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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 15 Dec 2010 15:27:59 +0000

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/2010/Dec/15/t12924269731xvv9r0yfkq5iyg.htm/, Retrieved Fri, 03 May 2024 08:12:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110474, Retrieved Fri, 03 May 2024 08:12:36 +0000

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Estimated Impact

147

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D      [(Partial) Autocorrelation Function] [workshop 9 link 1] [2010-12-15 15:27:59] [95216a33d813bfae7986b08ea3322626] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110474&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]2 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=110474&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110474&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.944304	7.3145	0
2	0.891301	6.904	0
3	0.829209	6.423	0
4	0.741943	5.7471	0
5	0.666093	5.1595	1e-06
6	0.580769	4.4986	1.6e-05
7	0.493164	3.82	0.000159
8	0.393615	3.0489	0.001707
9	0.311076	2.4096	0.009528
10	0.229731	1.7795	0.040112
11	0.158719	1.2294	0.111855
12	0.093222	0.7221	0.23652
13	0.017412	0.1349	0.446582
14	-0.060618	-0.4695	0.320192
15	-0.138094	-1.0697	0.144525
16	-0.202784	-1.5708	0.060749
17	-0.260869	-2.0207	0.023891

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.944304 & 7.3145 & 0 \tabularnewline
2 & 0.891301 & 6.904 & 0 \tabularnewline
3 & 0.829209 & 6.423 & 0 \tabularnewline
4 & 0.741943 & 5.7471 & 0 \tabularnewline
5 & 0.666093 & 5.1595 & 1e-06 \tabularnewline
6 & 0.580769 & 4.4986 & 1.6e-05 \tabularnewline
7 & 0.493164 & 3.82 & 0.000159 \tabularnewline
8 & 0.393615 & 3.0489 & 0.001707 \tabularnewline
9 & 0.311076 & 2.4096 & 0.009528 \tabularnewline
10 & 0.229731 & 1.7795 & 0.040112 \tabularnewline
11 & 0.158719 & 1.2294 & 0.111855 \tabularnewline
12 & 0.093222 & 0.7221 & 0.23652 \tabularnewline
13 & 0.017412 & 0.1349 & 0.446582 \tabularnewline
14 & -0.060618 & -0.4695 & 0.320192 \tabularnewline
15 & -0.138094 & -1.0697 & 0.144525 \tabularnewline
16 & -0.202784 & -1.5708 & 0.060749 \tabularnewline
17 & -0.260869 & -2.0207 & 0.023891 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110474&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]0.944304[/C][C]7.3145[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.891301[/C][C]6.904[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.829209[/C][C]6.423[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.741943[/C][C]5.7471[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.666093[/C][C]5.1595[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.580769[/C][C]4.4986[/C][C]1.6e-05[/C][/ROW]
[ROW][C]7[/C][C]0.493164[/C][C]3.82[/C][C]0.000159[/C][/ROW]
[ROW][C]8[/C][C]0.393615[/C][C]3.0489[/C][C]0.001707[/C][/ROW]
[ROW][C]9[/C][C]0.311076[/C][C]2.4096[/C][C]0.009528[/C][/ROW]
[ROW][C]10[/C][C]0.229731[/C][C]1.7795[/C][C]0.040112[/C][/ROW]
[ROW][C]11[/C][C]0.158719[/C][C]1.2294[/C][C]0.111855[/C][/ROW]
[ROW][C]12[/C][C]0.093222[/C][C]0.7221[/C][C]0.23652[/C][/ROW]
[ROW][C]13[/C][C]0.017412[/C][C]0.1349[/C][C]0.446582[/C][/ROW]
[ROW][C]14[/C][C]-0.060618[/C][C]-0.4695[/C][C]0.320192[/C][/ROW]
[ROW][C]15[/C][C]-0.138094[/C][C]-1.0697[/C][C]0.144525[/C][/ROW]
[ROW][C]16[/C][C]-0.202784[/C][C]-1.5708[/C][C]0.060749[/C][/ROW]
[ROW][C]17[/C][C]-0.260869[/C][C]-2.0207[/C][C]0.023891[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110474&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110474&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	0.944304	7.3145	0
2	0.891301	6.904	0
3	0.829209	6.423	0
4	0.741943	5.7471	0
5	0.666093	5.1595	1e-06
6	0.580769	4.4986	1.6e-05
7	0.493164	3.82	0.000159
8	0.393615	3.0489	0.001707
9	0.311076	2.4096	0.009528
10	0.229731	1.7795	0.040112
11	0.158719	1.2294	0.111855
12	0.093222	0.7221	0.23652
13	0.017412	0.1349	0.446582
14	-0.060618	-0.4695	0.320192
15	-0.138094	-1.0697	0.144525
16	-0.202784	-1.5708	0.060749
17	-0.260869	-2.0207	0.023891

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.944304	7.3145	0
2	-0.003767	-0.0292	0.488409
3	-0.111399	-0.8629	0.195816
4	-0.273458	-2.1182	0.019155
5	0.048716	0.3774	0.35362
6	-0.095671	-0.7411	0.230773
7	-0.04486	-0.3475	0.364723
8	-0.221311	-1.7143	0.045821
9	0.139981	1.0843	0.141288
10	-0.039646	-0.3071	0.379916
11	0.093884	0.7272	0.234959
12	-0.136835	-1.0599	0.146715
13	-0.11734	-0.9089	0.183517
14	-0.198544	-1.5379	0.064664
15	-0.011805	-0.0914	0.463723
16	0.017552	0.136	0.446155
17	0.043914	0.3402	0.367464

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.944304 & 7.3145 & 0 \tabularnewline
2 & -0.003767 & -0.0292 & 0.488409 \tabularnewline
3 & -0.111399 & -0.8629 & 0.195816 \tabularnewline
4 & -0.273458 & -2.1182 & 0.019155 \tabularnewline
5 & 0.048716 & 0.3774 & 0.35362 \tabularnewline
6 & -0.095671 & -0.7411 & 0.230773 \tabularnewline
7 & -0.04486 & -0.3475 & 0.364723 \tabularnewline
8 & -0.221311 & -1.7143 & 0.045821 \tabularnewline
9 & 0.139981 & 1.0843 & 0.141288 \tabularnewline
10 & -0.039646 & -0.3071 & 0.379916 \tabularnewline
11 & 0.093884 & 0.7272 & 0.234959 \tabularnewline
12 & -0.136835 & -1.0599 & 0.146715 \tabularnewline
13 & -0.11734 & -0.9089 & 0.183517 \tabularnewline
14 & -0.198544 & -1.5379 & 0.064664 \tabularnewline
15 & -0.011805 & -0.0914 & 0.463723 \tabularnewline
16 & 0.017552 & 0.136 & 0.446155 \tabularnewline
17 & 0.043914 & 0.3402 & 0.367464 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110474&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]0.944304[/C][C]7.3145[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.003767[/C][C]-0.0292[/C][C]0.488409[/C][/ROW]
[ROW][C]3[/C][C]-0.111399[/C][C]-0.8629[/C][C]0.195816[/C][/ROW]
[ROW][C]4[/C][C]-0.273458[/C][C]-2.1182[/C][C]0.019155[/C][/ROW]
[ROW][C]5[/C][C]0.048716[/C][C]0.3774[/C][C]0.35362[/C][/ROW]
[ROW][C]6[/C][C]-0.095671[/C][C]-0.7411[/C][C]0.230773[/C][/ROW]
[ROW][C]7[/C][C]-0.04486[/C][C]-0.3475[/C][C]0.364723[/C][/ROW]
[ROW][C]8[/C][C]-0.221311[/C][C]-1.7143[/C][C]0.045821[/C][/ROW]
[ROW][C]9[/C][C]0.139981[/C][C]1.0843[/C][C]0.141288[/C][/ROW]
[ROW][C]10[/C][C]-0.039646[/C][C]-0.3071[/C][C]0.379916[/C][/ROW]
[ROW][C]11[/C][C]0.093884[/C][C]0.7272[/C][C]0.234959[/C][/ROW]
[ROW][C]12[/C][C]-0.136835[/C][C]-1.0599[/C][C]0.146715[/C][/ROW]
[ROW][C]13[/C][C]-0.11734[/C][C]-0.9089[/C][C]0.183517[/C][/ROW]
[ROW][C]14[/C][C]-0.198544[/C][C]-1.5379[/C][C]0.064664[/C][/ROW]
[ROW][C]15[/C][C]-0.011805[/C][C]-0.0914[/C][C]0.463723[/C][/ROW]
[ROW][C]16[/C][C]0.017552[/C][C]0.136[/C][C]0.446155[/C][/ROW]
[ROW][C]17[/C][C]0.043914[/C][C]0.3402[/C][C]0.367464[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110474&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110474&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	0.944304	7.3145	0
2	-0.003767	-0.0292	0.488409
3	-0.111399	-0.8629	0.195816
4	-0.273458	-2.1182	0.019155
5	0.048716	0.3774	0.35362
6	-0.095671	-0.7411	0.230773
7	-0.04486	-0.3475	0.364723
8	-0.221311	-1.7143	0.045821
9	0.139981	1.0843	0.141288
10	-0.039646	-0.3071	0.379916
11	0.093884	0.7272	0.234959
12	-0.136835	-1.0599	0.146715
13	-0.11734	-0.9089	0.183517
14	-0.198544	-1.5379	0.064664
15	-0.011805	-0.0914	0.463723
16	0.017552	0.136	0.446155
17	0.043914	0.3402	0.367464

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 ; par8 = ;

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code