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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 18 Dec 2009 04:34:54 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/18/t12611361518vperermi2toloy.htm/, Retrieved Sat, 27 Apr 2024 20:26:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69247, Retrieved Sat, 27 Apr 2024 20:26:04 +0000

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-       [(Partial) Autocorrelation Function] [] [2009-12-18 11:34:54] [02cb93c9d037d32bf77dfc632a3a9fbe] [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=69247&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=69247&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69247&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	0.537847	3.7263	0.000256
2	-0.08553	-0.5926	0.278126
3	-0.485876	-3.3662	0.000754
4	-0.50964	-3.5309	0.000463
5	-0.152639	-1.0575	0.147785
6	0.222556	1.5419	0.064831
7	0.406781	2.8183	0.003496
8	0.281539	1.9506	0.028481
9	-0.031898	-0.221	0.413017
10	-0.186682	-1.2934	0.101036
11	-0.244558	-1.6943	0.04834
12	-0.245622	-1.7017	0.047639
13	-0.070217	-0.4865	0.314421
14	0.111648	0.7735	0.221503
15	0.139176	0.9642	0.169879
16	0.041246	0.2858	0.388145
17	-0.044554	-0.3087	0.379451

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.537847 & 3.7263 & 0.000256 \tabularnewline
2 & -0.08553 & -0.5926 & 0.278126 \tabularnewline
3 & -0.485876 & -3.3662 & 0.000754 \tabularnewline
4 & -0.50964 & -3.5309 & 0.000463 \tabularnewline
5 & -0.152639 & -1.0575 & 0.147785 \tabularnewline
6 & 0.222556 & 1.5419 & 0.064831 \tabularnewline
7 & 0.406781 & 2.8183 & 0.003496 \tabularnewline
8 & 0.281539 & 1.9506 & 0.028481 \tabularnewline
9 & -0.031898 & -0.221 & 0.413017 \tabularnewline
10 & -0.186682 & -1.2934 & 0.101036 \tabularnewline
11 & -0.244558 & -1.6943 & 0.04834 \tabularnewline
12 & -0.245622 & -1.7017 & 0.047639 \tabularnewline
13 & -0.070217 & -0.4865 & 0.314421 \tabularnewline
14 & 0.111648 & 0.7735 & 0.221503 \tabularnewline
15 & 0.139176 & 0.9642 & 0.169879 \tabularnewline
16 & 0.041246 & 0.2858 & 0.388145 \tabularnewline
17 & -0.044554 & -0.3087 & 0.379451 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69247&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]0.537847[/C][C]3.7263[/C][C]0.000256[/C][/ROW]
[ROW][C]2[/C][C]-0.08553[/C][C]-0.5926[/C][C]0.278126[/C][/ROW]
[ROW][C]3[/C][C]-0.485876[/C][C]-3.3662[/C][C]0.000754[/C][/ROW]
[ROW][C]4[/C][C]-0.50964[/C][C]-3.5309[/C][C]0.000463[/C][/ROW]
[ROW][C]5[/C][C]-0.152639[/C][C]-1.0575[/C][C]0.147785[/C][/ROW]
[ROW][C]6[/C][C]0.222556[/C][C]1.5419[/C][C]0.064831[/C][/ROW]
[ROW][C]7[/C][C]0.406781[/C][C]2.8183[/C][C]0.003496[/C][/ROW]
[ROW][C]8[/C][C]0.281539[/C][C]1.9506[/C][C]0.028481[/C][/ROW]
[ROW][C]9[/C][C]-0.031898[/C][C]-0.221[/C][C]0.413017[/C][/ROW]
[ROW][C]10[/C][C]-0.186682[/C][C]-1.2934[/C][C]0.101036[/C][/ROW]
[ROW][C]11[/C][C]-0.244558[/C][C]-1.6943[/C][C]0.04834[/C][/ROW]
[ROW][C]12[/C][C]-0.245622[/C][C]-1.7017[/C][C]0.047639[/C][/ROW]
[ROW][C]13[/C][C]-0.070217[/C][C]-0.4865[/C][C]0.314421[/C][/ROW]
[ROW][C]14[/C][C]0.111648[/C][C]0.7735[/C][C]0.221503[/C][/ROW]
[ROW][C]15[/C][C]0.139176[/C][C]0.9642[/C][C]0.169879[/C][/ROW]
[ROW][C]16[/C][C]0.041246[/C][C]0.2858[/C][C]0.388145[/C][/ROW]
[ROW][C]17[/C][C]-0.044554[/C][C]-0.3087[/C][C]0.379451[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69247&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69247&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	0.537847	3.7263	0.000256
2	-0.08553	-0.5926	0.278126
3	-0.485876	-3.3662	0.000754
4	-0.50964	-3.5309	0.000463
5	-0.152639	-1.0575	0.147785
6	0.222556	1.5419	0.064831
7	0.406781	2.8183	0.003496
8	0.281539	1.9506	0.028481
9	-0.031898	-0.221	0.413017
10	-0.186682	-1.2934	0.101036
11	-0.244558	-1.6943	0.04834
12	-0.245622	-1.7017	0.047639
13	-0.070217	-0.4865	0.314421
14	0.111648	0.7735	0.221503
15	0.139176	0.9642	0.169879
16	0.041246	0.2858	0.388145
17	-0.044554	-0.3087	0.379451

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.537847	3.7263	0.000256
2	-0.527365	-3.6537	0.000319
3	-0.257227	-1.7821	0.040528
4	-0.13586	-0.9413	0.17564
5	0.135442	0.9384	0.176377
6	0.010811	0.0749	0.470302
7	0.101826	0.7055	0.241964
8	-0.029703	-0.2058	0.418914
9	-0.037326	-0.2586	0.398524
10	0.162487	1.1257	0.132936
11	-0.14681	-1.0171	0.157095
12	-0.236373	-1.6376	0.054019
13	0.068142	0.4721	0.319497
14	0.009733	0.0674	0.473258
15	-0.187752	-1.3008	0.099772
16	-0.101787	-0.7052	0.242046
17	0.088478	0.613	0.271386

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.537847 & 3.7263 & 0.000256 \tabularnewline
2 & -0.527365 & -3.6537 & 0.000319 \tabularnewline
3 & -0.257227 & -1.7821 & 0.040528 \tabularnewline
4 & -0.13586 & -0.9413 & 0.17564 \tabularnewline
5 & 0.135442 & 0.9384 & 0.176377 \tabularnewline
6 & 0.010811 & 0.0749 & 0.470302 \tabularnewline
7 & 0.101826 & 0.7055 & 0.241964 \tabularnewline
8 & -0.029703 & -0.2058 & 0.418914 \tabularnewline
9 & -0.037326 & -0.2586 & 0.398524 \tabularnewline
10 & 0.162487 & 1.1257 & 0.132936 \tabularnewline
11 & -0.14681 & -1.0171 & 0.157095 \tabularnewline
12 & -0.236373 & -1.6376 & 0.054019 \tabularnewline
13 & 0.068142 & 0.4721 & 0.319497 \tabularnewline
14 & 0.009733 & 0.0674 & 0.473258 \tabularnewline
15 & -0.187752 & -1.3008 & 0.099772 \tabularnewline
16 & -0.101787 & -0.7052 & 0.242046 \tabularnewline
17 & 0.088478 & 0.613 & 0.271386 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69247&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]0.537847[/C][C]3.7263[/C][C]0.000256[/C][/ROW]
[ROW][C]2[/C][C]-0.527365[/C][C]-3.6537[/C][C]0.000319[/C][/ROW]
[ROW][C]3[/C][C]-0.257227[/C][C]-1.7821[/C][C]0.040528[/C][/ROW]
[ROW][C]4[/C][C]-0.13586[/C][C]-0.9413[/C][C]0.17564[/C][/ROW]
[ROW][C]5[/C][C]0.135442[/C][C]0.9384[/C][C]0.176377[/C][/ROW]
[ROW][C]6[/C][C]0.010811[/C][C]0.0749[/C][C]0.470302[/C][/ROW]
[ROW][C]7[/C][C]0.101826[/C][C]0.7055[/C][C]0.241964[/C][/ROW]
[ROW][C]8[/C][C]-0.029703[/C][C]-0.2058[/C][C]0.418914[/C][/ROW]
[ROW][C]9[/C][C]-0.037326[/C][C]-0.2586[/C][C]0.398524[/C][/ROW]
[ROW][C]10[/C][C]0.162487[/C][C]1.1257[/C][C]0.132936[/C][/ROW]
[ROW][C]11[/C][C]-0.14681[/C][C]-1.0171[/C][C]0.157095[/C][/ROW]
[ROW][C]12[/C][C]-0.236373[/C][C]-1.6376[/C][C]0.054019[/C][/ROW]
[ROW][C]13[/C][C]0.068142[/C][C]0.4721[/C][C]0.319497[/C][/ROW]
[ROW][C]14[/C][C]0.009733[/C][C]0.0674[/C][C]0.473258[/C][/ROW]
[ROW][C]15[/C][C]-0.187752[/C][C]-1.3008[/C][C]0.099772[/C][/ROW]
[ROW][C]16[/C][C]-0.101787[/C][C]-0.7052[/C][C]0.242046[/C][/ROW]
[ROW][C]17[/C][C]0.088478[/C][C]0.613[/C][C]0.271386[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69247&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69247&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	0.537847	3.7263	0.000256
2	-0.527365	-3.6537	0.000319
3	-0.257227	-1.7821	0.040528
4	-0.13586	-0.9413	0.17564
5	0.135442	0.9384	0.176377
6	0.010811	0.0749	0.470302
7	0.101826	0.7055	0.241964
8	-0.029703	-0.2058	0.418914
9	-0.037326	-0.2586	0.398524
10	0.162487	1.1257	0.132936
11	-0.14681	-1.0171	0.157095
12	-0.236373	-1.6376	0.054019
13	0.068142	0.4721	0.319497
14	0.009733	0.0674	0.473258
15	-0.187752	-1.3008	0.099772
16	-0.101787	-0.7052	0.242046
17	0.088478	0.613	0.271386

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code