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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 26 Nov 2009 10:18:03 -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/Nov/26/t125925593577bm8nagk4y3aol.htm/, Retrieved Sun, 28 Apr 2024 20:48:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60181, Retrieved Sun, 28 Apr 2024 20:48:20 +0000

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No (this computation is public)

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Estimated Impact

119

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

-       [(Partial) Autocorrelation Function] [] [2009-11-26 17:18:03] [14869f38c4320b00c96ca15cc00142de] [Current]
-    D    [(Partial) Autocorrelation Function] [] [2009-12-15 20:38:12] [73863f7f907331e734eff34b7de6fc83] 

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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=60181&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=60181&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60181&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	0.928986	7.8827	0
2	0.821815	6.9733	0
3	0.721994	6.1263	0
4	0.657582	5.5798	0
5	0.630335	5.3486	1e-06
6	0.599519	5.0871	1e-06
7	0.575326	4.8818	3e-06
8	0.554369	4.704	6e-06
9	0.564105	4.7866	4e-06
10	0.594696	5.0462	2e-06
11	0.622014	5.278	1e-06
12	0.619976	5.2607	1e-06
13	0.532308	4.5168	1.2e-05
14	0.424291	3.6002	0.00029
15	0.326717	2.7723	0.003541
16	0.257798	2.1875	0.015977
17	0.217243	1.8434	0.034695
18	0.176029	1.4937	0.069818

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.928986 & 7.8827 & 0 \tabularnewline
2 & 0.821815 & 6.9733 & 0 \tabularnewline
3 & 0.721994 & 6.1263 & 0 \tabularnewline
4 & 0.657582 & 5.5798 & 0 \tabularnewline
5 & 0.630335 & 5.3486 & 1e-06 \tabularnewline
6 & 0.599519 & 5.0871 & 1e-06 \tabularnewline
7 & 0.575326 & 4.8818 & 3e-06 \tabularnewline
8 & 0.554369 & 4.704 & 6e-06 \tabularnewline
9 & 0.564105 & 4.7866 & 4e-06 \tabularnewline
10 & 0.594696 & 5.0462 & 2e-06 \tabularnewline
11 & 0.622014 & 5.278 & 1e-06 \tabularnewline
12 & 0.619976 & 5.2607 & 1e-06 \tabularnewline
13 & 0.532308 & 4.5168 & 1.2e-05 \tabularnewline
14 & 0.424291 & 3.6002 & 0.00029 \tabularnewline
15 & 0.326717 & 2.7723 & 0.003541 \tabularnewline
16 & 0.257798 & 2.1875 & 0.015977 \tabularnewline
17 & 0.217243 & 1.8434 & 0.034695 \tabularnewline
18 & 0.176029 & 1.4937 & 0.069818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60181&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]0.928986[/C][C]7.8827[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.821815[/C][C]6.9733[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.721994[/C][C]6.1263[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.657582[/C][C]5.5798[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.630335[/C][C]5.3486[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.599519[/C][C]5.0871[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.575326[/C][C]4.8818[/C][C]3e-06[/C][/ROW]
[ROW][C]8[/C][C]0.554369[/C][C]4.704[/C][C]6e-06[/C][/ROW]
[ROW][C]9[/C][C]0.564105[/C][C]4.7866[/C][C]4e-06[/C][/ROW]
[ROW][C]10[/C][C]0.594696[/C][C]5.0462[/C][C]2e-06[/C][/ROW]
[ROW][C]11[/C][C]0.622014[/C][C]5.278[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]0.619976[/C][C]5.2607[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.532308[/C][C]4.5168[/C][C]1.2e-05[/C][/ROW]
[ROW][C]14[/C][C]0.424291[/C][C]3.6002[/C][C]0.00029[/C][/ROW]
[ROW][C]15[/C][C]0.326717[/C][C]2.7723[/C][C]0.003541[/C][/ROW]
[ROW][C]16[/C][C]0.257798[/C][C]2.1875[/C][C]0.015977[/C][/ROW]
[ROW][C]17[/C][C]0.217243[/C][C]1.8434[/C][C]0.034695[/C][/ROW]
[ROW][C]18[/C][C]0.176029[/C][C]1.4937[/C][C]0.069818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60181&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60181&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	0.928986	7.8827	0
2	0.821815	6.9733	0
3	0.721994	6.1263	0
4	0.657582	5.5798	0
5	0.630335	5.3486	1e-06
6	0.599519	5.0871	1e-06
7	0.575326	4.8818	3e-06
8	0.554369	4.704	6e-06
9	0.564105	4.7866	4e-06
10	0.594696	5.0462	2e-06
11	0.622014	5.278	1e-06
12	0.619976	5.2607	1e-06
13	0.532308	4.5168	1.2e-05
14	0.424291	3.6002	0.00029
15	0.326717	2.7723	0.003541
16	0.257798	2.1875	0.015977
17	0.217243	1.8434	0.034695
18	0.176029	1.4937	0.069818

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.928986	7.8827	0
2	-0.300773	-2.5521	0.006414
3	0.066832	0.5671	0.286209
4	0.177966	1.5101	0.067698
5	0.134717	1.1431	0.128389
6	-0.144721	-1.228	0.111723
7	0.147047	1.2477	0.108086
8	0.047408	0.4023	0.344338
9	0.251123	2.1309	0.018259
10	0.057461	0.4876	0.313667
11	0.038443	0.3262	0.37261
12	-0.125954	-1.0688	0.144374
13	-0.516681	-4.3842	1.9e-05
14	0.061719	0.5237	0.301047
15	-0.04803	-0.4076	0.342406
16	-0.092228	-0.7826	0.21822
17	-0.053932	-0.4576	0.3243
18	0.022671	0.1924	0.423998

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.928986 & 7.8827 & 0 \tabularnewline
2 & -0.300773 & -2.5521 & 0.006414 \tabularnewline
3 & 0.066832 & 0.5671 & 0.286209 \tabularnewline
4 & 0.177966 & 1.5101 & 0.067698 \tabularnewline
5 & 0.134717 & 1.1431 & 0.128389 \tabularnewline
6 & -0.144721 & -1.228 & 0.111723 \tabularnewline
7 & 0.147047 & 1.2477 & 0.108086 \tabularnewline
8 & 0.047408 & 0.4023 & 0.344338 \tabularnewline
9 & 0.251123 & 2.1309 & 0.018259 \tabularnewline
10 & 0.057461 & 0.4876 & 0.313667 \tabularnewline
11 & 0.038443 & 0.3262 & 0.37261 \tabularnewline
12 & -0.125954 & -1.0688 & 0.144374 \tabularnewline
13 & -0.516681 & -4.3842 & 1.9e-05 \tabularnewline
14 & 0.061719 & 0.5237 & 0.301047 \tabularnewline
15 & -0.04803 & -0.4076 & 0.342406 \tabularnewline
16 & -0.092228 & -0.7826 & 0.21822 \tabularnewline
17 & -0.053932 & -0.4576 & 0.3243 \tabularnewline
18 & 0.022671 & 0.1924 & 0.423998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60181&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]0.928986[/C][C]7.8827[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.300773[/C][C]-2.5521[/C][C]0.006414[/C][/ROW]
[ROW][C]3[/C][C]0.066832[/C][C]0.5671[/C][C]0.286209[/C][/ROW]
[ROW][C]4[/C][C]0.177966[/C][C]1.5101[/C][C]0.067698[/C][/ROW]
[ROW][C]5[/C][C]0.134717[/C][C]1.1431[/C][C]0.128389[/C][/ROW]
[ROW][C]6[/C][C]-0.144721[/C][C]-1.228[/C][C]0.111723[/C][/ROW]
[ROW][C]7[/C][C]0.147047[/C][C]1.2477[/C][C]0.108086[/C][/ROW]
[ROW][C]8[/C][C]0.047408[/C][C]0.4023[/C][C]0.344338[/C][/ROW]
[ROW][C]9[/C][C]0.251123[/C][C]2.1309[/C][C]0.018259[/C][/ROW]
[ROW][C]10[/C][C]0.057461[/C][C]0.4876[/C][C]0.313667[/C][/ROW]
[ROW][C]11[/C][C]0.038443[/C][C]0.3262[/C][C]0.37261[/C][/ROW]
[ROW][C]12[/C][C]-0.125954[/C][C]-1.0688[/C][C]0.144374[/C][/ROW]
[ROW][C]13[/C][C]-0.516681[/C][C]-4.3842[/C][C]1.9e-05[/C][/ROW]
[ROW][C]14[/C][C]0.061719[/C][C]0.5237[/C][C]0.301047[/C][/ROW]
[ROW][C]15[/C][C]-0.04803[/C][C]-0.4076[/C][C]0.342406[/C][/ROW]
[ROW][C]16[/C][C]-0.092228[/C][C]-0.7826[/C][C]0.21822[/C][/ROW]
[ROW][C]17[/C][C]-0.053932[/C][C]-0.4576[/C][C]0.3243[/C][/ROW]
[ROW][C]18[/C][C]0.022671[/C][C]0.1924[/C][C]0.423998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60181&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60181&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	0.928986	7.8827	0
2	-0.300773	-2.5521	0.006414
3	0.066832	0.5671	0.286209
4	0.177966	1.5101	0.067698
5	0.134717	1.1431	0.128389
6	-0.144721	-1.228	0.111723
7	0.147047	1.2477	0.108086
8	0.047408	0.4023	0.344338
9	0.251123	2.1309	0.018259
10	0.057461	0.4876	0.313667
11	0.038443	0.3262	0.37261
12	-0.125954	-1.0688	0.144374
13	-0.516681	-4.3842	1.9e-05
14	0.061719	0.5237	0.301047
15	-0.04803	-0.4076	0.342406
16	-0.092228	-0.7826	0.21822
17	-0.053932	-0.4576	0.3243
18	0.022671	0.1924	0.423998

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code