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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 13 Dec 2007 02:28:49 -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/t1197537302psg4b0hu2uf4dmu.htm/, Retrieved Sun, 05 May 2024 17:53:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3339, Retrieved Sun, 05 May 2024 17:53:39 +0000

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No (this computation is public)

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Estimated Impact

198

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

-       [(Partial) Autocorrelation Function] [Paper (P)ACF tijd...] [2007-12-13 09:28:49] [cb172450b25aceeff04d58e88e905157] [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=3339&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=3339&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3339&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	6.9282	0
1	0.228776	1.585	0.059766
2	0.372713	2.5822	0.006461
3	0.408895	2.8329	0.003362
4	0.029443	0.204	0.419612
5	0.210924	1.4613	0.075221
6	0.153302	1.0621	0.146751
7	0.057583	0.3989	0.345851
8	0.21992	1.5236	0.067079
9	-0.005021	-0.0348	0.513803
10	-0.00555	-0.0384	0.515255
11	7.7e-05	5e-04	0.499789
12	-0.220849	-1.5301	0.93372
13	-0.063378	-0.4391	0.668719
14	-0.105303	-0.7296	0.765398
15	-0.081063	-0.5616	0.711506
16	-0.010382	-0.0719	0.528521

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.9282 & 0 \tabularnewline
1 & 0.228776 & 1.585 & 0.059766 \tabularnewline
2 & 0.372713 & 2.5822 & 0.006461 \tabularnewline
3 & 0.408895 & 2.8329 & 0.003362 \tabularnewline
4 & 0.029443 & 0.204 & 0.419612 \tabularnewline
5 & 0.210924 & 1.4613 & 0.075221 \tabularnewline
6 & 0.153302 & 1.0621 & 0.146751 \tabularnewline
7 & 0.057583 & 0.3989 & 0.345851 \tabularnewline
8 & 0.21992 & 1.5236 & 0.067079 \tabularnewline
9 & -0.005021 & -0.0348 & 0.513803 \tabularnewline
10 & -0.00555 & -0.0384 & 0.515255 \tabularnewline
11 & 7.7e-05 & 5e-04 & 0.499789 \tabularnewline
12 & -0.220849 & -1.5301 & 0.93372 \tabularnewline
13 & -0.063378 & -0.4391 & 0.668719 \tabularnewline
14 & -0.105303 & -0.7296 & 0.765398 \tabularnewline
15 & -0.081063 & -0.5616 & 0.711506 \tabularnewline
16 & -0.010382 & -0.0719 & 0.528521 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3339&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]6.9282[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.228776[/C][C]1.585[/C][C]0.059766[/C][/ROW]
[ROW][C]2[/C][C]0.372713[/C][C]2.5822[/C][C]0.006461[/C][/ROW]
[ROW][C]3[/C][C]0.408895[/C][C]2.8329[/C][C]0.003362[/C][/ROW]
[ROW][C]4[/C][C]0.029443[/C][C]0.204[/C][C]0.419612[/C][/ROW]
[ROW][C]5[/C][C]0.210924[/C][C]1.4613[/C][C]0.075221[/C][/ROW]
[ROW][C]6[/C][C]0.153302[/C][C]1.0621[/C][C]0.146751[/C][/ROW]
[ROW][C]7[/C][C]0.057583[/C][C]0.3989[/C][C]0.345851[/C][/ROW]
[ROW][C]8[/C][C]0.21992[/C][C]1.5236[/C][C]0.067079[/C][/ROW]
[ROW][C]9[/C][C]-0.005021[/C][C]-0.0348[/C][C]0.513803[/C][/ROW]
[ROW][C]10[/C][C]-0.00555[/C][C]-0.0384[/C][C]0.515255[/C][/ROW]
[ROW][C]11[/C][C]7.7e-05[/C][C]5e-04[/C][C]0.499789[/C][/ROW]
[ROW][C]12[/C][C]-0.220849[/C][C]-1.5301[/C][C]0.93372[/C][/ROW]
[ROW][C]13[/C][C]-0.063378[/C][C]-0.4391[/C][C]0.668719[/C][/ROW]
[ROW][C]14[/C][C]-0.105303[/C][C]-0.7296[/C][C]0.765398[/C][/ROW]
[ROW][C]15[/C][C]-0.081063[/C][C]-0.5616[/C][C]0.711506[/C][/ROW]
[ROW][C]16[/C][C]-0.010382[/C][C]-0.0719[/C][C]0.528521[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3339&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3339&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	6.9282	0
1	0.228776	1.585	0.059766
2	0.372713	2.5822	0.006461
3	0.408895	2.8329	0.003362
4	0.029443	0.204	0.419612
5	0.210924	1.4613	0.075221
6	0.153302	1.0621	0.146751
7	0.057583	0.3989	0.345851
8	0.21992	1.5236	0.067079
9	-0.005021	-0.0348	0.513803
10	-0.00555	-0.0384	0.515255
11	7.7e-05	5e-04	0.499789
12	-0.220849	-1.5301	0.93372
13	-0.063378	-0.4391	0.668719
14	-0.105303	-0.7296	0.765398
15	-0.081063	-0.5616	0.711506
16	-0.010382	-0.0719	0.528521

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.228776	1.585	0.059766
1	0.338069	2.3422	0.011683
2	0.327765	2.2708	0.013841
3	-0.226457	-1.5689	0.938384
4	-0.015319	-0.1061	0.542039
5	0.093575	0.6483	0.259939
6	0.063615	0.4407	0.33069
7	0.097194	0.6734	0.251968
8	-0.153089	-1.0606	0.852918
9	-0.143902	-0.997	0.838113
10	-0.064081	-0.444	0.670468
11	-0.134754	-0.9336	0.822409
12	0.016186	0.1121	0.45559
13	0.032645	0.2262	0.411013
14	0.10693	0.7408	0.231202
15	-0.015327	-0.1062	0.542063
16	-0.016854	-0.1168	0.546235

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.228776 & 1.585 & 0.059766 \tabularnewline
1 & 0.338069 & 2.3422 & 0.011683 \tabularnewline
2 & 0.327765 & 2.2708 & 0.013841 \tabularnewline
3 & -0.226457 & -1.5689 & 0.938384 \tabularnewline
4 & -0.015319 & -0.1061 & 0.542039 \tabularnewline
5 & 0.093575 & 0.6483 & 0.259939 \tabularnewline
6 & 0.063615 & 0.4407 & 0.33069 \tabularnewline
7 & 0.097194 & 0.6734 & 0.251968 \tabularnewline
8 & -0.153089 & -1.0606 & 0.852918 \tabularnewline
9 & -0.143902 & -0.997 & 0.838113 \tabularnewline
10 & -0.064081 & -0.444 & 0.670468 \tabularnewline
11 & -0.134754 & -0.9336 & 0.822409 \tabularnewline
12 & 0.016186 & 0.1121 & 0.45559 \tabularnewline
13 & 0.032645 & 0.2262 & 0.411013 \tabularnewline
14 & 0.10693 & 0.7408 & 0.231202 \tabularnewline
15 & -0.015327 & -0.1062 & 0.542063 \tabularnewline
16 & -0.016854 & -0.1168 & 0.546235 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3339&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]0.228776[/C][C]1.585[/C][C]0.059766[/C][/ROW]
[ROW][C]1[/C][C]0.338069[/C][C]2.3422[/C][C]0.011683[/C][/ROW]
[ROW][C]2[/C][C]0.327765[/C][C]2.2708[/C][C]0.013841[/C][/ROW]
[ROW][C]3[/C][C]-0.226457[/C][C]-1.5689[/C][C]0.938384[/C][/ROW]
[ROW][C]4[/C][C]-0.015319[/C][C]-0.1061[/C][C]0.542039[/C][/ROW]
[ROW][C]5[/C][C]0.093575[/C][C]0.6483[/C][C]0.259939[/C][/ROW]
[ROW][C]6[/C][C]0.063615[/C][C]0.4407[/C][C]0.33069[/C][/ROW]
[ROW][C]7[/C][C]0.097194[/C][C]0.6734[/C][C]0.251968[/C][/ROW]
[ROW][C]8[/C][C]-0.153089[/C][C]-1.0606[/C][C]0.852918[/C][/ROW]
[ROW][C]9[/C][C]-0.143902[/C][C]-0.997[/C][C]0.838113[/C][/ROW]
[ROW][C]10[/C][C]-0.064081[/C][C]-0.444[/C][C]0.670468[/C][/ROW]
[ROW][C]11[/C][C]-0.134754[/C][C]-0.9336[/C][C]0.822409[/C][/ROW]
[ROW][C]12[/C][C]0.016186[/C][C]0.1121[/C][C]0.45559[/C][/ROW]
[ROW][C]13[/C][C]0.032645[/C][C]0.2262[/C][C]0.411013[/C][/ROW]
[ROW][C]14[/C][C]0.10693[/C][C]0.7408[/C][C]0.231202[/C][/ROW]
[ROW][C]15[/C][C]-0.015327[/C][C]-0.1062[/C][C]0.542063[/C][/ROW]
[ROW][C]16[/C][C]-0.016854[/C][C]-0.1168[/C][C]0.546235[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3339&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3339&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	0.228776	1.585	0.059766
1	0.338069	2.3422	0.011683
2	0.327765	2.2708	0.013841
3	-0.226457	-1.5689	0.938384
4	-0.015319	-0.1061	0.542039
5	0.093575	0.6483	0.259939
6	0.063615	0.4407	0.33069
7	0.097194	0.6734	0.251968
8	-0.153089	-1.0606	0.852918
9	-0.143902	-0.997	0.838113
10	-0.064081	-0.444	0.670468
11	-0.134754	-0.9336	0.822409
12	0.016186	0.1121	0.45559
13	0.032645	0.2262	0.411013
14	0.10693	0.7408	0.231202
15	-0.015327	-0.1062	0.542063
16	-0.016854	-0.1168	0.546235

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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