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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 27 Nov 2009 10:51:30 -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/t1259344367dmw9jnjqki9iq6k.htm/, Retrieved Sun, 28 Apr 2024 22:04:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61058, Retrieved Sun, 28 Apr 2024 22:04:37 +0000

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User-defined keywords

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118

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 12:16:10] [b98453cac15ba1066b407e146608df68]
-   PD          [(Partial) Autocorrelation Function] [ws8 methode 1] [2009-11-27 17:51:30] [d41d8cd98f00b204e9800998ecf8427e] [Current]
F   P             [(Partial) Autocorrelation Function] [ws8 methode 1 2] [2009-11-27 18:04:26] [74be16979710d4c4e7c6647856088456] 

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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=61058&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=61058&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61058&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	0.329881	2.7002	0.004383
2	0.383293	3.1374	0.001267
3	0.40306	3.2992	0.000778
4	0.232586	1.9038	0.030616
5	0.13503	1.1053	0.136498
6	0.105761	0.8657	0.194875
7	0.098236	0.8041	0.212092
8	0.133621	1.0937	0.138994
9	0.139608	1.1427	0.128606
10	0.059275	0.4852	0.314565
11	0.080643	0.6601	0.255729
12	0.154019	1.2607	0.105895
13	-0.014748	-0.1207	0.452137
14	0.043956	0.3598	0.360067
15	0.047211	0.3864	0.350197
16	-0.061073	-0.4999	0.309391
17	0.022354	0.183	0.427685
18	-0.078243	-0.6404	0.262033

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.329881 & 2.7002 & 0.004383 \tabularnewline
2 & 0.383293 & 3.1374 & 0.001267 \tabularnewline
3 & 0.40306 & 3.2992 & 0.000778 \tabularnewline
4 & 0.232586 & 1.9038 & 0.030616 \tabularnewline
5 & 0.13503 & 1.1053 & 0.136498 \tabularnewline
6 & 0.105761 & 0.8657 & 0.194875 \tabularnewline
7 & 0.098236 & 0.8041 & 0.212092 \tabularnewline
8 & 0.133621 & 1.0937 & 0.138994 \tabularnewline
9 & 0.139608 & 1.1427 & 0.128606 \tabularnewline
10 & 0.059275 & 0.4852 & 0.314565 \tabularnewline
11 & 0.080643 & 0.6601 & 0.255729 \tabularnewline
12 & 0.154019 & 1.2607 & 0.105895 \tabularnewline
13 & -0.014748 & -0.1207 & 0.452137 \tabularnewline
14 & 0.043956 & 0.3598 & 0.360067 \tabularnewline
15 & 0.047211 & 0.3864 & 0.350197 \tabularnewline
16 & -0.061073 & -0.4999 & 0.309391 \tabularnewline
17 & 0.022354 & 0.183 & 0.427685 \tabularnewline
18 & -0.078243 & -0.6404 & 0.262033 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61058&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]0.329881[/C][C]2.7002[/C][C]0.004383[/C][/ROW]
[ROW][C]2[/C][C]0.383293[/C][C]3.1374[/C][C]0.001267[/C][/ROW]
[ROW][C]3[/C][C]0.40306[/C][C]3.2992[/C][C]0.000778[/C][/ROW]
[ROW][C]4[/C][C]0.232586[/C][C]1.9038[/C][C]0.030616[/C][/ROW]
[ROW][C]5[/C][C]0.13503[/C][C]1.1053[/C][C]0.136498[/C][/ROW]
[ROW][C]6[/C][C]0.105761[/C][C]0.8657[/C][C]0.194875[/C][/ROW]
[ROW][C]7[/C][C]0.098236[/C][C]0.8041[/C][C]0.212092[/C][/ROW]
[ROW][C]8[/C][C]0.133621[/C][C]1.0937[/C][C]0.138994[/C][/ROW]
[ROW][C]9[/C][C]0.139608[/C][C]1.1427[/C][C]0.128606[/C][/ROW]
[ROW][C]10[/C][C]0.059275[/C][C]0.4852[/C][C]0.314565[/C][/ROW]
[ROW][C]11[/C][C]0.080643[/C][C]0.6601[/C][C]0.255729[/C][/ROW]
[ROW][C]12[/C][C]0.154019[/C][C]1.2607[/C][C]0.105895[/C][/ROW]
[ROW][C]13[/C][C]-0.014748[/C][C]-0.1207[/C][C]0.452137[/C][/ROW]
[ROW][C]14[/C][C]0.043956[/C][C]0.3598[/C][C]0.360067[/C][/ROW]
[ROW][C]15[/C][C]0.047211[/C][C]0.3864[/C][C]0.350197[/C][/ROW]
[ROW][C]16[/C][C]-0.061073[/C][C]-0.4999[/C][C]0.309391[/C][/ROW]
[ROW][C]17[/C][C]0.022354[/C][C]0.183[/C][C]0.427685[/C][/ROW]
[ROW][C]18[/C][C]-0.078243[/C][C]-0.6404[/C][C]0.262033[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61058&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61058&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	0.329881	2.7002	0.004383
2	0.383293	3.1374	0.001267
3	0.40306	3.2992	0.000778
4	0.232586	1.9038	0.030616
5	0.13503	1.1053	0.136498
6	0.105761	0.8657	0.194875
7	0.098236	0.8041	0.212092
8	0.133621	1.0937	0.138994
9	0.139608	1.1427	0.128606
10	0.059275	0.4852	0.314565
11	0.080643	0.6601	0.255729
12	0.154019	1.2607	0.105895
13	-0.014748	-0.1207	0.452137
14	0.043956	0.3598	0.360067
15	0.047211	0.3864	0.350197
16	-0.061073	-0.4999	0.309391
17	0.022354	0.183	0.427685
18	-0.078243	-0.6404	0.262033

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.329881	2.7002	0.004383
2	0.307987	2.521	0.007045
3	0.265249	2.1712	0.016733
4	-0.011787	-0.0965	0.461713
5	-0.132225	-1.0823	0.141498
6	-0.08292	-0.6787	0.249824
7	0.041052	0.336	0.36895
8	0.156786	1.2834	0.101895
9	0.127348	1.0424	0.15049
10	-0.082687	-0.6768	0.250425
11	-0.100861	-0.8256	0.205986
12	0.079928	0.6542	0.257599
13	-0.064742	-0.5299	0.298955
14	0.02685	0.2198	0.413357
15	0.013199	0.108	0.457143
16	-0.110122	-0.9014	0.185305
17	0.027395	0.2242	0.411627
18	-0.079667	-0.6521	0.258282

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.329881 & 2.7002 & 0.004383 \tabularnewline
2 & 0.307987 & 2.521 & 0.007045 \tabularnewline
3 & 0.265249 & 2.1712 & 0.016733 \tabularnewline
4 & -0.011787 & -0.0965 & 0.461713 \tabularnewline
5 & -0.132225 & -1.0823 & 0.141498 \tabularnewline
6 & -0.08292 & -0.6787 & 0.249824 \tabularnewline
7 & 0.041052 & 0.336 & 0.36895 \tabularnewline
8 & 0.156786 & 1.2834 & 0.101895 \tabularnewline
9 & 0.127348 & 1.0424 & 0.15049 \tabularnewline
10 & -0.082687 & -0.6768 & 0.250425 \tabularnewline
11 & -0.100861 & -0.8256 & 0.205986 \tabularnewline
12 & 0.079928 & 0.6542 & 0.257599 \tabularnewline
13 & -0.064742 & -0.5299 & 0.298955 \tabularnewline
14 & 0.02685 & 0.2198 & 0.413357 \tabularnewline
15 & 0.013199 & 0.108 & 0.457143 \tabularnewline
16 & -0.110122 & -0.9014 & 0.185305 \tabularnewline
17 & 0.027395 & 0.2242 & 0.411627 \tabularnewline
18 & -0.079667 & -0.6521 & 0.258282 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61058&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]0.329881[/C][C]2.7002[/C][C]0.004383[/C][/ROW]
[ROW][C]2[/C][C]0.307987[/C][C]2.521[/C][C]0.007045[/C][/ROW]
[ROW][C]3[/C][C]0.265249[/C][C]2.1712[/C][C]0.016733[/C][/ROW]
[ROW][C]4[/C][C]-0.011787[/C][C]-0.0965[/C][C]0.461713[/C][/ROW]
[ROW][C]5[/C][C]-0.132225[/C][C]-1.0823[/C][C]0.141498[/C][/ROW]
[ROW][C]6[/C][C]-0.08292[/C][C]-0.6787[/C][C]0.249824[/C][/ROW]
[ROW][C]7[/C][C]0.041052[/C][C]0.336[/C][C]0.36895[/C][/ROW]
[ROW][C]8[/C][C]0.156786[/C][C]1.2834[/C][C]0.101895[/C][/ROW]
[ROW][C]9[/C][C]0.127348[/C][C]1.0424[/C][C]0.15049[/C][/ROW]
[ROW][C]10[/C][C]-0.082687[/C][C]-0.6768[/C][C]0.250425[/C][/ROW]
[ROW][C]11[/C][C]-0.100861[/C][C]-0.8256[/C][C]0.205986[/C][/ROW]
[ROW][C]12[/C][C]0.079928[/C][C]0.6542[/C][C]0.257599[/C][/ROW]
[ROW][C]13[/C][C]-0.064742[/C][C]-0.5299[/C][C]0.298955[/C][/ROW]
[ROW][C]14[/C][C]0.02685[/C][C]0.2198[/C][C]0.413357[/C][/ROW]
[ROW][C]15[/C][C]0.013199[/C][C]0.108[/C][C]0.457143[/C][/ROW]
[ROW][C]16[/C][C]-0.110122[/C][C]-0.9014[/C][C]0.185305[/C][/ROW]
[ROW][C]17[/C][C]0.027395[/C][C]0.2242[/C][C]0.411627[/C][/ROW]
[ROW][C]18[/C][C]-0.079667[/C][C]-0.6521[/C][C]0.258282[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61058&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61058&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	0.329881	2.7002	0.004383
2	0.307987	2.521	0.007045
3	0.265249	2.1712	0.016733
4	-0.011787	-0.0965	0.461713
5	-0.132225	-1.0823	0.141498
6	-0.08292	-0.6787	0.249824
7	0.041052	0.336	0.36895
8	0.156786	1.2834	0.101895
9	0.127348	1.0424	0.15049
10	-0.082687	-0.6768	0.250425
11	-0.100861	-0.8256	0.205986
12	0.079928	0.6542	0.257599
13	-0.064742	-0.5299	0.298955
14	0.02685	0.2198	0.413357
15	0.013199	0.108	0.457143
16	-0.110122	-0.9014	0.185305
17	0.027395	0.2242	0.411627
18	-0.079667	-0.6521	0.258282

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; 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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code