	1.4822	0.071754
7	-0.135291	-1.048	0.850571
8	0.115282	0.893	0.18772
9	0.202163	1.5659	0.06131
10	-0.207435	-1.6068	0.943324
11	-0.057854	-0.4481	0.672166
12	-0.204951	-1.5875	0.941177
13	-0.253044	-1.9601	0.972682
14	0.092482	0.7164	0.238274
15	-0.135341	-1.0483	0.850657
16	-0.184691	-1.4306	0.921136
17	0.153394	1.1882	0.119722

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.143189 & 1.1091 & 0.135898 \tabularnewline
2 & 0.085576 & 0.6629 & 0.254975 \tabularnewline
3 & 0.263337 & 2.0398 & 0.02289 \tabularnewline
4 & -0.023449 & -0.1816 & 0.57176 \tabularnewline
5 & 0.087077 & 0.6745 & 0.251293 \tabularnewline
6 & 0.191357 & 1.4822 & 0.071754 \tabularnewline
7 & -0.135291 & -1.048 & 0.850571 \tabularnewline
8 & 0.115282 & 0.893 & 0.18772 \tabularnewline
9 & 0.202163 & 1.5659 & 0.06131 \tabularnewline
10 & -0.207435 & -1.6068 & 0.943324 \tabularnewline
11 & -0.057854 & -0.4481 & 0.672166 \tabularnewline
12 & -0.204951 & -1.5875 & 0.941177 \tabularnewline
13 & -0.253044 & -1.9601 & 0.972682 \tabularnewline
14 & 0.092482 & 0.7164 & 0.238274 \tabularnewline
15 & -0.135341 & -1.0483 & 0.850657 \tabularnewline
16 & -0.184691 & -1.4306 & 0.921136 \tabularnewline
17 & 0.153394 & 1.1882 & 0.119722 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6224&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.143189[/C][C]1.1091[/C][C]0.135898[/C][/ROW]
[ROW][C]2[/C][C]0.085576[/C][C]0.6629[/C][C]0.254975[/C][/ROW]
[ROW][C]3[/C][C]0.263337[/C][C]2.0398[/C][C]0.02289[/C][/ROW]
[ROW][C]4[/C][C]-0.023449[/C][C]-0.1816[/C][C]0.57176[/C][/ROW]
[ROW][C]5[/C][C]0.087077[/C][C]0.6745[/C][C]0.251293[/C][/ROW]
[ROW][C]6[/C][C]0.191357[/C][C]1.4822[/C][C]0.071754[/C][/ROW]
[ROW][C]7[/C][C]-0.135291[/C][C]-1.048[/C][C]0.850571[/C][/ROW]
[ROW][C]8[/C][C]0.115282[/C][C]0.893[/C][C]0.18772[/C][/ROW]
[ROW][C]9[/C][C]0.202163[/C][C]1.5659[/C][C]0.06131[/C][/ROW]
[ROW][C]10[/C][C]-0.207435[/C][C]-1.6068[/C][C]0.943324[/C][/ROW]
[ROW][C]11[/C][C]-0.057854[/C][C]-0.4481[/C][C]0.672166[/C][/ROW]
[ROW][C]12[/C][C]-0.204951[/C][C]-1.5875[/C][C]0.941177[/C][/ROW]
[ROW][C]13[/C][C]-0.253044[/C][C]-1.9601[/C][C]0.972682[/C][/ROW]
[ROW][C]14[/C][C]0.092482[/C][C]0.7164[/C][C]0.238274[/C][/ROW]
[ROW][C]15[/C][C]-0.135341[/C][C]-1.0483[/C][C]0.850657[/C][/ROW]
[ROW][C]16[/C][C]-0.184691[/C][C]-1.4306[/C][C]0.921136[/C][/ROW]
[ROW][C]17[/C][C]0.153394[/C][C]1.1882[/C][C]0.119722[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6224&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6224&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	7.746	0
1	0.143189	1.1091	0.135898
2	0.085576	0.6629	0.254975
3	0.263337	2.0398	0.02289
4	-0.023449	-0.1816	0.57176
5	0.087077	0.6745	0.251293
6	0.191357	1.4822	0.071754
7	-0.135291	-1.048	0.850571
8	0.115282	0.893	0.18772
9	0.202163	1.5659	0.06131
10	-0.207435	-1.6068	0.943324
11	-0.057854	-0.4481	0.672166
12	-0.204951	-1.5875	0.941177
13	-0.253044	-1.9601	0.972682
14	0.092482	0.7164	0.238274
15	-0.135341	-1.0483	0.850657
16	-0.184691	-1.4306	0.921136
17	0.153394	1.1882	0.119722

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.143189	1.1091	0.135898
1	0.066435	0.5146	0.304359
2	0.248556	1.9253	0.029467
3	-0.101358	-0.7851	0.782263
4	0.080627	0.6245	0.267321
5	0.121072	0.9378	0.176049
6	-0.171394	-1.3276	0.905333
7	0.120967	0.937	0.176256
8	0.135709	1.0512	0.148691
9	-0.224446	-1.7386	0.956378
10	-0.111703	-0.8652	0.804825
11	-0.264648	-2.05	0.977627
12	-0.065311	-0.5059	0.692608
13	0.141695	1.0976	0.13839
14	-0.083251	-0.6449	0.739262
15	-0.010799	-0.0836	0.533192
16	0.13827	1.071	0.144221
17	-0.105701	-0.8188	0.791917

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.143189 & 1.1091 & 0.135898 \tabularnewline
1 & 0.066435 & 0.5146 & 0.304359 \tabularnewline
2 & 0.248556 & 1.9253 & 0.029467 \tabularnewline
3 & -0.101358 & -0.7851 & 0.782263 \tabularnewline
4 & 0.080627 & 0.6245 & 0.267321 \tabularnewline
5 & 0.121072 & 0.9378 & 0.176049 \tabularnewline
6 & -0.171394 & -1.3276 & 0.905333 \tabularnewline
7 & 0.120967 & 0.937 & 0.176256 \tabularnewline
8 & 0.135709 & 1.0512 & 0.148691 \tabularnewline
9 & -0.224446 & -1.7386 & 0.956378 \tabularnewline
10 & -0.111703 & -0.8652 & 0.804825 \tabularnewline
11 & -0.264648 & -2.05 & 0.977627 \tabularnewline
12 & -0.065311 & -0.5059 & 0.692608 \tabularnewline
13 & 0.141695 & 1.0976 & 0.13839 \tabularnewline
14 & -0.083251 & -0.6449 & 0.739262 \tabularnewline
15 & -0.010799 & -0.0836 & 0.533192 \tabularnewline
16 & 0.13827 & 1.071 & 0.144221 \tabularnewline
17 & -0.105701 & -0.8188 & 0.791917 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6224&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]0.143189[/C][C]1.1091[/C][C]0.135898[/C][/ROW]
[ROW][C]1[/C][C]0.066435[/C][C]0.5146[/C][C]0.304359[/C][/ROW]
[ROW][C]2[/C][C]0.248556[/C][C]1.9253[/C][C]0.029467[/C][/ROW]
[ROW][C]3[/C][C]-0.101358[/C][C]-0.7851[/C][C]0.782263[/C][/ROW]
[ROW][C]4[/C][C]0.080627[/C][C]0.6245[/C][C]0.267321[/C][/ROW]
[ROW][C]5[/C][C]0.121072[/C][C]0.9378[/C][C]0.176049[/C][/ROW]
[ROW][C]6[/C][C]-0.171394[/C][C]-1.3276[/C][C]0.905333[/C][/ROW]
[ROW][C]7[/C][C]0.120967[/C][C]0.937[/C][C]0.176256[/C][/ROW]
[ROW][C]8[/C][C]0.135709[/C][C]1.0512[/C][C]0.148691[/C][/ROW]
[ROW][C]9[/C][C]-0.224446[/C][C]-1.7386[/C][C]0.956378[/C][/ROW]
[ROW][C]10[/C][C]-0.111703[/C][C]-0.8652[/C][C]0.804825[/C][/ROW]
[ROW][C]11[/C][C]-0.264648[/C][C]-2.05[/C][C]0.977627[/C][/ROW]
[ROW][C]12[/C][C]-0.065311[/C][C]-0.5059[/C][C]0.692608[/C][/ROW]
[ROW][C]13[/C][C]0.141695[/C][C]1.0976[/C][C]0.13839[/C][/ROW]
[ROW][C]14[/C][C]-0.083251[/C][C]-0.6449[/C][C]0.739262[/C][/ROW]
[ROW][C]15[/C][C]-0.010799[/C][C]-0.0836[/C][C]0.533192[/C][/ROW]
[ROW][C]16[/C][C]0.13827[/C][C]1.071[/C][C]0.144221[/C][/ROW]
[ROW][C]17[/C][C]-0.105701[/C][C]-0.8188[/C][C]0.791917[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6224&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6224&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	0.143189	1.1091	0.135898
1	0.066435	0.5146	0.304359
2	0.248556	1.9253	0.029467
3	-0.101358	-0.7851	0.782263
4	0.080627	0.6245	0.267321
5	0.121072	0.9378	0.176049
6	-0.171394	-1.3276	0.905333
7	0.120967	0.937	0.176256
8	0.135709	1.0512	0.148691
9	-0.224446	-1.7386	0.956378
10	-0.111703	-0.8652	0.804825
11	-0.264648	-2.05	0.977627
12	-0.065311	-0.5059	0.692608
13	0.141695	1.0976	0.13839
14	-0.083251	-0.6449	0.739262
15	-0.010799	-0.0836	0.533192
16	0.13827	1.071	0.144221
17	-0.105701	-0.8188	0.791917

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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