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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 03 Dec 2010 18:10:51 +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/03/t1291399732bmzawkrnfeggbd8.htm/, Retrieved Tue, 07 May 2024 13:27:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104955, Retrieved Tue, 07 May 2024 13:27:48 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

129

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] [W9] [2010-12-03 16:45:32] [247f085ab5b7724f755ad01dc754a3e8]
-   PD        [(Partial) Autocorrelation Function] [W9 d=1] [2010-12-03 18:10:51] [9d72585f2b7b60ae977d4816136e1c95] [Current]

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Dataseries X:

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Histogram

Boxplots

14731798.37
16471559.62
15213975.95
17637387.4
17972385.83
16896235.55
16697955.94
19691579.52
15930700.75
17444615.98
17699369.88
15189796.81
15672722.75
17180794.3
17664893.45
17862884.98
16162288.88
17463628.82
16772112.17
19106861.48
16721314.25
18161267.85
18509941.2
17802737.97
16409869.75
17967742.04
20286602.27
19537280.81
18021889.62
20194317.23
19049596.62
20244720.94
21473302.24
19673603.19
21053177.29
20159479.84
18203628.31
21289464.94
20432335.71
17180395.07
15816786.32
15071819.75
14521120.61
15668789.39
14346884.11
13881008.13
15465943.69
14238232.92
13557713.21
16127590.29
16793894.2
16014007.43
16867867.15
16014583.21
15878594.85
18664899.14
17962530.06
17332692.2
19542066.35
17203555.19

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=104955&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=104955&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104955&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	-0.370104	-2.8428	0.003067
2	-0.169242	-1.3	0.099334
3	0.299058	2.2971	0.012589
4	-0.11854	-0.9105	0.183125
5	-0.097728	-0.7507	0.22792
6	0.306942	2.3577	0.010863
7	-0.246401	-1.8926	0.031657
8	0.054437	0.4181	0.338681
9	0.069797	0.5361	0.296946
10	-0.217431	-1.6701	0.050096
11	-0.133851	-1.0281	0.154044
12	0.40039	3.0755	0.001591
13	-0.213967	-1.6435	0.052798
14	-0.097081	-0.7457	0.229406
15	0.037829	0.2906	0.386198
16	-0.019703	-0.1513	0.44011
17	-0.063246	-0.4858	0.314455

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.370104 & -2.8428 & 0.003067 \tabularnewline
2 & -0.169242 & -1.3 & 0.099334 \tabularnewline
3 & 0.299058 & 2.2971 & 0.012589 \tabularnewline
4 & -0.11854 & -0.9105 & 0.183125 \tabularnewline
5 & -0.097728 & -0.7507 & 0.22792 \tabularnewline
6 & 0.306942 & 2.3577 & 0.010863 \tabularnewline
7 & -0.246401 & -1.8926 & 0.031657 \tabularnewline
8 & 0.054437 & 0.4181 & 0.338681 \tabularnewline
9 & 0.069797 & 0.5361 & 0.296946 \tabularnewline
10 & -0.217431 & -1.6701 & 0.050096 \tabularnewline
11 & -0.133851 & -1.0281 & 0.154044 \tabularnewline
12 & 0.40039 & 3.0755 & 0.001591 \tabularnewline
13 & -0.213967 & -1.6435 & 0.052798 \tabularnewline
14 & -0.097081 & -0.7457 & 0.229406 \tabularnewline
15 & 0.037829 & 0.2906 & 0.386198 \tabularnewline
16 & -0.019703 & -0.1513 & 0.44011 \tabularnewline
17 & -0.063246 & -0.4858 & 0.314455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104955&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]-0.370104[/C][C]-2.8428[/C][C]0.003067[/C][/ROW]
[ROW][C]2[/C][C]-0.169242[/C][C]-1.3[/C][C]0.099334[/C][/ROW]
[ROW][C]3[/C][C]0.299058[/C][C]2.2971[/C][C]0.012589[/C][/ROW]
[ROW][C]4[/C][C]-0.11854[/C][C]-0.9105[/C][C]0.183125[/C][/ROW]
[ROW][C]5[/C][C]-0.097728[/C][C]-0.7507[/C][C]0.22792[/C][/ROW]
[ROW][C]6[/C][C]0.306942[/C][C]2.3577[/C][C]0.010863[/C][/ROW]
[ROW][C]7[/C][C]-0.246401[/C][C]-1.8926[/C][C]0.031657[/C][/ROW]
[ROW][C]8[/C][C]0.054437[/C][C]0.4181[/C][C]0.338681[/C][/ROW]
[ROW][C]9[/C][C]0.069797[/C][C]0.5361[/C][C]0.296946[/C][/ROW]
[ROW][C]10[/C][C]-0.217431[/C][C]-1.6701[/C][C]0.050096[/C][/ROW]
[ROW][C]11[/C][C]-0.133851[/C][C]-1.0281[/C][C]0.154044[/C][/ROW]
[ROW][C]12[/C][C]0.40039[/C][C]3.0755[/C][C]0.001591[/C][/ROW]
[ROW][C]13[/C][C]-0.213967[/C][C]-1.6435[/C][C]0.052798[/C][/ROW]
[ROW][C]14[/C][C]-0.097081[/C][C]-0.7457[/C][C]0.229406[/C][/ROW]
[ROW][C]15[/C][C]0.037829[/C][C]0.2906[/C][C]0.386198[/C][/ROW]
[ROW][C]16[/C][C]-0.019703[/C][C]-0.1513[/C][C]0.44011[/C][/ROW]
[ROW][C]17[/C][C]-0.063246[/C][C]-0.4858[/C][C]0.314455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104955&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104955&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	-0.370104	-2.8428	0.003067
2	-0.169242	-1.3	0.099334
3	0.299058	2.2971	0.012589
4	-0.11854	-0.9105	0.183125
5	-0.097728	-0.7507	0.22792
6	0.306942	2.3577	0.010863
7	-0.246401	-1.8926	0.031657
8	0.054437	0.4181	0.338681
9	0.069797	0.5361	0.296946
10	-0.217431	-1.6701	0.050096
11	-0.133851	-1.0281	0.154044
12	0.40039	3.0755	0.001591
13	-0.213967	-1.6435	0.052798
14	-0.097081	-0.7457	0.229406
15	0.037829	0.2906	0.386198
16	-0.019703	-0.1513	0.44011
17	-0.063246	-0.4858	0.314455

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.370104	-2.8428	0.003067
2	-0.354821	-2.7254	0.00422
3	0.10986	0.8438	0.201082
4	0.013001	0.0999	0.460395
5	-0.05344	-0.4105	0.341469
6	0.236395	1.8158	0.037243
7	-0.067086	-0.5153	0.304135
8	0.069375	0.5329	0.29806
9	-0.061425	-0.4718	0.319399
10	-0.195446	-1.5012	0.069312
11	-0.409989	-3.1492	0.001285
12	0.11973	0.9197	0.180746
13	0.101022	0.776	0.220434
14	0.029133	0.2238	0.411854
15	-0.190442	-1.4628	0.074413
16	-0.051233	-0.3935	0.347675
17	-0.039836	-0.306	0.380345

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.370104 & -2.8428 & 0.003067 \tabularnewline
2 & -0.354821 & -2.7254 & 0.00422 \tabularnewline
3 & 0.10986 & 0.8438 & 0.201082 \tabularnewline
4 & 0.013001 & 0.0999 & 0.460395 \tabularnewline
5 & -0.05344 & -0.4105 & 0.341469 \tabularnewline
6 & 0.236395 & 1.8158 & 0.037243 \tabularnewline
7 & -0.067086 & -0.5153 & 0.304135 \tabularnewline
8 & 0.069375 & 0.5329 & 0.29806 \tabularnewline
9 & -0.061425 & -0.4718 & 0.319399 \tabularnewline
10 & -0.195446 & -1.5012 & 0.069312 \tabularnewline
11 & -0.409989 & -3.1492 & 0.001285 \tabularnewline
12 & 0.11973 & 0.9197 & 0.180746 \tabularnewline
13 & 0.101022 & 0.776 & 0.220434 \tabularnewline
14 & 0.029133 & 0.2238 & 0.411854 \tabularnewline
15 & -0.190442 & -1.4628 & 0.074413 \tabularnewline
16 & -0.051233 & -0.3935 & 0.347675 \tabularnewline
17 & -0.039836 & -0.306 & 0.380345 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104955&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]-0.370104[/C][C]-2.8428[/C][C]0.003067[/C][/ROW]
[ROW][C]2[/C][C]-0.354821[/C][C]-2.7254[/C][C]0.00422[/C][/ROW]
[ROW][C]3[/C][C]0.10986[/C][C]0.8438[/C][C]0.201082[/C][/ROW]
[ROW][C]4[/C][C]0.013001[/C][C]0.0999[/C][C]0.460395[/C][/ROW]
[ROW][C]5[/C][C]-0.05344[/C][C]-0.4105[/C][C]0.341469[/C][/ROW]
[ROW][C]6[/C][C]0.236395[/C][C]1.8158[/C][C]0.037243[/C][/ROW]
[ROW][C]7[/C][C]-0.067086[/C][C]-0.5153[/C][C]0.304135[/C][/ROW]
[ROW][C]8[/C][C]0.069375[/C][C]0.5329[/C][C]0.29806[/C][/ROW]
[ROW][C]9[/C][C]-0.061425[/C][C]-0.4718[/C][C]0.319399[/C][/ROW]
[ROW][C]10[/C][C]-0.195446[/C][C]-1.5012[/C][C]0.069312[/C][/ROW]
[ROW][C]11[/C][C]-0.409989[/C][C]-3.1492[/C][C]0.001285[/C][/ROW]
[ROW][C]12[/C][C]0.11973[/C][C]0.9197[/C][C]0.180746[/C][/ROW]
[ROW][C]13[/C][C]0.101022[/C][C]0.776[/C][C]0.220434[/C][/ROW]
[ROW][C]14[/C][C]0.029133[/C][C]0.2238[/C][C]0.411854[/C][/ROW]
[ROW][C]15[/C][C]-0.190442[/C][C]-1.4628[/C][C]0.074413[/C][/ROW]
[ROW][C]16[/C][C]-0.051233[/C][C]-0.3935[/C][C]0.347675[/C][/ROW]
[ROW][C]17[/C][C]-0.039836[/C][C]-0.306[/C][C]0.380345[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104955&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104955&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	-0.370104	-2.8428	0.003067
2	-0.354821	-2.7254	0.00422
3	0.10986	0.8438	0.201082
4	0.013001	0.0999	0.460395
5	-0.05344	-0.4105	0.341469
6	0.236395	1.8158	0.037243
7	-0.067086	-0.5153	0.304135
8	0.069375	0.5329	0.29806
9	-0.061425	-0.4718	0.319399
10	-0.195446	-1.5012	0.069312
11	-0.409989	-3.1492	0.001285
12	0.11973	0.9197	0.180746
13	0.101022	0.776	0.220434
14	0.029133	0.2238	0.411854
15	-0.190442	-1.4628	0.074413
16	-0.051233	-0.3935	0.347675
17	-0.039836	-0.306	0.380345

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code