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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 27 Nov 2009 12:22:32 -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/2009/Nov/27/t1259349796ntlxgsj6v5c1gvp.htm/, Retrieved Mon, 29 Apr 2024 21:58:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61166, Retrieved Mon, 29 Apr 2024 21:58:07 +0000

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User-defined keywords

Estimated Impact

140

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:19:56] [b98453cac15ba1066b407e146608df68]
-   PD          [(Partial) Autocorrelation Function] [] [2009-11-27 19:22:32] [c88a5f1b97e332c6387d668c465455af] [Current]

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Summary of computational 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 computational 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=61166&T=0

[TABLE]
[ROW][C]Summary of computational 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=61166&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61166&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 computational 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
1	0.857101	5.9382	0
2	0.624399	4.326	3.8e-05
3	0.363064	2.5154	0.007646
4	0.174326	1.2078	0.116527
5	0.052881	0.3664	0.35785
6	-0.023409	-0.1622	0.435923
7	-0.064482	-0.4467	0.328535
8	-0.067535	-0.4679	0.320988
9	-0.041496	-0.2875	0.387486
10	-0.031104	-0.2155	0.415149
11	-0.013437	-0.0931	0.463108
12	-0.009048	-0.0627	0.475138
13	0.024082	0.1668	0.434097
14	0.018624	0.129	0.448937
15	0.01057	0.0732	0.470963
16	-0.020871	-0.1446	0.442816
17	-0.050103	-0.3471	0.365007

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.857101 & 5.9382 & 0 \tabularnewline
2 & 0.624399 & 4.326 & 3.8e-05 \tabularnewline
3 & 0.363064 & 2.5154 & 0.007646 \tabularnewline
4 & 0.174326 & 1.2078 & 0.116527 \tabularnewline
5 & 0.052881 & 0.3664 & 0.35785 \tabularnewline
6 & -0.023409 & -0.1622 & 0.435923 \tabularnewline
7 & -0.064482 & -0.4467 & 0.328535 \tabularnewline
8 & -0.067535 & -0.4679 & 0.320988 \tabularnewline
9 & -0.041496 & -0.2875 & 0.387486 \tabularnewline
10 & -0.031104 & -0.2155 & 0.415149 \tabularnewline
11 & -0.013437 & -0.0931 & 0.463108 \tabularnewline
12 & -0.009048 & -0.0627 & 0.475138 \tabularnewline
13 & 0.024082 & 0.1668 & 0.434097 \tabularnewline
14 & 0.018624 & 0.129 & 0.448937 \tabularnewline
15 & 0.01057 & 0.0732 & 0.470963 \tabularnewline
16 & -0.020871 & -0.1446 & 0.442816 \tabularnewline
17 & -0.050103 & -0.3471 & 0.365007 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61166&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]1[/C][C]0.857101[/C][C]5.9382[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.624399[/C][C]4.326[/C][C]3.8e-05[/C][/ROW]
[ROW][C]3[/C][C]0.363064[/C][C]2.5154[/C][C]0.007646[/C][/ROW]
[ROW][C]4[/C][C]0.174326[/C][C]1.2078[/C][C]0.116527[/C][/ROW]
[ROW][C]5[/C][C]0.052881[/C][C]0.3664[/C][C]0.35785[/C][/ROW]
[ROW][C]6[/C][C]-0.023409[/C][C]-0.1622[/C][C]0.435923[/C][/ROW]
[ROW][C]7[/C][C]-0.064482[/C][C]-0.4467[/C][C]0.328535[/C][/ROW]
[ROW][C]8[/C][C]-0.067535[/C][C]-0.4679[/C][C]0.320988[/C][/ROW]
[ROW][C]9[/C][C]-0.041496[/C][C]-0.2875[/C][C]0.387486[/C][/ROW]
[ROW][C]10[/C][C]-0.031104[/C][C]-0.2155[/C][C]0.415149[/C][/ROW]
[ROW][C]11[/C][C]-0.013437[/C][C]-0.0931[/C][C]0.463108[/C][/ROW]
[ROW][C]12[/C][C]-0.009048[/C][C]-0.0627[/C][C]0.475138[/C][/ROW]
[ROW][C]13[/C][C]0.024082[/C][C]0.1668[/C][C]0.434097[/C][/ROW]
[ROW][C]14[/C][C]0.018624[/C][C]0.129[/C][C]0.448937[/C][/ROW]
[ROW][C]15[/C][C]0.01057[/C][C]0.0732[/C][C]0.470963[/C][/ROW]
[ROW][C]16[/C][C]-0.020871[/C][C]-0.1446[/C][C]0.442816[/C][/ROW]
[ROW][C]17[/C][C]-0.050103[/C][C]-0.3471[/C][C]0.365007[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61166&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61166&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
1	0.857101	5.9382	0
2	0.624399	4.326	3.8e-05
3	0.363064	2.5154	0.007646
4	0.174326	1.2078	0.116527
5	0.052881	0.3664	0.35785
6	-0.023409	-0.1622	0.435923
7	-0.064482	-0.4467	0.328535
8	-0.067535	-0.4679	0.320988
9	-0.041496	-0.2875	0.387486
10	-0.031104	-0.2155	0.415149
11	-0.013437	-0.0931	0.463108
12	-0.009048	-0.0627	0.475138
13	0.024082	0.1668	0.434097
14	0.018624	0.129	0.448937
15	0.01057	0.0732	0.470963
16	-0.020871	-0.1446	0.442816
17	-0.050103	-0.3471	0.365007

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.857101	5.9382	0
2	-0.415348	-2.8776	0.002982
3	-0.174851	-1.2114	0.115835
4	0.173934	1.2051	0.117045
5	-0.030633	-0.2122	0.416413
6	-0.105323	-0.7297	0.234559
7	0.033971	0.2354	0.407467
8	0.0835	0.5785	0.282814
9	0.005802	0.0402	0.484052
10	-0.149397	-1.0351	0.152916
11	0.125517	0.8696	0.194421
12	-0.009466	-0.0656	0.473992
13	0.090137	0.6245	0.267633
14	-0.223362	-1.5475	0.064156
15	0.099901	0.6921	0.246094
16	-0.011006	-0.0762	0.469769
17	-0.068035	-0.4714	0.31976

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.857101 & 5.9382 & 0 \tabularnewline
2 & -0.415348 & -2.8776 & 0.002982 \tabularnewline
3 & -0.174851 & -1.2114 & 0.115835 \tabularnewline
4 & 0.173934 & 1.2051 & 0.117045 \tabularnewline
5 & -0.030633 & -0.2122 & 0.416413 \tabularnewline
6 & -0.105323 & -0.7297 & 0.234559 \tabularnewline
7 & 0.033971 & 0.2354 & 0.407467 \tabularnewline
8 & 0.0835 & 0.5785 & 0.282814 \tabularnewline
9 & 0.005802 & 0.0402 & 0.484052 \tabularnewline
10 & -0.149397 & -1.0351 & 0.152916 \tabularnewline
11 & 0.125517 & 0.8696 & 0.194421 \tabularnewline
12 & -0.009466 & -0.0656 & 0.473992 \tabularnewline
13 & 0.090137 & 0.6245 & 0.267633 \tabularnewline
14 & -0.223362 & -1.5475 & 0.064156 \tabularnewline
15 & 0.099901 & 0.6921 & 0.246094 \tabularnewline
16 & -0.011006 & -0.0762 & 0.469769 \tabularnewline
17 & -0.068035 & -0.4714 & 0.31976 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61166&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]1[/C][C]0.857101[/C][C]5.9382[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.415348[/C][C]-2.8776[/C][C]0.002982[/C][/ROW]
[ROW][C]3[/C][C]-0.174851[/C][C]-1.2114[/C][C]0.115835[/C][/ROW]
[ROW][C]4[/C][C]0.173934[/C][C]1.2051[/C][C]0.117045[/C][/ROW]
[ROW][C]5[/C][C]-0.030633[/C][C]-0.2122[/C][C]0.416413[/C][/ROW]
[ROW][C]6[/C][C]-0.105323[/C][C]-0.7297[/C][C]0.234559[/C][/ROW]
[ROW][C]7[/C][C]0.033971[/C][C]0.2354[/C][C]0.407467[/C][/ROW]
[ROW][C]8[/C][C]0.0835[/C][C]0.5785[/C][C]0.282814[/C][/ROW]
[ROW][C]9[/C][C]0.005802[/C][C]0.0402[/C][C]0.484052[/C][/ROW]
[ROW][C]10[/C][C]-0.149397[/C][C]-1.0351[/C][C]0.152916[/C][/ROW]
[ROW][C]11[/C][C]0.125517[/C][C]0.8696[/C][C]0.194421[/C][/ROW]
[ROW][C]12[/C][C]-0.009466[/C][C]-0.0656[/C][C]0.473992[/C][/ROW]
[ROW][C]13[/C][C]0.090137[/C][C]0.6245[/C][C]0.267633[/C][/ROW]
[ROW][C]14[/C][C]-0.223362[/C][C]-1.5475[/C][C]0.064156[/C][/ROW]
[ROW][C]15[/C][C]0.099901[/C][C]0.6921[/C][C]0.246094[/C][/ROW]
[ROW][C]16[/C][C]-0.011006[/C][C]-0.0762[/C][C]0.469769[/C][/ROW]
[ROW][C]17[/C][C]-0.068035[/C][C]-0.4714[/C][C]0.31976[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61166&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61166&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
1	0.857101	5.9382	0
2	-0.415348	-2.8776	0.002982
3	-0.174851	-1.2114	0.115835
4	0.173934	1.2051	0.117045
5	-0.030633	-0.2122	0.416413
6	-0.105323	-0.7297	0.234559
7	0.033971	0.2354	0.407467
8	0.0835	0.5785	0.282814
9	0.005802	0.0402	0.484052
10	-0.149397	-1.0351	0.152916
11	0.125517	0.8696	0.194421
12	-0.009466	-0.0656	0.473992
13	0.090137	0.6245	0.267633
14	-0.223362	-1.5475	0.064156
15	0.099901	0.6921	0.246094
16	-0.011006	-0.0762	0.469769
17	-0.068035	-0.4714	0.31976

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 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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 2:(par1+1)) {
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(abs(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,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(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code