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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 13 Dec 2007 04:37:06 -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/13/t1197544905z63905a4br1vo8t.htm/, Retrieved Sun, 05 May 2024 17:20:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3448, Retrieved Sun, 05 May 2024 17:20:36 +0000

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Original text written by user:

Stap 5

IsPrivate?

No (this computation is public)

User-defined keywords

ACF - PACF

Estimated Impact

192

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

-       [(Partial) Autocorrelation Function] [paper] [2007-12-13 11:37:06] [8ce1ad2ac57e06e10fb37a1292ae8cb6] [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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3448&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3448&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3448&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.2462	0
1	0.138447	1.1417	0.128799
2	0.072313	0.5963	0.276474
3	0.258459	2.1313	0.018341
4	-0.053284	-0.4394	0.669114
5	0.062272	0.5135	0.304631
6	0.183098	1.5099	0.067856
7	-0.152991	-1.2616	0.894298
8	0.122385	1.0092	0.158226
9	0.211692	1.7457	0.042693
10	-0.208084	-1.7159	0.954634
11	-0.045104	-0.3719	0.644453
12	-0.219134	-1.807	0.962409
13	-0.24416	-2.0134	0.975983
14	0.103499	0.8535	0.198196
15	-0.13178	-1.0867	0.859493
16	-0.136789	-1.128	0.868357
17	0.208311	1.7178	0.045194
18	-0.125763	-1.0371	0.848311

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.2462 & 0 \tabularnewline
1 & 0.138447 & 1.1417 & 0.128799 \tabularnewline
2 & 0.072313 & 0.5963 & 0.276474 \tabularnewline
3 & 0.258459 & 2.1313 & 0.018341 \tabularnewline
4 & -0.053284 & -0.4394 & 0.669114 \tabularnewline
5 & 0.062272 & 0.5135 & 0.304631 \tabularnewline
6 & 0.183098 & 1.5099 & 0.067856 \tabularnewline
7 & -0.152991 & -1.2616 & 0.894298 \tabularnewline
8 & 0.122385 & 1.0092 & 0.158226 \tabularnewline
9 & 0.211692 & 1.7457 & 0.042693 \tabularnewline
10 & -0.208084 & -1.7159 & 0.954634 \tabularnewline
11 & -0.045104 & -0.3719 & 0.644453 \tabularnewline
12 & -0.219134 & -1.807 & 0.962409 \tabularnewline
13 & -0.24416 & -2.0134 & 0.975983 \tabularnewline
14 & 0.103499 & 0.8535 & 0.198196 \tabularnewline
15 & -0.13178 & -1.0867 & 0.859493 \tabularnewline
16 & -0.136789 & -1.128 & 0.868357 \tabularnewline
17 & 0.208311 & 1.7178 & 0.045194 \tabularnewline
18 & -0.125763 & -1.0371 & 0.848311 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3448&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]0.138447[/C][C]1.1417[/C][C]0.128799[/C][/ROW]
[ROW][C]2[/C][C]0.072313[/C][C]0.5963[/C][C]0.276474[/C][/ROW]
[ROW][C]3[/C][C]0.258459[/C][C]2.1313[/C][C]0.018341[/C][/ROW]
[ROW][C]4[/C][C]-0.053284[/C][C]-0.4394[/C][C]0.669114[/C][/ROW]
[ROW][C]5[/C][C]0.062272[/C][C]0.5135[/C][C]0.304631[/C][/ROW]
[ROW][C]6[/C][C]0.183098[/C][C]1.5099[/C][C]0.067856[/C][/ROW]
[ROW][C]7[/C][C]-0.152991[/C][C]-1.2616[/C][C]0.894298[/C][/ROW]
[ROW][C]8[/C][C]0.122385[/C][C]1.0092[/C][C]0.158226[/C][/ROW]
[ROW][C]9[/C][C]0.211692[/C][C]1.7457[/C][C]0.042693[/C][/ROW]
[ROW][C]10[/C][C]-0.208084[/C][C]-1.7159[/C][C]0.954634[/C][/ROW]
[ROW][C]11[/C][C]-0.045104[/C][C]-0.3719[/C][C]0.644453[/C][/ROW]
[ROW][C]12[/C][C]-0.219134[/C][C]-1.807[/C][C]0.962409[/C][/ROW]
[ROW][C]13[/C][C]-0.24416[/C][C]-2.0134[/C][C]0.975983[/C][/ROW]
[ROW][C]14[/C][C]0.103499[/C][C]0.8535[/C][C]0.198196[/C][/ROW]
[ROW][C]15[/C][C]-0.13178[/C][C]-1.0867[/C][C]0.859493[/C][/ROW]
[ROW][C]16[/C][C]-0.136789[/C][C]-1.128[/C][C]0.868357[/C][/ROW]
[ROW][C]17[/C][C]0.208311[/C][C]1.7178[/C][C]0.045194[/C][/ROW]
[ROW][C]18[/C][C]-0.125763[/C][C]-1.0371[/C][C]0.848311[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3448&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3448&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	0.138447	1.1417	0.128799
2	0.072313	0.5963	0.276474
3	0.258459	2.1313	0.018341
4	-0.053284	-0.4394	0.669114
5	0.062272	0.5135	0.304631
6	0.183098	1.5099	0.067856
7	-0.152991	-1.2616	0.894298
8	0.122385	1.0092	0.158226
9	0.211692	1.7457	0.042693
10	-0.208084	-1.7159	0.954634
11	-0.045104	-0.3719	0.644453
12	-0.219134	-1.807	0.962409
13	-0.24416	-2.0134	0.975983
14	0.103499	0.8535	0.198196
15	-0.13178	-1.0867	0.859493
16	-0.136789	-1.128	0.868357
17	0.208311	1.7178	0.045194
18	-0.125763	-1.0371	0.848311

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.138447	1.1417	0.128799
1	0.054184	0.4468	0.328214
2	0.246932	2.0363	0.022811
3	-0.13006	-1.0725	0.856357
4	0.069684	0.5746	0.283719
5	0.118808	0.9797	0.16535
6	-0.173152	-1.4278	0.921044
7	0.144158	1.1888	0.119335
8	0.14042	1.1579	0.125471
9	-0.217058	-1.7899	0.961039
10	-0.102021	-0.8413	0.798431
11	-0.290463	-2.3952	0.990315
12	-0.026758	-0.2207	0.586989
13	0.13925	1.1483	0.127438
14	-0.086644	-0.7145	0.761313
15	0.03531	0.2912	0.385902
16	0.155711	1.284	0.101746
17	-0.107497	-0.8864	0.810748
18	-0.161735	-1.3337	0.906624

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.138447 & 1.1417 & 0.128799 \tabularnewline
1 & 0.054184 & 0.4468 & 0.328214 \tabularnewline
2 & 0.246932 & 2.0363 & 0.022811 \tabularnewline
3 & -0.13006 & -1.0725 & 0.856357 \tabularnewline
4 & 0.069684 & 0.5746 & 0.283719 \tabularnewline
5 & 0.118808 & 0.9797 & 0.16535 \tabularnewline
6 & -0.173152 & -1.4278 & 0.921044 \tabularnewline
7 & 0.144158 & 1.1888 & 0.119335 \tabularnewline
8 & 0.14042 & 1.1579 & 0.125471 \tabularnewline
9 & -0.217058 & -1.7899 & 0.961039 \tabularnewline
10 & -0.102021 & -0.8413 & 0.798431 \tabularnewline
11 & -0.290463 & -2.3952 & 0.990315 \tabularnewline
12 & -0.026758 & -0.2207 & 0.586989 \tabularnewline
13 & 0.13925 & 1.1483 & 0.127438 \tabularnewline
14 & -0.086644 & -0.7145 & 0.761313 \tabularnewline
15 & 0.03531 & 0.2912 & 0.385902 \tabularnewline
16 & 0.155711 & 1.284 & 0.101746 \tabularnewline
17 & -0.107497 & -0.8864 & 0.810748 \tabularnewline
18 & -0.161735 & -1.3337 & 0.906624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3448&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]0.138447[/C][C]1.1417[/C][C]0.128799[/C][/ROW]
[ROW][C]1[/C][C]0.054184[/C][C]0.4468[/C][C]0.328214[/C][/ROW]
[ROW][C]2[/C][C]0.246932[/C][C]2.0363[/C][C]0.022811[/C][/ROW]
[ROW][C]3[/C][C]-0.13006[/C][C]-1.0725[/C][C]0.856357[/C][/ROW]
[ROW][C]4[/C][C]0.069684[/C][C]0.5746[/C][C]0.283719[/C][/ROW]
[ROW][C]5[/C][C]0.118808[/C][C]0.9797[/C][C]0.16535[/C][/ROW]
[ROW][C]6[/C][C]-0.173152[/C][C]-1.4278[/C][C]0.921044[/C][/ROW]
[ROW][C]7[/C][C]0.144158[/C][C]1.1888[/C][C]0.119335[/C][/ROW]
[ROW][C]8[/C][C]0.14042[/C][C]1.1579[/C][C]0.125471[/C][/ROW]
[ROW][C]9[/C][C]-0.217058[/C][C]-1.7899[/C][C]0.961039[/C][/ROW]
[ROW][C]10[/C][C]-0.102021[/C][C]-0.8413[/C][C]0.798431[/C][/ROW]
[ROW][C]11[/C][C]-0.290463[/C][C]-2.3952[/C][C]0.990315[/C][/ROW]
[ROW][C]12[/C][C]-0.026758[/C][C]-0.2207[/C][C]0.586989[/C][/ROW]
[ROW][C]13[/C][C]0.13925[/C][C]1.1483[/C][C]0.127438[/C][/ROW]
[ROW][C]14[/C][C]-0.086644[/C][C]-0.7145[/C][C]0.761313[/C][/ROW]
[ROW][C]15[/C][C]0.03531[/C][C]0.2912[/C][C]0.385902[/C][/ROW]
[ROW][C]16[/C][C]0.155711[/C][C]1.284[/C][C]0.101746[/C][/ROW]
[ROW][C]17[/C][C]-0.107497[/C][C]-0.8864[/C][C]0.810748[/C][/ROW]
[ROW][C]18[/C][C]-0.161735[/C][C]-1.3337[/C][C]0.906624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3448&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3448&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	0.138447	1.1417	0.128799
1	0.054184	0.4468	0.328214
2	0.246932	2.0363	0.022811
3	-0.13006	-1.0725	0.856357
4	0.069684	0.5746	0.283719
5	0.118808	0.9797	0.16535
6	-0.173152	-1.4278	0.921044
7	0.144158	1.1888	0.119335
8	0.14042	1.1579	0.125471
9	-0.217058	-1.7899	0.961039
10	-0.102021	-0.8413	0.798431
11	-0.290463	-2.3952	0.990315
12	-0.026758	-0.2207	0.586989
13	0.13925	1.1483	0.127438
14	-0.086644	-0.7145	0.761313
15	0.03531	0.2912	0.385902
16	0.155711	1.284	0.101746
17	-0.107497	-0.8864	0.810748
18	-0.161735	-1.3337	0.906624

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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