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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

Mon, 14 Dec 2009 02:30:19 -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/14/t12607830915vitdebhdy6mogs.htm/, Retrieved Sun, 05 May 2024 14:20:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67467, Retrieved Sun, 05 May 2024 14:20:32 +0000

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No (this computation is public)

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Estimated Impact

160

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2009-12-14 09:30:19] [6df9bd2792d60592b4a24994398a86db] [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=67467&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=67467&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67467&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	-0.5228	-5.7031	0
2	0.123617	1.3485	0.09003
3	0.202998	2.2144	0.014351
4	-0.173331	-1.8908	0.03054
5	0.001175	0.0128	0.494899
6	0.215529	2.3511	0.01018
7	-0.309761	-3.3791	0.000492
8	0.114205	1.2458	0.107638
9	0.18292	1.9954	0.024141
10	-0.315898	-3.446	0.000393
11	0.155544	1.6968	0.046175
12	0.001195	0.013	0.494809
13	-0.225392	-2.4587	0.007691
14	0.139844	1.5255	0.064892
15	0.031417	0.3427	0.366208
16	-0.208156	-2.2707	0.012481
17	0.171577	1.8717	0.031853
18	0.002549	0.0278	0.488933
19	-0.180544	-1.9695	0.025609
20	0.184406	2.0116	0.023259
21	-0.041085	-0.4482	0.327416

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.5228 & -5.7031 & 0 \tabularnewline
2 & 0.123617 & 1.3485 & 0.09003 \tabularnewline
3 & 0.202998 & 2.2144 & 0.014351 \tabularnewline
4 & -0.173331 & -1.8908 & 0.03054 \tabularnewline
5 & 0.001175 & 0.0128 & 0.494899 \tabularnewline
6 & 0.215529 & 2.3511 & 0.01018 \tabularnewline
7 & -0.309761 & -3.3791 & 0.000492 \tabularnewline
8 & 0.114205 & 1.2458 & 0.107638 \tabularnewline
9 & 0.18292 & 1.9954 & 0.024141 \tabularnewline
10 & -0.315898 & -3.446 & 0.000393 \tabularnewline
11 & 0.155544 & 1.6968 & 0.046175 \tabularnewline
12 & 0.001195 & 0.013 & 0.494809 \tabularnewline
13 & -0.225392 & -2.4587 & 0.007691 \tabularnewline
14 & 0.139844 & 1.5255 & 0.064892 \tabularnewline
15 & 0.031417 & 0.3427 & 0.366208 \tabularnewline
16 & -0.208156 & -2.2707 & 0.012481 \tabularnewline
17 & 0.171577 & 1.8717 & 0.031853 \tabularnewline
18 & 0.002549 & 0.0278 & 0.488933 \tabularnewline
19 & -0.180544 & -1.9695 & 0.025609 \tabularnewline
20 & 0.184406 & 2.0116 & 0.023259 \tabularnewline
21 & -0.041085 & -0.4482 & 0.327416 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67467&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]-0.5228[/C][C]-5.7031[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.123617[/C][C]1.3485[/C][C]0.09003[/C][/ROW]
[ROW][C]3[/C][C]0.202998[/C][C]2.2144[/C][C]0.014351[/C][/ROW]
[ROW][C]4[/C][C]-0.173331[/C][C]-1.8908[/C][C]0.03054[/C][/ROW]
[ROW][C]5[/C][C]0.001175[/C][C]0.0128[/C][C]0.494899[/C][/ROW]
[ROW][C]6[/C][C]0.215529[/C][C]2.3511[/C][C]0.01018[/C][/ROW]
[ROW][C]7[/C][C]-0.309761[/C][C]-3.3791[/C][C]0.000492[/C][/ROW]
[ROW][C]8[/C][C]0.114205[/C][C]1.2458[/C][C]0.107638[/C][/ROW]
[ROW][C]9[/C][C]0.18292[/C][C]1.9954[/C][C]0.024141[/C][/ROW]
[ROW][C]10[/C][C]-0.315898[/C][C]-3.446[/C][C]0.000393[/C][/ROW]
[ROW][C]11[/C][C]0.155544[/C][C]1.6968[/C][C]0.046175[/C][/ROW]
[ROW][C]12[/C][C]0.001195[/C][C]0.013[/C][C]0.494809[/C][/ROW]
[ROW][C]13[/C][C]-0.225392[/C][C]-2.4587[/C][C]0.007691[/C][/ROW]
[ROW][C]14[/C][C]0.139844[/C][C]1.5255[/C][C]0.064892[/C][/ROW]
[ROW][C]15[/C][C]0.031417[/C][C]0.3427[/C][C]0.366208[/C][/ROW]
[ROW][C]16[/C][C]-0.208156[/C][C]-2.2707[/C][C]0.012481[/C][/ROW]
[ROW][C]17[/C][C]0.171577[/C][C]1.8717[/C][C]0.031853[/C][/ROW]
[ROW][C]18[/C][C]0.002549[/C][C]0.0278[/C][C]0.488933[/C][/ROW]
[ROW][C]19[/C][C]-0.180544[/C][C]-1.9695[/C][C]0.025609[/C][/ROW]
[ROW][C]20[/C][C]0.184406[/C][C]2.0116[/C][C]0.023259[/C][/ROW]
[ROW][C]21[/C][C]-0.041085[/C][C]-0.4482[/C][C]0.327416[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67467&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67467&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	-0.5228	-5.7031	0
2	0.123617	1.3485	0.09003
3	0.202998	2.2144	0.014351
4	-0.173331	-1.8908	0.03054
5	0.001175	0.0128	0.494899
6	0.215529	2.3511	0.01018
7	-0.309761	-3.3791	0.000492
8	0.114205	1.2458	0.107638
9	0.18292	1.9954	0.024141
10	-0.315898	-3.446	0.000393
11	0.155544	1.6968	0.046175
12	0.001195	0.013	0.494809
13	-0.225392	-2.4587	0.007691
14	0.139844	1.5255	0.064892
15	0.031417	0.3427	0.366208
16	-0.208156	-2.2707	0.012481
17	0.171577	1.8717	0.031853
18	0.002549	0.0278	0.488933
19	-0.180544	-1.9695	0.025609
20	0.184406	2.0116	0.023259
21	-0.041085	-0.4482	0.327416

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.5228	-5.7031	0
2	-0.20601	-2.2473	0.013232
3	0.24896	2.7158	0.003798
4	0.123281	1.3448	0.090618
5	-0.110401	-1.2043	0.115425
6	0.135763	1.481	0.070625
7	-0.118933	-1.2974	0.098501
8	-0.172064	-1.877	0.031484
9	0.193133	2.1068	0.018616
10	-0.010235	-0.1116	0.455646
11	-0.131311	-1.4324	0.077321
12	-0.094728	-1.0334	0.151766
13	-0.152261	-1.661	0.049676
14	-0.139416	-1.5209	0.065475
15	0.081216	0.886	0.188713
16	0.061575	0.6717	0.251536
17	-0.070782	-0.7721	0.220781
18	0.019719	0.2151	0.415026
19	-0.052214	-0.5696	0.285017
20	-0.09461	-1.0321	0.152066
21	0.066852	0.7293	0.233634

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.5228 & -5.7031 & 0 \tabularnewline
2 & -0.20601 & -2.2473 & 0.013232 \tabularnewline
3 & 0.24896 & 2.7158 & 0.003798 \tabularnewline
4 & 0.123281 & 1.3448 & 0.090618 \tabularnewline
5 & -0.110401 & -1.2043 & 0.115425 \tabularnewline
6 & 0.135763 & 1.481 & 0.070625 \tabularnewline
7 & -0.118933 & -1.2974 & 0.098501 \tabularnewline
8 & -0.172064 & -1.877 & 0.031484 \tabularnewline
9 & 0.193133 & 2.1068 & 0.018616 \tabularnewline
10 & -0.010235 & -0.1116 & 0.455646 \tabularnewline
11 & -0.131311 & -1.4324 & 0.077321 \tabularnewline
12 & -0.094728 & -1.0334 & 0.151766 \tabularnewline
13 & -0.152261 & -1.661 & 0.049676 \tabularnewline
14 & -0.139416 & -1.5209 & 0.065475 \tabularnewline
15 & 0.081216 & 0.886 & 0.188713 \tabularnewline
16 & 0.061575 & 0.6717 & 0.251536 \tabularnewline
17 & -0.070782 & -0.7721 & 0.220781 \tabularnewline
18 & 0.019719 & 0.2151 & 0.415026 \tabularnewline
19 & -0.052214 & -0.5696 & 0.285017 \tabularnewline
20 & -0.09461 & -1.0321 & 0.152066 \tabularnewline
21 & 0.066852 & 0.7293 & 0.233634 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67467&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]-0.5228[/C][C]-5.7031[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.20601[/C][C]-2.2473[/C][C]0.013232[/C][/ROW]
[ROW][C]3[/C][C]0.24896[/C][C]2.7158[/C][C]0.003798[/C][/ROW]
[ROW][C]4[/C][C]0.123281[/C][C]1.3448[/C][C]0.090618[/C][/ROW]
[ROW][C]5[/C][C]-0.110401[/C][C]-1.2043[/C][C]0.115425[/C][/ROW]
[ROW][C]6[/C][C]0.135763[/C][C]1.481[/C][C]0.070625[/C][/ROW]
[ROW][C]7[/C][C]-0.118933[/C][C]-1.2974[/C][C]0.098501[/C][/ROW]
[ROW][C]8[/C][C]-0.172064[/C][C]-1.877[/C][C]0.031484[/C][/ROW]
[ROW][C]9[/C][C]0.193133[/C][C]2.1068[/C][C]0.018616[/C][/ROW]
[ROW][C]10[/C][C]-0.010235[/C][C]-0.1116[/C][C]0.455646[/C][/ROW]
[ROW][C]11[/C][C]-0.131311[/C][C]-1.4324[/C][C]0.077321[/C][/ROW]
[ROW][C]12[/C][C]-0.094728[/C][C]-1.0334[/C][C]0.151766[/C][/ROW]
[ROW][C]13[/C][C]-0.152261[/C][C]-1.661[/C][C]0.049676[/C][/ROW]
[ROW][C]14[/C][C]-0.139416[/C][C]-1.5209[/C][C]0.065475[/C][/ROW]
[ROW][C]15[/C][C]0.081216[/C][C]0.886[/C][C]0.188713[/C][/ROW]
[ROW][C]16[/C][C]0.061575[/C][C]0.6717[/C][C]0.251536[/C][/ROW]
[ROW][C]17[/C][C]-0.070782[/C][C]-0.7721[/C][C]0.220781[/C][/ROW]
[ROW][C]18[/C][C]0.019719[/C][C]0.2151[/C][C]0.415026[/C][/ROW]
[ROW][C]19[/C][C]-0.052214[/C][C]-0.5696[/C][C]0.285017[/C][/ROW]
[ROW][C]20[/C][C]-0.09461[/C][C]-1.0321[/C][C]0.152066[/C][/ROW]
[ROW][C]21[/C][C]0.066852[/C][C]0.7293[/C][C]0.233634[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67467&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67467&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	-0.5228	-5.7031	0
2	-0.20601	-2.2473	0.013232
3	0.24896	2.7158	0.003798
4	0.123281	1.3448	0.090618
5	-0.110401	-1.2043	0.115425
6	0.135763	1.481	0.070625
7	-0.118933	-1.2974	0.098501
8	-0.172064	-1.877	0.031484
9	0.193133	2.1068	0.018616
10	-0.010235	-0.1116	0.455646
11	-0.131311	-1.4324	0.077321
12	-0.094728	-1.0334	0.151766
13	-0.152261	-1.661	0.049676
14	-0.139416	-1.5209	0.065475
15	0.081216	0.886	0.188713
16	0.061575	0.6717	0.251536
17	-0.070782	-0.7721	0.220781
18	0.019719	0.2151	0.415026
19	-0.052214	-0.5696	0.285017
20	-0.09461	-1.0321	0.152066
21	0.066852	0.7293	0.233634

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Invoer (België 1998-2008) ; par2 = Belgostat ; par3 = u ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code