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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

Tue, 27 Nov 2007 03:15:50 -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/27/t1196157975tepkcjlb0zeyx0r.htm/, Retrieved Sun, 05 May 2024 11:56:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6810, Retrieved Sun, 05 May 2024 11:56:39 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

groep MENS

Estimated Impact

187

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

-       [(Partial) Autocorrelation Function] [energie_Q2] [2007-11-27 10:15:50] [68ccea1ea79fa519d33f2664ba3973dd] [Current]
-    D    [(Partial) Autocorrelation Function] [Autocorrelatie En...] [2008-12-06 13:39:32] [4300be8b33fd3dcdacd2aa9800ceba23] 
- R  D    [(Partial) Autocorrelation Function] [Partiele autocorr...] [2008-12-06 13:42:05] [4300be8b33fd3dcdacd2aa9800ceba23] 

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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=6810&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=6810&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6810&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	8.544	0
1	0.942845	8.0557	0
2	0.887599	7.5836	0
3	0.844614	7.2164	0
4	0.80593	6.8859	0
5	0.764084	6.5283	0
6	0.722694	6.1747	0
7	0.675864	5.7746	0
8	0.621779	5.3125	1e-06
9	0.573643	4.9012	3e-06
10	0.525993	4.4941	1.3e-05
11	0.48316	4.1281	4.8e-05
12	0.445145	3.8033	0.000147
13	0.407514	3.4818	0.000422
14	0.385617	3.2947	0.000761
15	0.366764	3.1336	0.001243
16	0.352813	3.0144	0.00177
17	0.332191	2.8382	0.002935

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.544 & 0 \tabularnewline
1 & 0.942845 & 8.0557 & 0 \tabularnewline
2 & 0.887599 & 7.5836 & 0 \tabularnewline
3 & 0.844614 & 7.2164 & 0 \tabularnewline
4 & 0.80593 & 6.8859 & 0 \tabularnewline
5 & 0.764084 & 6.5283 & 0 \tabularnewline
6 & 0.722694 & 6.1747 & 0 \tabularnewline
7 & 0.675864 & 5.7746 & 0 \tabularnewline
8 & 0.621779 & 5.3125 & 1e-06 \tabularnewline
9 & 0.573643 & 4.9012 & 3e-06 \tabularnewline
10 & 0.525993 & 4.4941 & 1.3e-05 \tabularnewline
11 & 0.48316 & 4.1281 & 4.8e-05 \tabularnewline
12 & 0.445145 & 3.8033 & 0.000147 \tabularnewline
13 & 0.407514 & 3.4818 & 0.000422 \tabularnewline
14 & 0.385617 & 3.2947 & 0.000761 \tabularnewline
15 & 0.366764 & 3.1336 & 0.001243 \tabularnewline
16 & 0.352813 & 3.0144 & 0.00177 \tabularnewline
17 & 0.332191 & 2.8382 & 0.002935 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6810&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]8.544[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.942845[/C][C]8.0557[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.887599[/C][C]7.5836[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.844614[/C][C]7.2164[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.80593[/C][C]6.8859[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.764084[/C][C]6.5283[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.722694[/C][C]6.1747[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.675864[/C][C]5.7746[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.621779[/C][C]5.3125[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]0.573643[/C][C]4.9012[/C][C]3e-06[/C][/ROW]
[ROW][C]10[/C][C]0.525993[/C][C]4.4941[/C][C]1.3e-05[/C][/ROW]
[ROW][C]11[/C][C]0.48316[/C][C]4.1281[/C][C]4.8e-05[/C][/ROW]
[ROW][C]12[/C][C]0.445145[/C][C]3.8033[/C][C]0.000147[/C][/ROW]
[ROW][C]13[/C][C]0.407514[/C][C]3.4818[/C][C]0.000422[/C][/ROW]
[ROW][C]14[/C][C]0.385617[/C][C]3.2947[/C][C]0.000761[/C][/ROW]
[ROW][C]15[/C][C]0.366764[/C][C]3.1336[/C][C]0.001243[/C][/ROW]
[ROW][C]16[/C][C]0.352813[/C][C]3.0144[/C][C]0.00177[/C][/ROW]
[ROW][C]17[/C][C]0.332191[/C][C]2.8382[/C][C]0.002935[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6810&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6810&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	8.544	0
1	0.942845	8.0557	0
2	0.887599	7.5836	0
3	0.844614	7.2164	0
4	0.80593	6.8859	0
5	0.764084	6.5283	0
6	0.722694	6.1747	0
7	0.675864	5.7746	0
8	0.621779	5.3125	1e-06
9	0.573643	4.9012	3e-06
10	0.525993	4.4941	1.3e-05
11	0.48316	4.1281	4.8e-05
12	0.445145	3.8033	0.000147
13	0.407514	3.4818	0.000422
14	0.385617	3.2947	0.000761
15	0.366764	3.1336	0.001243
16	0.352813	3.0144	0.00177
17	0.332191	2.8382	0.002935

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.942845	8.0557	0
1	-0.012219	-0.1044	0.541431
2	0.08143	0.6957	0.244402
3	0.018748	0.1602	0.43659
4	-0.037726	-0.3223	0.625939
5	-0.011937	-0.102	0.540478
6	-0.076096	-0.6502	0.741186
7	-0.09583	-0.8188	0.792208
8	0.0095	0.0812	0.467764
9	-0.042881	-0.3664	0.642427
10	0.01953	0.1669	0.43397
11	0.022613	0.1932	0.423668
12	-0.012848	-0.1098	0.543556
13	0.139625	1.193	0.118375
14	0.018967	0.1621	0.435855
15	0.056203	0.4802	0.316261
16	-0.056354	-0.4815	0.684196
17	-0.098846	-0.8445	0.799436

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.942845 & 8.0557 & 0 \tabularnewline
1 & -0.012219 & -0.1044 & 0.541431 \tabularnewline
2 & 0.08143 & 0.6957 & 0.244402 \tabularnewline
3 & 0.018748 & 0.1602 & 0.43659 \tabularnewline
4 & -0.037726 & -0.3223 & 0.625939 \tabularnewline
5 & -0.011937 & -0.102 & 0.540478 \tabularnewline
6 & -0.076096 & -0.6502 & 0.741186 \tabularnewline
7 & -0.09583 & -0.8188 & 0.792208 \tabularnewline
8 & 0.0095 & 0.0812 & 0.467764 \tabularnewline
9 & -0.042881 & -0.3664 & 0.642427 \tabularnewline
10 & 0.01953 & 0.1669 & 0.43397 \tabularnewline
11 & 0.022613 & 0.1932 & 0.423668 \tabularnewline
12 & -0.012848 & -0.1098 & 0.543556 \tabularnewline
13 & 0.139625 & 1.193 & 0.118375 \tabularnewline
14 & 0.018967 & 0.1621 & 0.435855 \tabularnewline
15 & 0.056203 & 0.4802 & 0.316261 \tabularnewline
16 & -0.056354 & -0.4815 & 0.684196 \tabularnewline
17 & -0.098846 & -0.8445 & 0.799436 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6810&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]0.942845[/C][C]8.0557[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.012219[/C][C]-0.1044[/C][C]0.541431[/C][/ROW]
[ROW][C]2[/C][C]0.08143[/C][C]0.6957[/C][C]0.244402[/C][/ROW]
[ROW][C]3[/C][C]0.018748[/C][C]0.1602[/C][C]0.43659[/C][/ROW]
[ROW][C]4[/C][C]-0.037726[/C][C]-0.3223[/C][C]0.625939[/C][/ROW]
[ROW][C]5[/C][C]-0.011937[/C][C]-0.102[/C][C]0.540478[/C][/ROW]
[ROW][C]6[/C][C]-0.076096[/C][C]-0.6502[/C][C]0.741186[/C][/ROW]
[ROW][C]7[/C][C]-0.09583[/C][C]-0.8188[/C][C]0.792208[/C][/ROW]
[ROW][C]8[/C][C]0.0095[/C][C]0.0812[/C][C]0.467764[/C][/ROW]
[ROW][C]9[/C][C]-0.042881[/C][C]-0.3664[/C][C]0.642427[/C][/ROW]
[ROW][C]10[/C][C]0.01953[/C][C]0.1669[/C][C]0.43397[/C][/ROW]
[ROW][C]11[/C][C]0.022613[/C][C]0.1932[/C][C]0.423668[/C][/ROW]
[ROW][C]12[/C][C]-0.012848[/C][C]-0.1098[/C][C]0.543556[/C][/ROW]
[ROW][C]13[/C][C]0.139625[/C][C]1.193[/C][C]0.118375[/C][/ROW]
[ROW][C]14[/C][C]0.018967[/C][C]0.1621[/C][C]0.435855[/C][/ROW]
[ROW][C]15[/C][C]0.056203[/C][C]0.4802[/C][C]0.316261[/C][/ROW]
[ROW][C]16[/C][C]-0.056354[/C][C]-0.4815[/C][C]0.684196[/C][/ROW]
[ROW][C]17[/C][C]-0.098846[/C][C]-0.8445[/C][C]0.799436[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6810&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6810&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	0.942845	8.0557	0
1	-0.012219	-0.1044	0.541431
2	0.08143	0.6957	0.244402
3	0.018748	0.1602	0.43659
4	-0.037726	-0.3223	0.625939
5	-0.011937	-0.102	0.540478
6	-0.076096	-0.6502	0.741186
7	-0.09583	-0.8188	0.792208
8	0.0095	0.0812	0.467764
9	-0.042881	-0.3664	0.642427
10	0.01953	0.1669	0.43397
11	0.022613	0.1932	0.423668
12	-0.012848	-0.1098	0.543556
13	0.139625	1.193	0.118375
14	0.018967	0.1621	0.435855
15	0.056203	0.4802	0.316261
16	-0.056354	-0.4815	0.684196
17	-0.098846	-0.8445	0.799436

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 = 0 ; 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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Dataset

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Figures (Output of Computation)

Input Parameters & R Code