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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 08 Dec 2009 09:06:44 -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/08/t12602884493mmyxvl6emx81cz.htm/, Retrieved Sun, 28 Apr 2024 13:32:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64720, Retrieved Sun, 28 Apr 2024 13:32:28 +0000

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No (this computation is public)

User-defined keywords

Gegevens: Werkloosheid in Belgi�

Estimated Impact

110

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Spectral Analysis] [Identifying Integ...] [2009-11-22 12:38:17] [b98453cac15ba1066b407e146608df68]
-   PD        [Spectral Analysis] [Workshop 8: Spect...] [2009-11-27 16:53:51] [7c2a5b25a196bd646844b8f5223c9b3e]
- RMP             [(Partial) Autocorrelation Function] [Review: Autocorre...] [2009-12-08 16:06:44] [a5ada8bd39e806b5b90f09589c89554a] [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=64720&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=64720&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64720&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	0.110573	0.8275	0.205746
2	0.327046	2.4474	0.008776
3	0.325809	2.4381	0.008981
4	0.23373	1.7491	0.042879
5	0.096115	0.7193	0.237485
6	0.17861	1.3366	0.09338
7	0.073774	0.5521	0.291548
8	0.137498	1.0289	0.153965
9	0.091972	0.6883	0.247066
10	-0.094533	-0.7074	0.24112
11	0.351469	2.6302	0.0055
12	-0.152496	-1.1412	0.129327
13	0.030609	0.2291	0.40983
14	0.107029	0.8009	0.213279
15	0.07255	0.5429	0.294672
16	-0.03605	-0.2698	0.394163
17	0.097312	0.7282	0.234757
18	-0.117905	-0.8823	0.190687

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.110573 & 0.8275 & 0.205746 \tabularnewline
2 & 0.327046 & 2.4474 & 0.008776 \tabularnewline
3 & 0.325809 & 2.4381 & 0.008981 \tabularnewline
4 & 0.23373 & 1.7491 & 0.042879 \tabularnewline
5 & 0.096115 & 0.7193 & 0.237485 \tabularnewline
6 & 0.17861 & 1.3366 & 0.09338 \tabularnewline
7 & 0.073774 & 0.5521 & 0.291548 \tabularnewline
8 & 0.137498 & 1.0289 & 0.153965 \tabularnewline
9 & 0.091972 & 0.6883 & 0.247066 \tabularnewline
10 & -0.094533 & -0.7074 & 0.24112 \tabularnewline
11 & 0.351469 & 2.6302 & 0.0055 \tabularnewline
12 & -0.152496 & -1.1412 & 0.129327 \tabularnewline
13 & 0.030609 & 0.2291 & 0.40983 \tabularnewline
14 & 0.107029 & 0.8009 & 0.213279 \tabularnewline
15 & 0.07255 & 0.5429 & 0.294672 \tabularnewline
16 & -0.03605 & -0.2698 & 0.394163 \tabularnewline
17 & 0.097312 & 0.7282 & 0.234757 \tabularnewline
18 & -0.117905 & -0.8823 & 0.190687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64720&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]0.110573[/C][C]0.8275[/C][C]0.205746[/C][/ROW]
[ROW][C]2[/C][C]0.327046[/C][C]2.4474[/C][C]0.008776[/C][/ROW]
[ROW][C]3[/C][C]0.325809[/C][C]2.4381[/C][C]0.008981[/C][/ROW]
[ROW][C]4[/C][C]0.23373[/C][C]1.7491[/C][C]0.042879[/C][/ROW]
[ROW][C]5[/C][C]0.096115[/C][C]0.7193[/C][C]0.237485[/C][/ROW]
[ROW][C]6[/C][C]0.17861[/C][C]1.3366[/C][C]0.09338[/C][/ROW]
[ROW][C]7[/C][C]0.073774[/C][C]0.5521[/C][C]0.291548[/C][/ROW]
[ROW][C]8[/C][C]0.137498[/C][C]1.0289[/C][C]0.153965[/C][/ROW]
[ROW][C]9[/C][C]0.091972[/C][C]0.6883[/C][C]0.247066[/C][/ROW]
[ROW][C]10[/C][C]-0.094533[/C][C]-0.7074[/C][C]0.24112[/C][/ROW]
[ROW][C]11[/C][C]0.351469[/C][C]2.6302[/C][C]0.0055[/C][/ROW]
[ROW][C]12[/C][C]-0.152496[/C][C]-1.1412[/C][C]0.129327[/C][/ROW]
[ROW][C]13[/C][C]0.030609[/C][C]0.2291[/C][C]0.40983[/C][/ROW]
[ROW][C]14[/C][C]0.107029[/C][C]0.8009[/C][C]0.213279[/C][/ROW]
[ROW][C]15[/C][C]0.07255[/C][C]0.5429[/C][C]0.294672[/C][/ROW]
[ROW][C]16[/C][C]-0.03605[/C][C]-0.2698[/C][C]0.394163[/C][/ROW]
[ROW][C]17[/C][C]0.097312[/C][C]0.7282[/C][C]0.234757[/C][/ROW]
[ROW][C]18[/C][C]-0.117905[/C][C]-0.8823[/C][C]0.190687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64720&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64720&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	0.110573	0.8275	0.205746
2	0.327046	2.4474	0.008776
3	0.325809	2.4381	0.008981
4	0.23373	1.7491	0.042879
5	0.096115	0.7193	0.237485
6	0.17861	1.3366	0.09338
7	0.073774	0.5521	0.291548
8	0.137498	1.0289	0.153965
9	0.091972	0.6883	0.247066
10	-0.094533	-0.7074	0.24112
11	0.351469	2.6302	0.0055
12	-0.152496	-1.1412	0.129327
13	0.030609	0.2291	0.40983
14	0.107029	0.8009	0.213279
15	0.07255	0.5429	0.294672
16	-0.03605	-0.2698	0.394163
17	0.097312	0.7282	0.234757
18	-0.117905	-0.8823	0.190687

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.110573	0.8275	0.205746
2	0.318717	2.3851	0.010243
3	0.299661	2.2425	0.014454
4	0.136572	1.022	0.155584
5	-0.10965	-0.8205	0.207692
6	-0.028713	-0.2149	0.415326
7	-0.039041	-0.2922	0.385624
8	0.086924	0.6505	0.259022
9	0.065269	0.4884	0.313578
10	-0.220206	-1.6479	0.05249
11	0.336502	2.5182	0.007341
12	-0.201259	-1.5061	0.068833
13	-0.076542	-0.5728	0.28454
14	0.083916	0.628	0.266289
15	0.073955	0.5534	0.291088
16	0.044319	0.3317	0.370695
17	-0.069631	-0.5211	0.302185
18	-0.204152	-1.5277	0.066104

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.110573 & 0.8275 & 0.205746 \tabularnewline
2 & 0.318717 & 2.3851 & 0.010243 \tabularnewline
3 & 0.299661 & 2.2425 & 0.014454 \tabularnewline
4 & 0.136572 & 1.022 & 0.155584 \tabularnewline
5 & -0.10965 & -0.8205 & 0.207692 \tabularnewline
6 & -0.028713 & -0.2149 & 0.415326 \tabularnewline
7 & -0.039041 & -0.2922 & 0.385624 \tabularnewline
8 & 0.086924 & 0.6505 & 0.259022 \tabularnewline
9 & 0.065269 & 0.4884 & 0.313578 \tabularnewline
10 & -0.220206 & -1.6479 & 0.05249 \tabularnewline
11 & 0.336502 & 2.5182 & 0.007341 \tabularnewline
12 & -0.201259 & -1.5061 & 0.068833 \tabularnewline
13 & -0.076542 & -0.5728 & 0.28454 \tabularnewline
14 & 0.083916 & 0.628 & 0.266289 \tabularnewline
15 & 0.073955 & 0.5534 & 0.291088 \tabularnewline
16 & 0.044319 & 0.3317 & 0.370695 \tabularnewline
17 & -0.069631 & -0.5211 & 0.302185 \tabularnewline
18 & -0.204152 & -1.5277 & 0.066104 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64720&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]0.110573[/C][C]0.8275[/C][C]0.205746[/C][/ROW]
[ROW][C]2[/C][C]0.318717[/C][C]2.3851[/C][C]0.010243[/C][/ROW]
[ROW][C]3[/C][C]0.299661[/C][C]2.2425[/C][C]0.014454[/C][/ROW]
[ROW][C]4[/C][C]0.136572[/C][C]1.022[/C][C]0.155584[/C][/ROW]
[ROW][C]5[/C][C]-0.10965[/C][C]-0.8205[/C][C]0.207692[/C][/ROW]
[ROW][C]6[/C][C]-0.028713[/C][C]-0.2149[/C][C]0.415326[/C][/ROW]
[ROW][C]7[/C][C]-0.039041[/C][C]-0.2922[/C][C]0.385624[/C][/ROW]
[ROW][C]8[/C][C]0.086924[/C][C]0.6505[/C][C]0.259022[/C][/ROW]
[ROW][C]9[/C][C]0.065269[/C][C]0.4884[/C][C]0.313578[/C][/ROW]
[ROW][C]10[/C][C]-0.220206[/C][C]-1.6479[/C][C]0.05249[/C][/ROW]
[ROW][C]11[/C][C]0.336502[/C][C]2.5182[/C][C]0.007341[/C][/ROW]
[ROW][C]12[/C][C]-0.201259[/C][C]-1.5061[/C][C]0.068833[/C][/ROW]
[ROW][C]13[/C][C]-0.076542[/C][C]-0.5728[/C][C]0.28454[/C][/ROW]
[ROW][C]14[/C][C]0.083916[/C][C]0.628[/C][C]0.266289[/C][/ROW]
[ROW][C]15[/C][C]0.073955[/C][C]0.5534[/C][C]0.291088[/C][/ROW]
[ROW][C]16[/C][C]0.044319[/C][C]0.3317[/C][C]0.370695[/C][/ROW]
[ROW][C]17[/C][C]-0.069631[/C][C]-0.5211[/C][C]0.302185[/C][/ROW]
[ROW][C]18[/C][C]-0.204152[/C][C]-1.5277[/C][C]0.066104[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64720&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64720&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	0.110573	0.8275	0.205746
2	0.318717	2.3851	0.010243
3	0.299661	2.2425	0.014454
4	0.136572	1.022	0.155584
5	-0.10965	-0.8205	0.207692
6	-0.028713	-0.2149	0.415326
7	-0.039041	-0.2922	0.385624
8	0.086924	0.6505	0.259022
9	0.065269	0.4884	0.313578
10	-0.220206	-1.6479	0.05249
11	0.336502	2.5182	0.007341
12	-0.201259	-1.5061	0.068833
13	-0.076542	-0.5728	0.28454
14	0.083916	0.628	0.266289
15	0.073955	0.5534	0.291088
16	0.044319	0.3317	0.370695
17	-0.069631	-0.5211	0.302185
18	-0.204152	-1.5277	0.066104

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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