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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 25 Nov 2007 05:09:15 -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/25/t1195992003qfeozor9dbbz2qv.htm/, Retrieved Sat, 04 May 2024 12:13:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6415, Retrieved Sat, 04 May 2024 12:13:20 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

210

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

-       [(Partial) Autocorrelation Function] [Autocorrelation f...] [2007-11-25 12:09:15] [9fe578921d87f9af8e79a90d6142ba02] [Current]

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Boxplots

7,7
7,8
7,7
7,7
7,7
7,7
7,6
7,5
7,4
7,4
7,5
7,6
7,6
8,1
7,8
8
7,9
7,9
7,8
6,7
6,6
6,6
7,7
7,9
8
7,7
7,5
7,6
7,8
7,8
7,7
7,4
7,5
7,2
7,5
7,6
7,6
7,8
7,7
7,7
8,2
8,2
8,1
7,8
7,8
7,7
6,7
6,7
6,7
7,2
6,9
6,8
7,2
7,1
6,9
6,9
6,7
6,5
6,6
6,6
6,5

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=6415&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=6415&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6415&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	7.8102	0
1	0.772003	6.0295	0
2	0.538906	4.209	4.3e-05
3	0.31967	2.4967	0.007626
4	0.206196	1.6104	0.056232
5	0.144884	1.1316	0.131119
6	0.074939	0.5853	0.280255
7	0.069754	0.5448	0.293941
8	0.059898	0.4678	0.320791
9	0.091044	0.7111	0.239873
10	0.12532	0.9788	0.165778
11	0.151668	1.1846	0.120392
12	0.188319	1.4708	0.07324
13	0.114712	0.8959	0.186907
14	0.000786	0.0061	0.497562
15	-0.115388	-0.9012	0.81449
16	-0.176619	-1.3794	0.913602

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.8102 & 0 \tabularnewline
1 & 0.772003 & 6.0295 & 0 \tabularnewline
2 & 0.538906 & 4.209 & 4.3e-05 \tabularnewline
3 & 0.31967 & 2.4967 & 0.007626 \tabularnewline
4 & 0.206196 & 1.6104 & 0.056232 \tabularnewline
5 & 0.144884 & 1.1316 & 0.131119 \tabularnewline
6 & 0.074939 & 0.5853 & 0.280255 \tabularnewline
7 & 0.069754 & 0.5448 & 0.293941 \tabularnewline
8 & 0.059898 & 0.4678 & 0.320791 \tabularnewline
9 & 0.091044 & 0.7111 & 0.239873 \tabularnewline
10 & 0.12532 & 0.9788 & 0.165778 \tabularnewline
11 & 0.151668 & 1.1846 & 0.120392 \tabularnewline
12 & 0.188319 & 1.4708 & 0.07324 \tabularnewline
13 & 0.114712 & 0.8959 & 0.186907 \tabularnewline
14 & 0.000786 & 0.0061 & 0.497562 \tabularnewline
15 & -0.115388 & -0.9012 & 0.81449 \tabularnewline
16 & -0.176619 & -1.3794 & 0.913602 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6415&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]7.8102[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.772003[/C][C]6.0295[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.538906[/C][C]4.209[/C][C]4.3e-05[/C][/ROW]
[ROW][C]3[/C][C]0.31967[/C][C]2.4967[/C][C]0.007626[/C][/ROW]
[ROW][C]4[/C][C]0.206196[/C][C]1.6104[/C][C]0.056232[/C][/ROW]
[ROW][C]5[/C][C]0.144884[/C][C]1.1316[/C][C]0.131119[/C][/ROW]
[ROW][C]6[/C][C]0.074939[/C][C]0.5853[/C][C]0.280255[/C][/ROW]
[ROW][C]7[/C][C]0.069754[/C][C]0.5448[/C][C]0.293941[/C][/ROW]
[ROW][C]8[/C][C]0.059898[/C][C]0.4678[/C][C]0.320791[/C][/ROW]
[ROW][C]9[/C][C]0.091044[/C][C]0.7111[/C][C]0.239873[/C][/ROW]
[ROW][C]10[/C][C]0.12532[/C][C]0.9788[/C][C]0.165778[/C][/ROW]
[ROW][C]11[/C][C]0.151668[/C][C]1.1846[/C][C]0.120392[/C][/ROW]
[ROW][C]12[/C][C]0.188319[/C][C]1.4708[/C][C]0.07324[/C][/ROW]
[ROW][C]13[/C][C]0.114712[/C][C]0.8959[/C][C]0.186907[/C][/ROW]
[ROW][C]14[/C][C]0.000786[/C][C]0.0061[/C][C]0.497562[/C][/ROW]
[ROW][C]15[/C][C]-0.115388[/C][C]-0.9012[/C][C]0.81449[/C][/ROW]
[ROW][C]16[/C][C]-0.176619[/C][C]-1.3794[/C][C]0.913602[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6415&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6415&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	7.8102	0
1	0.772003	6.0295	0
2	0.538906	4.209	4.3e-05
3	0.31967	2.4967	0.007626
4	0.206196	1.6104	0.056232
5	0.144884	1.1316	0.131119
6	0.074939	0.5853	0.280255
7	0.069754	0.5448	0.293941
8	0.059898	0.4678	0.320791
9	0.091044	0.7111	0.239873
10	0.12532	0.9788	0.165778
11	0.151668	1.1846	0.120392
12	0.188319	1.4708	0.07324
13	0.114712	0.8959	0.186907
14	0.000786	0.0061	0.497562
15	-0.115388	-0.9012	0.81449
16	-0.176619	-1.3794	0.913602

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.772003	6.0295	0
1	-0.141288	-1.1035	0.862927
2	-0.116362	-0.9088	0.816488
3	0.10374	0.8102	0.210476
4	0.015984	0.1248	0.45053
5	-0.104478	-0.816	0.791161
6	0.128759	1.0056	0.159281
7	-0.016937	-0.1323	0.552403
8	0.064841	0.5064	0.307193
9	0.066979	0.5231	0.301391
10	0.022052	0.1722	0.431913
11	0.076211	0.5952	0.276947
12	-0.201443	-1.5733	0.939591
13	-0.131429	-1.0265	0.845643
14	-0.025796	-0.2015	0.579502
15	-0.028444	-0.2222	0.587531
16	-0.008957	-0.07	0.527772

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.772003 & 6.0295 & 0 \tabularnewline
1 & -0.141288 & -1.1035 & 0.862927 \tabularnewline
2 & -0.116362 & -0.9088 & 0.816488 \tabularnewline
3 & 0.10374 & 0.8102 & 0.210476 \tabularnewline
4 & 0.015984 & 0.1248 & 0.45053 \tabularnewline
5 & -0.104478 & -0.816 & 0.791161 \tabularnewline
6 & 0.128759 & 1.0056 & 0.159281 \tabularnewline
7 & -0.016937 & -0.1323 & 0.552403 \tabularnewline
8 & 0.064841 & 0.5064 & 0.307193 \tabularnewline
9 & 0.066979 & 0.5231 & 0.301391 \tabularnewline
10 & 0.022052 & 0.1722 & 0.431913 \tabularnewline
11 & 0.076211 & 0.5952 & 0.276947 \tabularnewline
12 & -0.201443 & -1.5733 & 0.939591 \tabularnewline
13 & -0.131429 & -1.0265 & 0.845643 \tabularnewline
14 & -0.025796 & -0.2015 & 0.579502 \tabularnewline
15 & -0.028444 & -0.2222 & 0.587531 \tabularnewline
16 & -0.008957 & -0.07 & 0.527772 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6415&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]0.772003[/C][C]6.0295[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.141288[/C][C]-1.1035[/C][C]0.862927[/C][/ROW]
[ROW][C]2[/C][C]-0.116362[/C][C]-0.9088[/C][C]0.816488[/C][/ROW]
[ROW][C]3[/C][C]0.10374[/C][C]0.8102[/C][C]0.210476[/C][/ROW]
[ROW][C]4[/C][C]0.015984[/C][C]0.1248[/C][C]0.45053[/C][/ROW]
[ROW][C]5[/C][C]-0.104478[/C][C]-0.816[/C][C]0.791161[/C][/ROW]
[ROW][C]6[/C][C]0.128759[/C][C]1.0056[/C][C]0.159281[/C][/ROW]
[ROW][C]7[/C][C]-0.016937[/C][C]-0.1323[/C][C]0.552403[/C][/ROW]
[ROW][C]8[/C][C]0.064841[/C][C]0.5064[/C][C]0.307193[/C][/ROW]
[ROW][C]9[/C][C]0.066979[/C][C]0.5231[/C][C]0.301391[/C][/ROW]
[ROW][C]10[/C][C]0.022052[/C][C]0.1722[/C][C]0.431913[/C][/ROW]
[ROW][C]11[/C][C]0.076211[/C][C]0.5952[/C][C]0.276947[/C][/ROW]
[ROW][C]12[/C][C]-0.201443[/C][C]-1.5733[/C][C]0.939591[/C][/ROW]
[ROW][C]13[/C][C]-0.131429[/C][C]-1.0265[/C][C]0.845643[/C][/ROW]
[ROW][C]14[/C][C]-0.025796[/C][C]-0.2015[/C][C]0.579502[/C][/ROW]
[ROW][C]15[/C][C]-0.028444[/C][C]-0.2222[/C][C]0.587531[/C][/ROW]
[ROW][C]16[/C][C]-0.008957[/C][C]-0.07[/C][C]0.527772[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6415&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6415&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	0.772003	6.0295	0
1	-0.141288	-1.1035	0.862927
2	-0.116362	-0.9088	0.816488
3	0.10374	0.8102	0.210476
4	0.015984	0.1248	0.45053
5	-0.104478	-0.816	0.791161
6	0.128759	1.0056	0.159281
7	-0.016937	-0.1323	0.552403
8	0.064841	0.5064	0.307193
9	0.066979	0.5231	0.301391
10	0.022052	0.1722	0.431913
11	0.076211	0.5952	0.276947
12	-0.201443	-1.5733	0.939591
13	-0.131429	-1.0265	0.845643
14	-0.025796	-0.2015	0.579502
15	-0.028444	-0.2222	0.587531
16	-0.008957	-0.07	0.527772

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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