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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2011 06:29:16 -0500

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/2011/Dec/23/t13246398125u5qozku71239ot.htm/, Retrieved Mon, 29 Apr 2024 23:56:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160293, Retrieved Mon, 29 Apr 2024 23:56:41 +0000

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User-defined keywords

Estimated Impact

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]
- RMPD  [Exponential Smoothing] [Workshop_8: Niet-...] [2011-11-28 23:01:38] [f722e8e78b9e5c5ebaa2263f273aa636]
- R P     [Exponential Smoothing] [Workshop_8: Niet-...] [2011-11-29 10:03:27] [74be16979710d4c4e7c6647856088456]
- RMPD        [(Partial) Autocorrelation Function] [Paper: ACF] [2011-12-23 11:29:16] [3e64eea457df40fcb7af8f28e1ee6256] [Current]
- R             [(Partial) Autocorrelation Function] [Paper: ACF] [2011-12-23 11:34:41] [f722e8e78b9e5c5ebaa2263f273aa636] 

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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	'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160293&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160293&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160293&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.003997	0.0641	0.474481
2	-0.037041	-0.5938	0.276579
3	-0.073894	-1.1846	0.118633
4	-0.053481	-0.8574	0.19602
5	-0.09936	-1.5929	0.056211
6	0.009082	0.1456	0.442179
7	0.030868	0.4949	0.310561
8	-0.019019	-0.3049	0.380345
9	-0.00445	-0.0713	0.471592
10	-0.037411	-0.5998	0.2746
11	0.132673	2.1269	0.01719
12	0.126058	2.0209	0.022165
13	0.045338	0.7268	0.233997
14	-0.116609	-1.8694	0.031353
15	-0.157619	-2.5268	0.006055
16	-0.0125	-0.2004	0.42067
17	-0.000331	-0.0053	0.497884
18	0.017823	0.2857	0.387662
19	0.053793	0.8624	0.194645
20	0.031898	0.5114	0.304769
21	-0.027681	-0.4438	0.328797
22	-0.093954	-1.5062	0.066623
23	0.112872	1.8095	0.035772
24	0.049589	0.795	0.21368

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.003997 & 0.0641 & 0.474481 \tabularnewline
2 & -0.037041 & -0.5938 & 0.276579 \tabularnewline
3 & -0.073894 & -1.1846 & 0.118633 \tabularnewline
4 & -0.053481 & -0.8574 & 0.19602 \tabularnewline
5 & -0.09936 & -1.5929 & 0.056211 \tabularnewline
6 & 0.009082 & 0.1456 & 0.442179 \tabularnewline
7 & 0.030868 & 0.4949 & 0.310561 \tabularnewline
8 & -0.019019 & -0.3049 & 0.380345 \tabularnewline
9 & -0.00445 & -0.0713 & 0.471592 \tabularnewline
10 & -0.037411 & -0.5998 & 0.2746 \tabularnewline
11 & 0.132673 & 2.1269 & 0.01719 \tabularnewline
12 & 0.126058 & 2.0209 & 0.022165 \tabularnewline
13 & 0.045338 & 0.7268 & 0.233997 \tabularnewline
14 & -0.116609 & -1.8694 & 0.031353 \tabularnewline
15 & -0.157619 & -2.5268 & 0.006055 \tabularnewline
16 & -0.0125 & -0.2004 & 0.42067 \tabularnewline
17 & -0.000331 & -0.0053 & 0.497884 \tabularnewline
18 & 0.017823 & 0.2857 & 0.387662 \tabularnewline
19 & 0.053793 & 0.8624 & 0.194645 \tabularnewline
20 & 0.031898 & 0.5114 & 0.304769 \tabularnewline
21 & -0.027681 & -0.4438 & 0.328797 \tabularnewline
22 & -0.093954 & -1.5062 & 0.066623 \tabularnewline
23 & 0.112872 & 1.8095 & 0.035772 \tabularnewline
24 & 0.049589 & 0.795 & 0.21368 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160293&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]0.003997[/C][C]0.0641[/C][C]0.474481[/C][/ROW]
[ROW][C]2[/C][C]-0.037041[/C][C]-0.5938[/C][C]0.276579[/C][/ROW]
[ROW][C]3[/C][C]-0.073894[/C][C]-1.1846[/C][C]0.118633[/C][/ROW]
[ROW][C]4[/C][C]-0.053481[/C][C]-0.8574[/C][C]0.19602[/C][/ROW]
[ROW][C]5[/C][C]-0.09936[/C][C]-1.5929[/C][C]0.056211[/C][/ROW]
[ROW][C]6[/C][C]0.009082[/C][C]0.1456[/C][C]0.442179[/C][/ROW]
[ROW][C]7[/C][C]0.030868[/C][C]0.4949[/C][C]0.310561[/C][/ROW]
[ROW][C]8[/C][C]-0.019019[/C][C]-0.3049[/C][C]0.380345[/C][/ROW]
[ROW][C]9[/C][C]-0.00445[/C][C]-0.0713[/C][C]0.471592[/C][/ROW]
[ROW][C]10[/C][C]-0.037411[/C][C]-0.5998[/C][C]0.2746[/C][/ROW]
[ROW][C]11[/C][C]0.132673[/C][C]2.1269[/C][C]0.01719[/C][/ROW]
[ROW][C]12[/C][C]0.126058[/C][C]2.0209[/C][C]0.022165[/C][/ROW]
[ROW][C]13[/C][C]0.045338[/C][C]0.7268[/C][C]0.233997[/C][/ROW]
[ROW][C]14[/C][C]-0.116609[/C][C]-1.8694[/C][C]0.031353[/C][/ROW]
[ROW][C]15[/C][C]-0.157619[/C][C]-2.5268[/C][C]0.006055[/C][/ROW]
[ROW][C]16[/C][C]-0.0125[/C][C]-0.2004[/C][C]0.42067[/C][/ROW]
[ROW][C]17[/C][C]-0.000331[/C][C]-0.0053[/C][C]0.497884[/C][/ROW]
[ROW][C]18[/C][C]0.017823[/C][C]0.2857[/C][C]0.387662[/C][/ROW]
[ROW][C]19[/C][C]0.053793[/C][C]0.8624[/C][C]0.194645[/C][/ROW]
[ROW][C]20[/C][C]0.031898[/C][C]0.5114[/C][C]0.304769[/C][/ROW]
[ROW][C]21[/C][C]-0.027681[/C][C]-0.4438[/C][C]0.328797[/C][/ROW]
[ROW][C]22[/C][C]-0.093954[/C][C]-1.5062[/C][C]0.066623[/C][/ROW]
[ROW][C]23[/C][C]0.112872[/C][C]1.8095[/C][C]0.035772[/C][/ROW]
[ROW][C]24[/C][C]0.049589[/C][C]0.795[/C][C]0.21368[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160293&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160293&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	0.003997	0.0641	0.474481
2	-0.037041	-0.5938	0.276579
3	-0.073894	-1.1846	0.118633
4	-0.053481	-0.8574	0.19602
5	-0.09936	-1.5929	0.056211
6	0.009082	0.1456	0.442179
7	0.030868	0.4949	0.310561
8	-0.019019	-0.3049	0.380345
9	-0.00445	-0.0713	0.471592
10	-0.037411	-0.5998	0.2746
11	0.132673	2.1269	0.01719
12	0.126058	2.0209	0.022165
13	0.045338	0.7268	0.233997
14	-0.116609	-1.8694	0.031353
15	-0.157619	-2.5268	0.006055
16	-0.0125	-0.2004	0.42067
17	-0.000331	-0.0053	0.497884
18	0.017823	0.2857	0.387662
19	0.053793	0.8624	0.194645
20	0.031898	0.5114	0.304769
21	-0.027681	-0.4438	0.328797
22	-0.093954	-1.5062	0.066623
23	0.112872	1.8095	0.035772
24	0.049589	0.795	0.21368

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.003997	0.0641	0.474481
2	-0.037058	-0.5941	0.276491
3	-0.073695	-1.1814	0.119265
4	-0.054817	-0.8788	0.19017
5	-0.10591	-1.6979	0.045371
6	-0.001641	-0.0263	0.489514
7	0.014456	0.2317	0.40846
8	-0.037575	-0.6024	0.273727
9	-0.0137	-0.2196	0.413169
10	-0.047759	-0.7656	0.222299
11	0.133267	2.1364	0.016794
12	0.129514	2.0763	0.019432
13	0.049589	0.795	0.213682
14	-0.096116	-1.5409	0.062292
15	-0.142192	-2.2795	0.011728
16	0.022805	0.3656	0.357484
17	0.011694	0.1875	0.425724
18	-0.011105	-0.178	0.429418
19	0.012857	0.2061	0.418436
20	0.003603	0.0578	0.476991
21	0.000344	0.0055	0.497803
22	-0.095891	-1.5372	0.062732
23	0.087235	1.3985	0.081587
24	0.023449	0.3759	0.353647

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.003997 & 0.0641 & 0.474481 \tabularnewline
2 & -0.037058 & -0.5941 & 0.276491 \tabularnewline
3 & -0.073695 & -1.1814 & 0.119265 \tabularnewline
4 & -0.054817 & -0.8788 & 0.19017 \tabularnewline
5 & -0.10591 & -1.6979 & 0.045371 \tabularnewline
6 & -0.001641 & -0.0263 & 0.489514 \tabularnewline
7 & 0.014456 & 0.2317 & 0.40846 \tabularnewline
8 & -0.037575 & -0.6024 & 0.273727 \tabularnewline
9 & -0.0137 & -0.2196 & 0.413169 \tabularnewline
10 & -0.047759 & -0.7656 & 0.222299 \tabularnewline
11 & 0.133267 & 2.1364 & 0.016794 \tabularnewline
12 & 0.129514 & 2.0763 & 0.019432 \tabularnewline
13 & 0.049589 & 0.795 & 0.213682 \tabularnewline
14 & -0.096116 & -1.5409 & 0.062292 \tabularnewline
15 & -0.142192 & -2.2795 & 0.011728 \tabularnewline
16 & 0.022805 & 0.3656 & 0.357484 \tabularnewline
17 & 0.011694 & 0.1875 & 0.425724 \tabularnewline
18 & -0.011105 & -0.178 & 0.429418 \tabularnewline
19 & 0.012857 & 0.2061 & 0.418436 \tabularnewline
20 & 0.003603 & 0.0578 & 0.476991 \tabularnewline
21 & 0.000344 & 0.0055 & 0.497803 \tabularnewline
22 & -0.095891 & -1.5372 & 0.062732 \tabularnewline
23 & 0.087235 & 1.3985 & 0.081587 \tabularnewline
24 & 0.023449 & 0.3759 & 0.353647 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160293&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]0.003997[/C][C]0.0641[/C][C]0.474481[/C][/ROW]
[ROW][C]2[/C][C]-0.037058[/C][C]-0.5941[/C][C]0.276491[/C][/ROW]
[ROW][C]3[/C][C]-0.073695[/C][C]-1.1814[/C][C]0.119265[/C][/ROW]
[ROW][C]4[/C][C]-0.054817[/C][C]-0.8788[/C][C]0.19017[/C][/ROW]
[ROW][C]5[/C][C]-0.10591[/C][C]-1.6979[/C][C]0.045371[/C][/ROW]
[ROW][C]6[/C][C]-0.001641[/C][C]-0.0263[/C][C]0.489514[/C][/ROW]
[ROW][C]7[/C][C]0.014456[/C][C]0.2317[/C][C]0.40846[/C][/ROW]
[ROW][C]8[/C][C]-0.037575[/C][C]-0.6024[/C][C]0.273727[/C][/ROW]
[ROW][C]9[/C][C]-0.0137[/C][C]-0.2196[/C][C]0.413169[/C][/ROW]
[ROW][C]10[/C][C]-0.047759[/C][C]-0.7656[/C][C]0.222299[/C][/ROW]
[ROW][C]11[/C][C]0.133267[/C][C]2.1364[/C][C]0.016794[/C][/ROW]
[ROW][C]12[/C][C]0.129514[/C][C]2.0763[/C][C]0.019432[/C][/ROW]
[ROW][C]13[/C][C]0.049589[/C][C]0.795[/C][C]0.213682[/C][/ROW]
[ROW][C]14[/C][C]-0.096116[/C][C]-1.5409[/C][C]0.062292[/C][/ROW]
[ROW][C]15[/C][C]-0.142192[/C][C]-2.2795[/C][C]0.011728[/C][/ROW]
[ROW][C]16[/C][C]0.022805[/C][C]0.3656[/C][C]0.357484[/C][/ROW]
[ROW][C]17[/C][C]0.011694[/C][C]0.1875[/C][C]0.425724[/C][/ROW]
[ROW][C]18[/C][C]-0.011105[/C][C]-0.178[/C][C]0.429418[/C][/ROW]
[ROW][C]19[/C][C]0.012857[/C][C]0.2061[/C][C]0.418436[/C][/ROW]
[ROW][C]20[/C][C]0.003603[/C][C]0.0578[/C][C]0.476991[/C][/ROW]
[ROW][C]21[/C][C]0.000344[/C][C]0.0055[/C][C]0.497803[/C][/ROW]
[ROW][C]22[/C][C]-0.095891[/C][C]-1.5372[/C][C]0.062732[/C][/ROW]
[ROW][C]23[/C][C]0.087235[/C][C]1.3985[/C][C]0.081587[/C][/ROW]
[ROW][C]24[/C][C]0.023449[/C][C]0.3759[/C][C]0.353647[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160293&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160293&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	0.003997	0.0641	0.474481
2	-0.037058	-0.5941	0.276491
3	-0.073695	-1.1814	0.119265
4	-0.054817	-0.8788	0.19017
5	-0.10591	-1.6979	0.045371
6	-0.001641	-0.0263	0.489514
7	0.014456	0.2317	0.40846
8	-0.037575	-0.6024	0.273727
9	-0.0137	-0.2196	0.413169
10	-0.047759	-0.7656	0.222299
11	0.133267	2.1364	0.016794
12	0.129514	2.0763	0.019432
13	0.049589	0.795	0.213682
14	-0.096116	-1.5409	0.062292
15	-0.142192	-2.2795	0.011728
16	0.022805	0.3656	0.357484
17	0.011694	0.1875	0.425724
18	-0.011105	-0.178	0.429418
19	0.012857	0.2061	0.418436
20	0.003603	0.0578	0.476991
21	0.000344	0.0055	0.497803
22	-0.095891	-1.5372	0.062732
23	0.087235	1.3985	0.081587
24	0.023449	0.3759	0.353647

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 = Valutakoersen Eur-Dollar ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code