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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 27 Nov 2009 11:59:57 -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/t12593485069csutmtgcjrnzjb.htm/, Retrieved Mon, 29 Apr 2024 23:07:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61134, Retrieved Mon, 29 Apr 2024 23:07:37 +0000

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No (this computation is public)

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Estimated Impact

110

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-       [(Partial) Autocorrelation Function] [] [2009-11-27 18:59:57] [99bf2a1e962091d45abf4c2600a412f9] [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=61134&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=61134&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61134&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	0.89392	6.9243	0
2	0.73179	5.6684	0
3	0.610798	4.7312	7e-06
4	0.554571	4.2957	3.2e-05
5	0.552561	4.2801	3.4e-05
6	0.535436	4.1475	5.4e-05
7	0.46632	3.6121	0.000311
8	0.387629	3.0026	0.00195
9	0.362084	2.8047	0.003389
10	0.386803	2.9962	0.001985
11	0.445926	3.4541	0.000509
12	0.455557	3.5287	0.000404
13	0.321152	2.4876	0.007828
14	0.158761	1.2298	0.111794
15	0.041171	0.3189	0.375451
16	-0.013558	-0.105	0.458357
17	-0.023209	-0.1798	0.428967

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.89392 & 6.9243 & 0 \tabularnewline
2 & 0.73179 & 5.6684 & 0 \tabularnewline
3 & 0.610798 & 4.7312 & 7e-06 \tabularnewline
4 & 0.554571 & 4.2957 & 3.2e-05 \tabularnewline
5 & 0.552561 & 4.2801 & 3.4e-05 \tabularnewline
6 & 0.535436 & 4.1475 & 5.4e-05 \tabularnewline
7 & 0.46632 & 3.6121 & 0.000311 \tabularnewline
8 & 0.387629 & 3.0026 & 0.00195 \tabularnewline
9 & 0.362084 & 2.8047 & 0.003389 \tabularnewline
10 & 0.386803 & 2.9962 & 0.001985 \tabularnewline
11 & 0.445926 & 3.4541 & 0.000509 \tabularnewline
12 & 0.455557 & 3.5287 & 0.000404 \tabularnewline
13 & 0.321152 & 2.4876 & 0.007828 \tabularnewline
14 & 0.158761 & 1.2298 & 0.111794 \tabularnewline
15 & 0.041171 & 0.3189 & 0.375451 \tabularnewline
16 & -0.013558 & -0.105 & 0.458357 \tabularnewline
17 & -0.023209 & -0.1798 & 0.428967 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61134&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]0.89392[/C][C]6.9243[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.73179[/C][C]5.6684[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.610798[/C][C]4.7312[/C][C]7e-06[/C][/ROW]
[ROW][C]4[/C][C]0.554571[/C][C]4.2957[/C][C]3.2e-05[/C][/ROW]
[ROW][C]5[/C][C]0.552561[/C][C]4.2801[/C][C]3.4e-05[/C][/ROW]
[ROW][C]6[/C][C]0.535436[/C][C]4.1475[/C][C]5.4e-05[/C][/ROW]
[ROW][C]7[/C][C]0.46632[/C][C]3.6121[/C][C]0.000311[/C][/ROW]
[ROW][C]8[/C][C]0.387629[/C][C]3.0026[/C][C]0.00195[/C][/ROW]
[ROW][C]9[/C][C]0.362084[/C][C]2.8047[/C][C]0.003389[/C][/ROW]
[ROW][C]10[/C][C]0.386803[/C][C]2.9962[/C][C]0.001985[/C][/ROW]
[ROW][C]11[/C][C]0.445926[/C][C]3.4541[/C][C]0.000509[/C][/ROW]
[ROW][C]12[/C][C]0.455557[/C][C]3.5287[/C][C]0.000404[/C][/ROW]
[ROW][C]13[/C][C]0.321152[/C][C]2.4876[/C][C]0.007828[/C][/ROW]
[ROW][C]14[/C][C]0.158761[/C][C]1.2298[/C][C]0.111794[/C][/ROW]
[ROW][C]15[/C][C]0.041171[/C][C]0.3189[/C][C]0.375451[/C][/ROW]
[ROW][C]16[/C][C]-0.013558[/C][C]-0.105[/C][C]0.458357[/C][/ROW]
[ROW][C]17[/C][C]-0.023209[/C][C]-0.1798[/C][C]0.428967[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61134&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61134&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	0.89392	6.9243	0
2	0.73179	5.6684	0
3	0.610798	4.7312	7e-06
4	0.554571	4.2957	3.2e-05
5	0.552561	4.2801	3.4e-05
6	0.535436	4.1475	5.4e-05
7	0.46632	3.6121	0.000311
8	0.387629	3.0026	0.00195
9	0.362084	2.8047	0.003389
10	0.386803	2.9962	0.001985
11	0.445926	3.4541	0.000509
12	0.455557	3.5287	0.000404
13	0.321152	2.4876	0.007828
14	0.158761	1.2298	0.111794
15	0.041171	0.3189	0.375451
16	-0.013558	-0.105	0.458357
17	-0.023209	-0.1798	0.428967

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.89392	6.9243	0
2	-0.335002	-2.5949	0.005938
3	0.207201	1.605	0.056875
4	0.141392	1.0952	0.1389
5	0.158423	1.2271	0.112281
6	-0.134661	-1.0431	0.150548
7	-0.119095	-0.9225	0.17998
8	0.077978	0.604	0.274054
9	0.211026	1.6346	0.053685
10	0.040986	0.3175	0.375991
11	0.155535	1.2048	0.116512
12	-0.204899	-1.5871	0.058869
13	-0.57561	-4.4587	1.8e-05
14	0.134604	1.0426	0.15065
15	-0.073207	-0.5671	0.286394
16	-0.054918	-0.4254	0.336035
17	-0.042218	-0.327	0.372397

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.89392 & 6.9243 & 0 \tabularnewline
2 & -0.335002 & -2.5949 & 0.005938 \tabularnewline
3 & 0.207201 & 1.605 & 0.056875 \tabularnewline
4 & 0.141392 & 1.0952 & 0.1389 \tabularnewline
5 & 0.158423 & 1.2271 & 0.112281 \tabularnewline
6 & -0.134661 & -1.0431 & 0.150548 \tabularnewline
7 & -0.119095 & -0.9225 & 0.17998 \tabularnewline
8 & 0.077978 & 0.604 & 0.274054 \tabularnewline
9 & 0.211026 & 1.6346 & 0.053685 \tabularnewline
10 & 0.040986 & 0.3175 & 0.375991 \tabularnewline
11 & 0.155535 & 1.2048 & 0.116512 \tabularnewline
12 & -0.204899 & -1.5871 & 0.058869 \tabularnewline
13 & -0.57561 & -4.4587 & 1.8e-05 \tabularnewline
14 & 0.134604 & 1.0426 & 0.15065 \tabularnewline
15 & -0.073207 & -0.5671 & 0.286394 \tabularnewline
16 & -0.054918 & -0.4254 & 0.336035 \tabularnewline
17 & -0.042218 & -0.327 & 0.372397 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61134&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]0.89392[/C][C]6.9243[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.335002[/C][C]-2.5949[/C][C]0.005938[/C][/ROW]
[ROW][C]3[/C][C]0.207201[/C][C]1.605[/C][C]0.056875[/C][/ROW]
[ROW][C]4[/C][C]0.141392[/C][C]1.0952[/C][C]0.1389[/C][/ROW]
[ROW][C]5[/C][C]0.158423[/C][C]1.2271[/C][C]0.112281[/C][/ROW]
[ROW][C]6[/C][C]-0.134661[/C][C]-1.0431[/C][C]0.150548[/C][/ROW]
[ROW][C]7[/C][C]-0.119095[/C][C]-0.9225[/C][C]0.17998[/C][/ROW]
[ROW][C]8[/C][C]0.077978[/C][C]0.604[/C][C]0.274054[/C][/ROW]
[ROW][C]9[/C][C]0.211026[/C][C]1.6346[/C][C]0.053685[/C][/ROW]
[ROW][C]10[/C][C]0.040986[/C][C]0.3175[/C][C]0.375991[/C][/ROW]
[ROW][C]11[/C][C]0.155535[/C][C]1.2048[/C][C]0.116512[/C][/ROW]
[ROW][C]12[/C][C]-0.204899[/C][C]-1.5871[/C][C]0.058869[/C][/ROW]
[ROW][C]13[/C][C]-0.57561[/C][C]-4.4587[/C][C]1.8e-05[/C][/ROW]
[ROW][C]14[/C][C]0.134604[/C][C]1.0426[/C][C]0.15065[/C][/ROW]
[ROW][C]15[/C][C]-0.073207[/C][C]-0.5671[/C][C]0.286394[/C][/ROW]
[ROW][C]16[/C][C]-0.054918[/C][C]-0.4254[/C][C]0.336035[/C][/ROW]
[ROW][C]17[/C][C]-0.042218[/C][C]-0.327[/C][C]0.372397[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61134&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61134&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	0.89392	6.9243	0
2	-0.335002	-2.5949	0.005938
3	0.207201	1.605	0.056875
4	0.141392	1.0952	0.1389
5	0.158423	1.2271	0.112281
6	-0.134661	-1.0431	0.150548
7	-0.119095	-0.9225	0.17998
8	0.077978	0.604	0.274054
9	0.211026	1.6346	0.053685
10	0.040986	0.3175	0.375991
11	0.155535	1.2048	0.116512
12	-0.204899	-1.5871	0.058869
13	-0.57561	-4.4587	1.8e-05
14	0.134604	1.0426	0.15065
15	-0.073207	-0.5671	0.286394
16	-0.054918	-0.4254	0.336035
17	-0.042218	-0.327	0.372397

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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Figures (Output of Computation)

Input Parameters & R Code