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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 02 Dec 2007 13:03:03 -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/02/t11966250858wzhf28f7u2hmr4.htm/, Retrieved Sun, 28 Apr 2024 16:57:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2289, Retrieved Sun, 28 Apr 2024 16:57:48 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

319

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

-       [(Partial) Autocorrelation Function] [AcF tot.uitvoer] [2007-12-02 20:03:03] [89d26cd0a44959d9c8b169f34617598a] [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=2289&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=2289&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2289&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	6.9282	0
1	-0.584481	-4.0494	0.999907
2	-0.047481	-0.329	0.62819
3	0.319374	2.2127	0.015855
4	-0.206481	-1.4305	0.92048
5	-0.003168	-0.022	0.508711
6	0.226498	1.5692	0.061582
7	-0.33336	-2.3096	0.987371
8	0.181991	1.2609	0.106725
9	0.045748	0.317	0.376327
10	-0.145027	-1.0048	0.839978
11	0.145184	1.0059	0.159763
12	-0.140571	-0.9739	0.832507
13	-0.016171	-0.112	0.544369
14	0.17293	1.1981	0.118381
15	-0.067844	-0.47	0.679771
16	-0.169736	-1.176	0.877296

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.9282 & 0 \tabularnewline
1 & -0.584481 & -4.0494 & 0.999907 \tabularnewline
2 & -0.047481 & -0.329 & 0.62819 \tabularnewline
3 & 0.319374 & 2.2127 & 0.015855 \tabularnewline
4 & -0.206481 & -1.4305 & 0.92048 \tabularnewline
5 & -0.003168 & -0.022 & 0.508711 \tabularnewline
6 & 0.226498 & 1.5692 & 0.061582 \tabularnewline
7 & -0.33336 & -2.3096 & 0.987371 \tabularnewline
8 & 0.181991 & 1.2609 & 0.106725 \tabularnewline
9 & 0.045748 & 0.317 & 0.376327 \tabularnewline
10 & -0.145027 & -1.0048 & 0.839978 \tabularnewline
11 & 0.145184 & 1.0059 & 0.159763 \tabularnewline
12 & -0.140571 & -0.9739 & 0.832507 \tabularnewline
13 & -0.016171 & -0.112 & 0.544369 \tabularnewline
14 & 0.17293 & 1.1981 & 0.118381 \tabularnewline
15 & -0.067844 & -0.47 & 0.679771 \tabularnewline
16 & -0.169736 & -1.176 & 0.877296 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2289&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]-0.584481[/C][C]-4.0494[/C][C]0.999907[/C][/ROW]
[ROW][C]2[/C][C]-0.047481[/C][C]-0.329[/C][C]0.62819[/C][/ROW]
[ROW][C]3[/C][C]0.319374[/C][C]2.2127[/C][C]0.015855[/C][/ROW]
[ROW][C]4[/C][C]-0.206481[/C][C]-1.4305[/C][C]0.92048[/C][/ROW]
[ROW][C]5[/C][C]-0.003168[/C][C]-0.022[/C][C]0.508711[/C][/ROW]
[ROW][C]6[/C][C]0.226498[/C][C]1.5692[/C][C]0.061582[/C][/ROW]
[ROW][C]7[/C][C]-0.33336[/C][C]-2.3096[/C][C]0.987371[/C][/ROW]
[ROW][C]8[/C][C]0.181991[/C][C]1.2609[/C][C]0.106725[/C][/ROW]
[ROW][C]9[/C][C]0.045748[/C][C]0.317[/C][C]0.376327[/C][/ROW]
[ROW][C]10[/C][C]-0.145027[/C][C]-1.0048[/C][C]0.839978[/C][/ROW]
[ROW][C]11[/C][C]0.145184[/C][C]1.0059[/C][C]0.159763[/C][/ROW]
[ROW][C]12[/C][C]-0.140571[/C][C]-0.9739[/C][C]0.832507[/C][/ROW]
[ROW][C]13[/C][C]-0.016171[/C][C]-0.112[/C][C]0.544369[/C][/ROW]
[ROW][C]14[/C][C]0.17293[/C][C]1.1981[/C][C]0.118381[/C][/ROW]
[ROW][C]15[/C][C]-0.067844[/C][C]-0.47[/C][C]0.679771[/C][/ROW]
[ROW][C]16[/C][C]-0.169736[/C][C]-1.176[/C][C]0.877296[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2289&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2289&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	-0.584481	-4.0494	0.999907
2	-0.047481	-0.329	0.62819
3	0.319374	2.2127	0.015855
4	-0.206481	-1.4305	0.92048
5	-0.003168	-0.022	0.508711
6	0.226498	1.5692	0.061582
7	-0.33336	-2.3096	0.987371
8	0.181991	1.2609	0.106725
9	0.045748	0.317	0.376327
10	-0.145027	-1.0048	0.839978
11	0.145184	1.0059	0.159763
12	-0.140571	-0.9739	0.832507
13	-0.016171	-0.112	0.544369
14	0.17293	1.1981	0.118381
15	-0.067844	-0.47	0.679771
16	-0.169736	-1.176	0.877296

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.584481	-4.0494	0.999907
1	-0.590993	-4.0945	0.999919
2	-0.163862	-1.1353	0.86905
3	-0.02311	-0.1601	0.563266
4	0.010874	0.0753	0.470129
5	0.311237	2.1563	0.01805
6	-0.002846	-0.0197	0.507825
7	-0.100845	-0.6987	0.755935
8	-0.157998	-1.0946	0.860432
9	-0.097219	-0.6736	0.748087
10	0.136263	0.9441	0.174935
11	-0.049119	-0.3403	0.632445
12	-0.219908	-1.5236	0.932911
13	-0.20491	-1.4197	0.918915
14	0.171082	1.1853	0.120869
15	0.099421	0.6888	0.247129
16	-0.084945	-0.5885	0.720528

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.584481 & -4.0494 & 0.999907 \tabularnewline
1 & -0.590993 & -4.0945 & 0.999919 \tabularnewline
2 & -0.163862 & -1.1353 & 0.86905 \tabularnewline
3 & -0.02311 & -0.1601 & 0.563266 \tabularnewline
4 & 0.010874 & 0.0753 & 0.470129 \tabularnewline
5 & 0.311237 & 2.1563 & 0.01805 \tabularnewline
6 & -0.002846 & -0.0197 & 0.507825 \tabularnewline
7 & -0.100845 & -0.6987 & 0.755935 \tabularnewline
8 & -0.157998 & -1.0946 & 0.860432 \tabularnewline
9 & -0.097219 & -0.6736 & 0.748087 \tabularnewline
10 & 0.136263 & 0.9441 & 0.174935 \tabularnewline
11 & -0.049119 & -0.3403 & 0.632445 \tabularnewline
12 & -0.219908 & -1.5236 & 0.932911 \tabularnewline
13 & -0.20491 & -1.4197 & 0.918915 \tabularnewline
14 & 0.171082 & 1.1853 & 0.120869 \tabularnewline
15 & 0.099421 & 0.6888 & 0.247129 \tabularnewline
16 & -0.084945 & -0.5885 & 0.720528 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2289&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]-0.584481[/C][C]-4.0494[/C][C]0.999907[/C][/ROW]
[ROW][C]1[/C][C]-0.590993[/C][C]-4.0945[/C][C]0.999919[/C][/ROW]
[ROW][C]2[/C][C]-0.163862[/C][C]-1.1353[/C][C]0.86905[/C][/ROW]
[ROW][C]3[/C][C]-0.02311[/C][C]-0.1601[/C][C]0.563266[/C][/ROW]
[ROW][C]4[/C][C]0.010874[/C][C]0.0753[/C][C]0.470129[/C][/ROW]
[ROW][C]5[/C][C]0.311237[/C][C]2.1563[/C][C]0.01805[/C][/ROW]
[ROW][C]6[/C][C]-0.002846[/C][C]-0.0197[/C][C]0.507825[/C][/ROW]
[ROW][C]7[/C][C]-0.100845[/C][C]-0.6987[/C][C]0.755935[/C][/ROW]
[ROW][C]8[/C][C]-0.157998[/C][C]-1.0946[/C][C]0.860432[/C][/ROW]
[ROW][C]9[/C][C]-0.097219[/C][C]-0.6736[/C][C]0.748087[/C][/ROW]
[ROW][C]10[/C][C]0.136263[/C][C]0.9441[/C][C]0.174935[/C][/ROW]
[ROW][C]11[/C][C]-0.049119[/C][C]-0.3403[/C][C]0.632445[/C][/ROW]
[ROW][C]12[/C][C]-0.219908[/C][C]-1.5236[/C][C]0.932911[/C][/ROW]
[ROW][C]13[/C][C]-0.20491[/C][C]-1.4197[/C][C]0.918915[/C][/ROW]
[ROW][C]14[/C][C]0.171082[/C][C]1.1853[/C][C]0.120869[/C][/ROW]
[ROW][C]15[/C][C]0.099421[/C][C]0.6888[/C][C]0.247129[/C][/ROW]
[ROW][C]16[/C][C]-0.084945[/C][C]-0.5885[/C][C]0.720528[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2289&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2289&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	-0.584481	-4.0494	0.999907
1	-0.590993	-4.0945	0.999919
2	-0.163862	-1.1353	0.86905
3	-0.02311	-0.1601	0.563266
4	0.010874	0.0753	0.470129
5	0.311237	2.1563	0.01805
6	-0.002846	-0.0197	0.507825
7	-0.100845	-0.6987	0.755935
8	-0.157998	-1.0946	0.860432
9	-0.097219	-0.6736	0.748087
10	0.136263	0.9441	0.174935
11	-0.049119	-0.3403	0.632445
12	-0.219908	-1.5236	0.932911
13	-0.20491	-1.4197	0.918915
14	0.171082	1.1853	0.120869
15	0.099421	0.6888	0.247129
16	-0.084945	-0.5885	0.720528

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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Input Parameters & R Code