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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 24 Nov 2007 07:33:17 -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/2007/Nov/24/t1195914290t2kz658ox69nrma.htm/, Retrieved Fri, 03 May 2024 06:07:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6320, Retrieved Fri, 03 May 2024 06:07:56 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

WS7PACFM

Estimated Impact

220

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

-       [(Partial) Autocorrelation Function] [WS7 - PACF - Medical] [2007-11-24 14:33:17] [e51d7ab0e549b3dc96ac85a81d9bd259] [Current]

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Summary of compuational 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 compuational 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=6320&T=0

[TABLE]
[ROW][C]Summary of compuational 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=6320&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6320&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 compuational 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
0	1	8.2462	0
1	0.152226	1.2553	0.106835
2	0.064752	0.534	0.297555
3	0.106425	0.8776	0.191624
4	0.090349	0.745	0.229408
5	0.031389	0.2588	0.39827
6	0.057102	0.4709	0.319619
7	-0.271203	-2.2364	0.985695
8	-0.174254	-1.4369	0.922339
9	-0.055374	-0.4566	0.675303
10	-0.179433	-1.4796	0.928206
11	-0.161091	-1.3284	0.905755
12	-0.527595	-4.3507	0.999977
13	-0.242728	-2.0016	0.975339
14	-0.077439	-0.6386	0.737379
15	0.017346	0.143	0.443342
16	-0.130202	-1.0737	0.856617
17	0.213853	1.7635	0.041156
18	0.018351	0.1513	0.440083

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.2462 & 0 \tabularnewline
1 & 0.152226 & 1.2553 & 0.106835 \tabularnewline
2 & 0.064752 & 0.534 & 0.297555 \tabularnewline
3 & 0.106425 & 0.8776 & 0.191624 \tabularnewline
4 & 0.090349 & 0.745 & 0.229408 \tabularnewline
5 & 0.031389 & 0.2588 & 0.39827 \tabularnewline
6 & 0.057102 & 0.4709 & 0.319619 \tabularnewline
7 & -0.271203 & -2.2364 & 0.985695 \tabularnewline
8 & -0.174254 & -1.4369 & 0.922339 \tabularnewline
9 & -0.055374 & -0.4566 & 0.675303 \tabularnewline
10 & -0.179433 & -1.4796 & 0.928206 \tabularnewline
11 & -0.161091 & -1.3284 & 0.905755 \tabularnewline
12 & -0.527595 & -4.3507 & 0.999977 \tabularnewline
13 & -0.242728 & -2.0016 & 0.975339 \tabularnewline
14 & -0.077439 & -0.6386 & 0.737379 \tabularnewline
15 & 0.017346 & 0.143 & 0.443342 \tabularnewline
16 & -0.130202 & -1.0737 & 0.856617 \tabularnewline
17 & 0.213853 & 1.7635 & 0.041156 \tabularnewline
18 & 0.018351 & 0.1513 & 0.440083 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6320&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]0[/C][C]1[/C][C]8.2462[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.152226[/C][C]1.2553[/C][C]0.106835[/C][/ROW]
[ROW][C]2[/C][C]0.064752[/C][C]0.534[/C][C]0.297555[/C][/ROW]
[ROW][C]3[/C][C]0.106425[/C][C]0.8776[/C][C]0.191624[/C][/ROW]
[ROW][C]4[/C][C]0.090349[/C][C]0.745[/C][C]0.229408[/C][/ROW]
[ROW][C]5[/C][C]0.031389[/C][C]0.2588[/C][C]0.39827[/C][/ROW]
[ROW][C]6[/C][C]0.057102[/C][C]0.4709[/C][C]0.319619[/C][/ROW]
[ROW][C]7[/C][C]-0.271203[/C][C]-2.2364[/C][C]0.985695[/C][/ROW]
[ROW][C]8[/C][C]-0.174254[/C][C]-1.4369[/C][C]0.922339[/C][/ROW]
[ROW][C]9[/C][C]-0.055374[/C][C]-0.4566[/C][C]0.675303[/C][/ROW]
[ROW][C]10[/C][C]-0.179433[/C][C]-1.4796[/C][C]0.928206[/C][/ROW]
[ROW][C]11[/C][C]-0.161091[/C][C]-1.3284[/C][C]0.905755[/C][/ROW]
[ROW][C]12[/C][C]-0.527595[/C][C]-4.3507[/C][C]0.999977[/C][/ROW]
[ROW][C]13[/C][C]-0.242728[/C][C]-2.0016[/C][C]0.975339[/C][/ROW]
[ROW][C]14[/C][C]-0.077439[/C][C]-0.6386[/C][C]0.737379[/C][/ROW]
[ROW][C]15[/C][C]0.017346[/C][C]0.143[/C][C]0.443342[/C][/ROW]
[ROW][C]16[/C][C]-0.130202[/C][C]-1.0737[/C][C]0.856617[/C][/ROW]
[ROW][C]17[/C][C]0.213853[/C][C]1.7635[/C][C]0.041156[/C][/ROW]
[ROW][C]18[/C][C]0.018351[/C][C]0.1513[/C][C]0.440083[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6320&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6320&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
0	1	8.2462	0
1	0.152226	1.2553	0.106835
2	0.064752	0.534	0.297555
3	0.106425	0.8776	0.191624
4	0.090349	0.745	0.229408
5	0.031389	0.2588	0.39827
6	0.057102	0.4709	0.319619
7	-0.271203	-2.2364	0.985695
8	-0.174254	-1.4369	0.922339
9	-0.055374	-0.4566	0.675303
10	-0.179433	-1.4796	0.928206
11	-0.161091	-1.3284	0.905755
12	-0.527595	-4.3507	0.999977
13	-0.242728	-2.0016	0.975339
14	-0.077439	-0.6386	0.737379
15	0.017346	0.143	0.443342
16	-0.130202	-1.0737	0.856617
17	0.213853	1.7635	0.041156
18	0.018351	0.1513	0.440083

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.152226	1.2553	0.106835
1	0.042566	0.351	0.363334
2	0.092824	0.7654	0.223328
3	0.061292	0.5054	0.307448
4	0.001467	0.0121	0.49519
5	0.038682	0.319	0.375358
6	-0.31103	-2.5648	0.993733
7	-0.120427	-0.9931	0.837901
8	-0.010297	-0.0849	0.533709
9	-0.133128	-1.0978	0.861919
10	-0.056865	-0.4689	0.679686
11	-0.541538	-4.4656	0.999985
12	-0.124911	-1.03	0.846681
13	-0.131067	-1.0808	0.858199
14	0.032273	0.2661	0.395473
15	-0.109169	-0.9002	0.814413
16	0.247839	2.0437	0.022428
17	-0.01311	-0.1081	0.542884
18	-0.122855	-1.0131	0.842695

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.152226 & 1.2553 & 0.106835 \tabularnewline
1 & 0.042566 & 0.351 & 0.363334 \tabularnewline
2 & 0.092824 & 0.7654 & 0.223328 \tabularnewline
3 & 0.061292 & 0.5054 & 0.307448 \tabularnewline
4 & 0.001467 & 0.0121 & 0.49519 \tabularnewline
5 & 0.038682 & 0.319 & 0.375358 \tabularnewline
6 & -0.31103 & -2.5648 & 0.993733 \tabularnewline
7 & -0.120427 & -0.9931 & 0.837901 \tabularnewline
8 & -0.010297 & -0.0849 & 0.533709 \tabularnewline
9 & -0.133128 & -1.0978 & 0.861919 \tabularnewline
10 & -0.056865 & -0.4689 & 0.679686 \tabularnewline
11 & -0.541538 & -4.4656 & 0.999985 \tabularnewline
12 & -0.124911 & -1.03 & 0.846681 \tabularnewline
13 & -0.131067 & -1.0808 & 0.858199 \tabularnewline
14 & 0.032273 & 0.2661 & 0.395473 \tabularnewline
15 & -0.109169 & -0.9002 & 0.814413 \tabularnewline
16 & 0.247839 & 2.0437 & 0.022428 \tabularnewline
17 & -0.01311 & -0.1081 & 0.542884 \tabularnewline
18 & -0.122855 & -1.0131 & 0.842695 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6320&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]0[/C][C]0.152226[/C][C]1.2553[/C][C]0.106835[/C][/ROW]
[ROW][C]1[/C][C]0.042566[/C][C]0.351[/C][C]0.363334[/C][/ROW]
[ROW][C]2[/C][C]0.092824[/C][C]0.7654[/C][C]0.223328[/C][/ROW]
[ROW][C]3[/C][C]0.061292[/C][C]0.5054[/C][C]0.307448[/C][/ROW]
[ROW][C]4[/C][C]0.001467[/C][C]0.0121[/C][C]0.49519[/C][/ROW]
[ROW][C]5[/C][C]0.038682[/C][C]0.319[/C][C]0.375358[/C][/ROW]
[ROW][C]6[/C][C]-0.31103[/C][C]-2.5648[/C][C]0.993733[/C][/ROW]
[ROW][C]7[/C][C]-0.120427[/C][C]-0.9931[/C][C]0.837901[/C][/ROW]
[ROW][C]8[/C][C]-0.010297[/C][C]-0.0849[/C][C]0.533709[/C][/ROW]
[ROW][C]9[/C][C]-0.133128[/C][C]-1.0978[/C][C]0.861919[/C][/ROW]
[ROW][C]10[/C][C]-0.056865[/C][C]-0.4689[/C][C]0.679686[/C][/ROW]
[ROW][C]11[/C][C]-0.541538[/C][C]-4.4656[/C][C]0.999985[/C][/ROW]
[ROW][C]12[/C][C]-0.124911[/C][C]-1.03[/C][C]0.846681[/C][/ROW]
[ROW][C]13[/C][C]-0.131067[/C][C]-1.0808[/C][C]0.858199[/C][/ROW]
[ROW][C]14[/C][C]0.032273[/C][C]0.2661[/C][C]0.395473[/C][/ROW]
[ROW][C]15[/C][C]-0.109169[/C][C]-0.9002[/C][C]0.814413[/C][/ROW]
[ROW][C]16[/C][C]0.247839[/C][C]2.0437[/C][C]0.022428[/C][/ROW]
[ROW][C]17[/C][C]-0.01311[/C][C]-0.1081[/C][C]0.542884[/C][/ROW]
[ROW][C]18[/C][C]-0.122855[/C][C]-1.0131[/C][C]0.842695[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6320&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6320&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
0	0.152226	1.2553	0.106835
1	0.042566	0.351	0.363334
2	0.092824	0.7654	0.223328
3	0.061292	0.5054	0.307448
4	0.001467	0.0121	0.49519
5	0.038682	0.319	0.375358
6	-0.31103	-2.5648	0.993733
7	-0.120427	-0.9931	0.837901
8	-0.010297	-0.0849	0.533709
9	-0.133128	-1.0978	0.861919
10	-0.056865	-0.4689	0.679686
11	-0.541538	-4.4656	0.999985
12	-0.124911	-1.03	0.846681
13	-0.131067	-1.0808	0.858199
14	0.032273	0.2661	0.395473
15	-0.109169	-0.9002	0.814413
16	0.247839	2.0437	0.022428
17	-0.01311	-0.1081	0.542884
18	-0.122855	-1.0131	0.842695

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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