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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 27 Dec 2010 21:58:03 +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/27/t12934869719tj6fz4x8n1oc0c.htm/, Retrieved Mon, 06 May 2024 12:20:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116156, Retrieved Mon, 06 May 2024 12:20:40 +0000

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Estimated Impact

105

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

-     [Spectral Analysis] [] [2010-12-27 20:46:00] [f57e4c4cbbe8f12a19647529ae7266aa]
- RMP     [(Partial) Autocorrelation Function] [] [2010-12-27 21:58:03] [c984196f1244e05baf3e7c2e52d47a33] [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=116156&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=116156&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116156&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	0.545154	4.2578	3.6e-05
2	0.389335	3.0408	0.001737
3	0.496235	3.8757	0.000131
4	0.451583	3.527	0.000402
5	0.326388	2.5492	0.006664
6	0.311861	2.4357	0.0089
7	0.133592	1.0434	0.150443
8	0.159375	1.2448	0.108991
9	-0.006271	-0.049	0.48055
10	-0.178376	-1.3932	0.084314
11	-0.058628	-0.4579	0.324325
12	0.144987	1.1324	0.130951
13	-0.157168	-1.2275	0.112172
14	-0.27827	-2.1734	0.016823
15	-0.187966	-1.4681	0.073613
16	-0.117102	-0.9146	0.182002
17	-0.171916	-1.3427	0.092172

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.545154 & 4.2578 & 3.6e-05 \tabularnewline
2 & 0.389335 & 3.0408 & 0.001737 \tabularnewline
3 & 0.496235 & 3.8757 & 0.000131 \tabularnewline
4 & 0.451583 & 3.527 & 0.000402 \tabularnewline
5 & 0.326388 & 2.5492 & 0.006664 \tabularnewline
6 & 0.311861 & 2.4357 & 0.0089 \tabularnewline
7 & 0.133592 & 1.0434 & 0.150443 \tabularnewline
8 & 0.159375 & 1.2448 & 0.108991 \tabularnewline
9 & -0.006271 & -0.049 & 0.48055 \tabularnewline
10 & -0.178376 & -1.3932 & 0.084314 \tabularnewline
11 & -0.058628 & -0.4579 & 0.324325 \tabularnewline
12 & 0.144987 & 1.1324 & 0.130951 \tabularnewline
13 & -0.157168 & -1.2275 & 0.112172 \tabularnewline
14 & -0.27827 & -2.1734 & 0.016823 \tabularnewline
15 & -0.187966 & -1.4681 & 0.073613 \tabularnewline
16 & -0.117102 & -0.9146 & 0.182002 \tabularnewline
17 & -0.171916 & -1.3427 & 0.092172 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116156&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]0.545154[/C][C]4.2578[/C][C]3.6e-05[/C][/ROW]
[ROW][C]2[/C][C]0.389335[/C][C]3.0408[/C][C]0.001737[/C][/ROW]
[ROW][C]3[/C][C]0.496235[/C][C]3.8757[/C][C]0.000131[/C][/ROW]
[ROW][C]4[/C][C]0.451583[/C][C]3.527[/C][C]0.000402[/C][/ROW]
[ROW][C]5[/C][C]0.326388[/C][C]2.5492[/C][C]0.006664[/C][/ROW]
[ROW][C]6[/C][C]0.311861[/C][C]2.4357[/C][C]0.0089[/C][/ROW]
[ROW][C]7[/C][C]0.133592[/C][C]1.0434[/C][C]0.150443[/C][/ROW]
[ROW][C]8[/C][C]0.159375[/C][C]1.2448[/C][C]0.108991[/C][/ROW]
[ROW][C]9[/C][C]-0.006271[/C][C]-0.049[/C][C]0.48055[/C][/ROW]
[ROW][C]10[/C][C]-0.178376[/C][C]-1.3932[/C][C]0.084314[/C][/ROW]
[ROW][C]11[/C][C]-0.058628[/C][C]-0.4579[/C][C]0.324325[/C][/ROW]
[ROW][C]12[/C][C]0.144987[/C][C]1.1324[/C][C]0.130951[/C][/ROW]
[ROW][C]13[/C][C]-0.157168[/C][C]-1.2275[/C][C]0.112172[/C][/ROW]
[ROW][C]14[/C][C]-0.27827[/C][C]-2.1734[/C][C]0.016823[/C][/ROW]
[ROW][C]15[/C][C]-0.187966[/C][C]-1.4681[/C][C]0.073613[/C][/ROW]
[ROW][C]16[/C][C]-0.117102[/C][C]-0.9146[/C][C]0.182002[/C][/ROW]
[ROW][C]17[/C][C]-0.171916[/C][C]-1.3427[/C][C]0.092172[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116156&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116156&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	0.545154	4.2578	3.6e-05
2	0.389335	3.0408	0.001737
3	0.496235	3.8757	0.000131
4	0.451583	3.527	0.000402
5	0.326388	2.5492	0.006664
6	0.311861	2.4357	0.0089
7	0.133592	1.0434	0.150443
8	0.159375	1.2448	0.108991
9	-0.006271	-0.049	0.48055
10	-0.178376	-1.3932	0.084314
11	-0.058628	-0.4579	0.324325
12	0.144987	1.1324	0.130951
13	-0.157168	-1.2275	0.112172
14	-0.27827	-2.1734	0.016823
15	-0.187966	-1.4681	0.073613
16	-0.117102	-0.9146	0.182002
17	-0.171916	-1.3427	0.092172

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.545154	4.2578	3.6e-05
2	0.131106	1.024	0.154946
3	0.347954	2.7176	0.004274
4	0.103115	0.8054	0.211871
5	-0.016998	-0.1328	0.447411
6	0.017692	0.1382	0.445276
7	-0.283351	-2.213	0.015323
8	0.074315	0.5804	0.281886
9	-0.343195	-2.6804	0.004721
10	-0.206787	-1.6151	0.055729
11	0.144943	1.132	0.131024
12	0.447733	3.4969	0.000442
13	-0.133348	-1.0415	0.150881
14	-0.250712	-1.9581	0.027397
15	-0.136751	-1.0681	0.144851
16	0.057846	0.4518	0.326511
17	-0.00743	-0.058	0.476958

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.545154 & 4.2578 & 3.6e-05 \tabularnewline
2 & 0.131106 & 1.024 & 0.154946 \tabularnewline
3 & 0.347954 & 2.7176 & 0.004274 \tabularnewline
4 & 0.103115 & 0.8054 & 0.211871 \tabularnewline
5 & -0.016998 & -0.1328 & 0.447411 \tabularnewline
6 & 0.017692 & 0.1382 & 0.445276 \tabularnewline
7 & -0.283351 & -2.213 & 0.015323 \tabularnewline
8 & 0.074315 & 0.5804 & 0.281886 \tabularnewline
9 & -0.343195 & -2.6804 & 0.004721 \tabularnewline
10 & -0.206787 & -1.6151 & 0.055729 \tabularnewline
11 & 0.144943 & 1.132 & 0.131024 \tabularnewline
12 & 0.447733 & 3.4969 & 0.000442 \tabularnewline
13 & -0.133348 & -1.0415 & 0.150881 \tabularnewline
14 & -0.250712 & -1.9581 & 0.027397 \tabularnewline
15 & -0.136751 & -1.0681 & 0.144851 \tabularnewline
16 & 0.057846 & 0.4518 & 0.326511 \tabularnewline
17 & -0.00743 & -0.058 & 0.476958 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116156&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]0.545154[/C][C]4.2578[/C][C]3.6e-05[/C][/ROW]
[ROW][C]2[/C][C]0.131106[/C][C]1.024[/C][C]0.154946[/C][/ROW]
[ROW][C]3[/C][C]0.347954[/C][C]2.7176[/C][C]0.004274[/C][/ROW]
[ROW][C]4[/C][C]0.103115[/C][C]0.8054[/C][C]0.211871[/C][/ROW]
[ROW][C]5[/C][C]-0.016998[/C][C]-0.1328[/C][C]0.447411[/C][/ROW]
[ROW][C]6[/C][C]0.017692[/C][C]0.1382[/C][C]0.445276[/C][/ROW]
[ROW][C]7[/C][C]-0.283351[/C][C]-2.213[/C][C]0.015323[/C][/ROW]
[ROW][C]8[/C][C]0.074315[/C][C]0.5804[/C][C]0.281886[/C][/ROW]
[ROW][C]9[/C][C]-0.343195[/C][C]-2.6804[/C][C]0.004721[/C][/ROW]
[ROW][C]10[/C][C]-0.206787[/C][C]-1.6151[/C][C]0.055729[/C][/ROW]
[ROW][C]11[/C][C]0.144943[/C][C]1.132[/C][C]0.131024[/C][/ROW]
[ROW][C]12[/C][C]0.447733[/C][C]3.4969[/C][C]0.000442[/C][/ROW]
[ROW][C]13[/C][C]-0.133348[/C][C]-1.0415[/C][C]0.150881[/C][/ROW]
[ROW][C]14[/C][C]-0.250712[/C][C]-1.9581[/C][C]0.027397[/C][/ROW]
[ROW][C]15[/C][C]-0.136751[/C][C]-1.0681[/C][C]0.144851[/C][/ROW]
[ROW][C]16[/C][C]0.057846[/C][C]0.4518[/C][C]0.326511[/C][/ROW]
[ROW][C]17[/C][C]-0.00743[/C][C]-0.058[/C][C]0.476958[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116156&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116156&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	0.545154	4.2578	3.6e-05
2	0.131106	1.024	0.154946
3	0.347954	2.7176	0.004274
4	0.103115	0.8054	0.211871
5	-0.016998	-0.1328	0.447411
6	0.017692	0.1382	0.445276
7	-0.283351	-2.213	0.015323
8	0.074315	0.5804	0.281886
9	-0.343195	-2.6804	0.004721
10	-0.206787	-1.6151	0.055729
11	0.144943	1.132	0.131024
12	0.447733	3.4969	0.000442
13	-0.133348	-1.0415	0.150881
14	-0.250712	-1.9581	0.027397
15	-0.136751	-1.0681	0.144851
16	0.057846	0.4518	0.326511
17	-0.00743	-0.058	0.476958

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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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Input Parameters & R Code