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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 21 Dec 2009 09:35:55 -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/Dec/21/t12614133723wdoobvwrn6vrdo.htm/, Retrieved Sun, 05 May 2024 14:18:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70335, Retrieved Sun, 05 May 2024 14:18:17 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

131

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

-     [Variance Reduction Matrix] [Variance Reductio...] [2008-12-14 12:53:01] [1dc7b54f2fa28720a65b8f3f53c2ed9f]
- RMP   [Variance Reduction Matrix] [] [2009-12-21 16:31:51] [8eb28aba8de3868ee2c810eecf1cb9a8]
- RM        [(Partial) Autocorrelation Function] [] [2009-12-21 16:35:55] [ce16745b5fa1a53fd3d9c8db848c7076] [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=70335&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=70335&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70335&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	0.894362	6.8697	0
2	0.787491	6.0488	0
3	0.738083	5.6693	0
4	0.686946	5.2765	1e-06
5	0.608289	4.6724	9e-06
6	0.539123	4.1411	5.6e-05
7	0.497943	3.8248	0.000159
8	0.445524	3.4221	0.000567
9	0.366854	2.8179	0.003284
10	0.281428	2.1617	0.017355
11	0.197715	1.5187	0.067092
12	0.127402	0.9786	0.165889
13	0.051302	0.3941	0.347479
14	0.016054	0.1233	0.451138
15	-0.031091	-0.2388	0.406039
16	-0.086939	-0.6678	0.253436
17	-0.119281	-0.9162	0.181643

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.894362 & 6.8697 & 0 \tabularnewline
2 & 0.787491 & 6.0488 & 0 \tabularnewline
3 & 0.738083 & 5.6693 & 0 \tabularnewline
4 & 0.686946 & 5.2765 & 1e-06 \tabularnewline
5 & 0.608289 & 4.6724 & 9e-06 \tabularnewline
6 & 0.539123 & 4.1411 & 5.6e-05 \tabularnewline
7 & 0.497943 & 3.8248 & 0.000159 \tabularnewline
8 & 0.445524 & 3.4221 & 0.000567 \tabularnewline
9 & 0.366854 & 2.8179 & 0.003284 \tabularnewline
10 & 0.281428 & 2.1617 & 0.017355 \tabularnewline
11 & 0.197715 & 1.5187 & 0.067092 \tabularnewline
12 & 0.127402 & 0.9786 & 0.165889 \tabularnewline
13 & 0.051302 & 0.3941 & 0.347479 \tabularnewline
14 & 0.016054 & 0.1233 & 0.451138 \tabularnewline
15 & -0.031091 & -0.2388 & 0.406039 \tabularnewline
16 & -0.086939 & -0.6678 & 0.253436 \tabularnewline
17 & -0.119281 & -0.9162 & 0.181643 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70335&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]0.894362[/C][C]6.8697[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.787491[/C][C]6.0488[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.738083[/C][C]5.6693[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.686946[/C][C]5.2765[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.608289[/C][C]4.6724[/C][C]9e-06[/C][/ROW]
[ROW][C]6[/C][C]0.539123[/C][C]4.1411[/C][C]5.6e-05[/C][/ROW]
[ROW][C]7[/C][C]0.497943[/C][C]3.8248[/C][C]0.000159[/C][/ROW]
[ROW][C]8[/C][C]0.445524[/C][C]3.4221[/C][C]0.000567[/C][/ROW]
[ROW][C]9[/C][C]0.366854[/C][C]2.8179[/C][C]0.003284[/C][/ROW]
[ROW][C]10[/C][C]0.281428[/C][C]2.1617[/C][C]0.017355[/C][/ROW]
[ROW][C]11[/C][C]0.197715[/C][C]1.5187[/C][C]0.067092[/C][/ROW]
[ROW][C]12[/C][C]0.127402[/C][C]0.9786[/C][C]0.165889[/C][/ROW]
[ROW][C]13[/C][C]0.051302[/C][C]0.3941[/C][C]0.347479[/C][/ROW]
[ROW][C]14[/C][C]0.016054[/C][C]0.1233[/C][C]0.451138[/C][/ROW]
[ROW][C]15[/C][C]-0.031091[/C][C]-0.2388[/C][C]0.406039[/C][/ROW]
[ROW][C]16[/C][C]-0.086939[/C][C]-0.6678[/C][C]0.253436[/C][/ROW]
[ROW][C]17[/C][C]-0.119281[/C][C]-0.9162[/C][C]0.181643[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70335&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70335&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	0.894362	6.8697	0
2	0.787491	6.0488	0
3	0.738083	5.6693	0
4	0.686946	5.2765	1e-06
5	0.608289	4.6724	9e-06
6	0.539123	4.1411	5.6e-05
7	0.497943	3.8248	0.000159
8	0.445524	3.4221	0.000567
9	0.366854	2.8179	0.003284
10	0.281428	2.1617	0.017355
11	0.197715	1.5187	0.067092
12	0.127402	0.9786	0.165889
13	0.051302	0.3941	0.347479
14	0.016054	0.1233	0.451138
15	-0.031091	-0.2388	0.406039
16	-0.086939	-0.6678	0.253436
17	-0.119281	-0.9162	0.181643

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.894362	6.8697	0
2	-0.061928	-0.4757	0.31803
3	0.228501	1.7552	0.042212
4	-0.048619	-0.3735	0.355076
5	-0.100576	-0.7725	0.221439
6	0.002203	0.0169	0.493279
7	0.050227	0.3858	0.350515
8	-0.072443	-0.5564	0.290005
9	-0.111262	-0.8546	0.198109
10	-0.117891	-0.9055	0.184431
11	-0.120372	-0.9246	0.179471
12	-0.005114	-0.0393	0.4844
13	-0.09017	-0.6926	0.245637
14	0.18175	1.396	0.083965
15	-0.155798	-1.1967	0.118103
16	0.006114	0.047	0.481352
17	0.043558	0.3346	0.369565

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.894362 & 6.8697 & 0 \tabularnewline
2 & -0.061928 & -0.4757 & 0.31803 \tabularnewline
3 & 0.228501 & 1.7552 & 0.042212 \tabularnewline
4 & -0.048619 & -0.3735 & 0.355076 \tabularnewline
5 & -0.100576 & -0.7725 & 0.221439 \tabularnewline
6 & 0.002203 & 0.0169 & 0.493279 \tabularnewline
7 & 0.050227 & 0.3858 & 0.350515 \tabularnewline
8 & -0.072443 & -0.5564 & 0.290005 \tabularnewline
9 & -0.111262 & -0.8546 & 0.198109 \tabularnewline
10 & -0.117891 & -0.9055 & 0.184431 \tabularnewline
11 & -0.120372 & -0.9246 & 0.179471 \tabularnewline
12 & -0.005114 & -0.0393 & 0.4844 \tabularnewline
13 & -0.09017 & -0.6926 & 0.245637 \tabularnewline
14 & 0.18175 & 1.396 & 0.083965 \tabularnewline
15 & -0.155798 & -1.1967 & 0.118103 \tabularnewline
16 & 0.006114 & 0.047 & 0.481352 \tabularnewline
17 & 0.043558 & 0.3346 & 0.369565 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70335&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]0.894362[/C][C]6.8697[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.061928[/C][C]-0.4757[/C][C]0.31803[/C][/ROW]
[ROW][C]3[/C][C]0.228501[/C][C]1.7552[/C][C]0.042212[/C][/ROW]
[ROW][C]4[/C][C]-0.048619[/C][C]-0.3735[/C][C]0.355076[/C][/ROW]
[ROW][C]5[/C][C]-0.100576[/C][C]-0.7725[/C][C]0.221439[/C][/ROW]
[ROW][C]6[/C][C]0.002203[/C][C]0.0169[/C][C]0.493279[/C][/ROW]
[ROW][C]7[/C][C]0.050227[/C][C]0.3858[/C][C]0.350515[/C][/ROW]
[ROW][C]8[/C][C]-0.072443[/C][C]-0.5564[/C][C]0.290005[/C][/ROW]
[ROW][C]9[/C][C]-0.111262[/C][C]-0.8546[/C][C]0.198109[/C][/ROW]
[ROW][C]10[/C][C]-0.117891[/C][C]-0.9055[/C][C]0.184431[/C][/ROW]
[ROW][C]11[/C][C]-0.120372[/C][C]-0.9246[/C][C]0.179471[/C][/ROW]
[ROW][C]12[/C][C]-0.005114[/C][C]-0.0393[/C][C]0.4844[/C][/ROW]
[ROW][C]13[/C][C]-0.09017[/C][C]-0.6926[/C][C]0.245637[/C][/ROW]
[ROW][C]14[/C][C]0.18175[/C][C]1.396[/C][C]0.083965[/C][/ROW]
[ROW][C]15[/C][C]-0.155798[/C][C]-1.1967[/C][C]0.118103[/C][/ROW]
[ROW][C]16[/C][C]0.006114[/C][C]0.047[/C][C]0.481352[/C][/ROW]
[ROW][C]17[/C][C]0.043558[/C][C]0.3346[/C][C]0.369565[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70335&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70335&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	0.894362	6.8697	0
2	-0.061928	-0.4757	0.31803
3	0.228501	1.7552	0.042212
4	-0.048619	-0.3735	0.355076
5	-0.100576	-0.7725	0.221439
6	0.002203	0.0169	0.493279
7	0.050227	0.3858	0.350515
8	-0.072443	-0.5564	0.290005
9	-0.111262	-0.8546	0.198109
10	-0.117891	-0.9055	0.184431
11	-0.120372	-0.9246	0.179471
12	-0.005114	-0.0393	0.4844
13	-0.09017	-0.6926	0.245637
14	0.18175	1.396	0.083965
15	-0.155798	-1.1967	0.118103
16	0.006114	0.047	0.481352
17	0.043558	0.3346	0.369565

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 0.0 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;

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