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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 06 Dec 2007 07:56:15 -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/Dec/06/t119695219731n0bj5zrio886o.htm/, Retrieved Fri, 03 May 2024 14:22:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2646, Retrieved Fri, 03 May 2024 14:22:06 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

171

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

-       [(Partial) Autocorrelation Function] [WS4: Q2 Uitvoer] [2007-12-06 14:56:15] [9b75aacdafaeee3fe66fbd4de075ccd6] [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=2646&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=2646&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2646&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	7.746	0
1	0.572434	4.4341	2e-05
2	0.458872	3.5544	0.000373
3	0.535748	4.1499	5.3e-05
4	0.504991	3.9116	0.000118
5	0.45197	3.5009	0.000441
6	0.556454	4.3103	3.1e-05
7	0.36509	2.828	0.003179
8	0.438041	3.393	0.000615
9	0.364426	2.8228	0.003224
10	0.161095	1.2478	0.10847
11	0.283482	2.1958	0.01599
12	0.501345	3.8834	0.00013
13	0.209416	1.6221	0.05501
14	0.159334	1.2342	0.110971
15	0.151959	1.1771	0.121909
16	0.104481	0.8093	0.210768

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.572434 & 4.4341 & 2e-05 \tabularnewline
2 & 0.458872 & 3.5544 & 0.000373 \tabularnewline
3 & 0.535748 & 4.1499 & 5.3e-05 \tabularnewline
4 & 0.504991 & 3.9116 & 0.000118 \tabularnewline
5 & 0.45197 & 3.5009 & 0.000441 \tabularnewline
6 & 0.556454 & 4.3103 & 3.1e-05 \tabularnewline
7 & 0.36509 & 2.828 & 0.003179 \tabularnewline
8 & 0.438041 & 3.393 & 0.000615 \tabularnewline
9 & 0.364426 & 2.8228 & 0.003224 \tabularnewline
10 & 0.161095 & 1.2478 & 0.10847 \tabularnewline
11 & 0.283482 & 2.1958 & 0.01599 \tabularnewline
12 & 0.501345 & 3.8834 & 0.00013 \tabularnewline
13 & 0.209416 & 1.6221 & 0.05501 \tabularnewline
14 & 0.159334 & 1.2342 & 0.110971 \tabularnewline
15 & 0.151959 & 1.1771 & 0.121909 \tabularnewline
16 & 0.104481 & 0.8093 & 0.210768 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2646&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.572434[/C][C]4.4341[/C][C]2e-05[/C][/ROW]
[ROW][C]2[/C][C]0.458872[/C][C]3.5544[/C][C]0.000373[/C][/ROW]
[ROW][C]3[/C][C]0.535748[/C][C]4.1499[/C][C]5.3e-05[/C][/ROW]
[ROW][C]4[/C][C]0.504991[/C][C]3.9116[/C][C]0.000118[/C][/ROW]
[ROW][C]5[/C][C]0.45197[/C][C]3.5009[/C][C]0.000441[/C][/ROW]
[ROW][C]6[/C][C]0.556454[/C][C]4.3103[/C][C]3.1e-05[/C][/ROW]
[ROW][C]7[/C][C]0.36509[/C][C]2.828[/C][C]0.003179[/C][/ROW]
[ROW][C]8[/C][C]0.438041[/C][C]3.393[/C][C]0.000615[/C][/ROW]
[ROW][C]9[/C][C]0.364426[/C][C]2.8228[/C][C]0.003224[/C][/ROW]
[ROW][C]10[/C][C]0.161095[/C][C]1.2478[/C][C]0.10847[/C][/ROW]
[ROW][C]11[/C][C]0.283482[/C][C]2.1958[/C][C]0.01599[/C][/ROW]
[ROW][C]12[/C][C]0.501345[/C][C]3.8834[/C][C]0.00013[/C][/ROW]
[ROW][C]13[/C][C]0.209416[/C][C]1.6221[/C][C]0.05501[/C][/ROW]
[ROW][C]14[/C][C]0.159334[/C][C]1.2342[/C][C]0.110971[/C][/ROW]
[ROW][C]15[/C][C]0.151959[/C][C]1.1771[/C][C]0.121909[/C][/ROW]
[ROW][C]16[/C][C]0.104481[/C][C]0.8093[/C][C]0.210768[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2646&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2646&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	7.746	0
1	0.572434	4.4341	2e-05
2	0.458872	3.5544	0.000373
3	0.535748	4.1499	5.3e-05
4	0.504991	3.9116	0.000118
5	0.45197	3.5009	0.000441
6	0.556454	4.3103	3.1e-05
7	0.36509	2.828	0.003179
8	0.438041	3.393	0.000615
9	0.364426	2.8228	0.003224
10	0.161095	1.2478	0.10847
11	0.283482	2.1958	0.01599
12	0.501345	3.8834	0.00013
13	0.209416	1.6221	0.05501
14	0.159334	1.2342	0.110971
15	0.151959	1.1771	0.121909
16	0.104481	0.8093	0.210768

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.572434	4.4341	2e-05
1	0.195131	1.5115	0.067958
2	0.328783	2.5467	0.006728
3	0.146129	1.1319	0.131087
4	0.085155	0.6596	0.256016
5	0.270875	2.0982	0.020054
6	-0.216634	-1.678	0.95073
7	0.220257	1.7061	0.04658
8	-0.226515	-1.7546	0.957782
9	-0.306739	-2.376	0.989644
10	0.214331	1.6602	0.051046
11	0.300062	2.3243	0.011757
12	-0.235426	-1.8236	0.963403
13	-0.13444	-1.0414	0.849059
14	-0.109586	-0.8488	0.80033
15	0.017571	0.1361	0.446096
16	-0.071109	-0.5508	0.708094

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.572434 & 4.4341 & 2e-05 \tabularnewline
1 & 0.195131 & 1.5115 & 0.067958 \tabularnewline
2 & 0.328783 & 2.5467 & 0.006728 \tabularnewline
3 & 0.146129 & 1.1319 & 0.131087 \tabularnewline
4 & 0.085155 & 0.6596 & 0.256016 \tabularnewline
5 & 0.270875 & 2.0982 & 0.020054 \tabularnewline
6 & -0.216634 & -1.678 & 0.95073 \tabularnewline
7 & 0.220257 & 1.7061 & 0.04658 \tabularnewline
8 & -0.226515 & -1.7546 & 0.957782 \tabularnewline
9 & -0.306739 & -2.376 & 0.989644 \tabularnewline
10 & 0.214331 & 1.6602 & 0.051046 \tabularnewline
11 & 0.300062 & 2.3243 & 0.011757 \tabularnewline
12 & -0.235426 & -1.8236 & 0.963403 \tabularnewline
13 & -0.13444 & -1.0414 & 0.849059 \tabularnewline
14 & -0.109586 & -0.8488 & 0.80033 \tabularnewline
15 & 0.017571 & 0.1361 & 0.446096 \tabularnewline
16 & -0.071109 & -0.5508 & 0.708094 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2646&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]0.572434[/C][C]4.4341[/C][C]2e-05[/C][/ROW]
[ROW][C]1[/C][C]0.195131[/C][C]1.5115[/C][C]0.067958[/C][/ROW]
[ROW][C]2[/C][C]0.328783[/C][C]2.5467[/C][C]0.006728[/C][/ROW]
[ROW][C]3[/C][C]0.146129[/C][C]1.1319[/C][C]0.131087[/C][/ROW]
[ROW][C]4[/C][C]0.085155[/C][C]0.6596[/C][C]0.256016[/C][/ROW]
[ROW][C]5[/C][C]0.270875[/C][C]2.0982[/C][C]0.020054[/C][/ROW]
[ROW][C]6[/C][C]-0.216634[/C][C]-1.678[/C][C]0.95073[/C][/ROW]
[ROW][C]7[/C][C]0.220257[/C][C]1.7061[/C][C]0.04658[/C][/ROW]
[ROW][C]8[/C][C]-0.226515[/C][C]-1.7546[/C][C]0.957782[/C][/ROW]
[ROW][C]9[/C][C]-0.306739[/C][C]-2.376[/C][C]0.989644[/C][/ROW]
[ROW][C]10[/C][C]0.214331[/C][C]1.6602[/C][C]0.051046[/C][/ROW]
[ROW][C]11[/C][C]0.300062[/C][C]2.3243[/C][C]0.011757[/C][/ROW]
[ROW][C]12[/C][C]-0.235426[/C][C]-1.8236[/C][C]0.963403[/C][/ROW]
[ROW][C]13[/C][C]-0.13444[/C][C]-1.0414[/C][C]0.849059[/C][/ROW]
[ROW][C]14[/C][C]-0.109586[/C][C]-0.8488[/C][C]0.80033[/C][/ROW]
[ROW][C]15[/C][C]0.017571[/C][C]0.1361[/C][C]0.446096[/C][/ROW]
[ROW][C]16[/C][C]-0.071109[/C][C]-0.5508[/C][C]0.708094[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2646&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2646&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	0.572434	4.4341	2e-05
1	0.195131	1.5115	0.067958
2	0.328783	2.5467	0.006728
3	0.146129	1.1319	0.131087
4	0.085155	0.6596	0.256016
5	0.270875	2.0982	0.020054
6	-0.216634	-1.678	0.95073
7	0.220257	1.7061	0.04658
8	-0.226515	-1.7546	0.957782
9	-0.306739	-2.376	0.989644
10	0.214331	1.6602	0.051046
11	0.300062	2.3243	0.011757
12	-0.235426	-1.8236	0.963403
13	-0.13444	-1.0414	0.849059
14	-0.109586	-0.8488	0.80033
15	0.017571	0.1361	0.446096
16	-0.071109	-0.5508	0.708094

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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