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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 27 Nov 2007 09:42:07 -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/27/t1196181177ljgagmhn4azvt2u.htm/, Retrieved Sun, 05 May 2024 18:13:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6882, Retrieved Sun, 05 May 2024 18:13:20 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

groep MENS

Estimated Impact

180

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

-       [(Partial) Autocorrelation Function] [Voeding_Q2_autoco...] [2007-11-27 16:42:07] [183840e644503a44411d430a3cdac4ba] [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=6882&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=6882&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6882&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	8.4853	0
1	0.183451	1.5566	0.061971
2	0.116138	0.9855	0.163847
3	-0.027539	-0.2337	0.592051
4	0.028955	0.2457	0.40331
5	0.017771	0.1508	0.440282
6	0.179076	1.5195	0.066507
7	-0.084495	-0.717	0.762141
8	-0.039837	-0.338	0.631837
9	-0.060662	-0.5147	0.695844
10	-0.063351	-0.5376	0.703728
11	-0.049049	-0.4162	0.660746
12	0.067201	0.5702	0.285151
13	-0.104922	-0.8903	0.811864
14	-0.027428	-0.2327	0.591685
15	0.011025	0.0936	0.462862
16	-0.038437	-0.3261	0.627371
17	0.044499	0.3776	0.353426

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.183451 & 1.5566 & 0.061971 \tabularnewline
2 & 0.116138 & 0.9855 & 0.163847 \tabularnewline
3 & -0.027539 & -0.2337 & 0.592051 \tabularnewline
4 & 0.028955 & 0.2457 & 0.40331 \tabularnewline
5 & 0.017771 & 0.1508 & 0.440282 \tabularnewline
6 & 0.179076 & 1.5195 & 0.066507 \tabularnewline
7 & -0.084495 & -0.717 & 0.762141 \tabularnewline
8 & -0.039837 & -0.338 & 0.631837 \tabularnewline
9 & -0.060662 & -0.5147 & 0.695844 \tabularnewline
10 & -0.063351 & -0.5376 & 0.703728 \tabularnewline
11 & -0.049049 & -0.4162 & 0.660746 \tabularnewline
12 & 0.067201 & 0.5702 & 0.285151 \tabularnewline
13 & -0.104922 & -0.8903 & 0.811864 \tabularnewline
14 & -0.027428 & -0.2327 & 0.591685 \tabularnewline
15 & 0.011025 & 0.0936 & 0.462862 \tabularnewline
16 & -0.038437 & -0.3261 & 0.627371 \tabularnewline
17 & 0.044499 & 0.3776 & 0.353426 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6882&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]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.183451[/C][C]1.5566[/C][C]0.061971[/C][/ROW]
[ROW][C]2[/C][C]0.116138[/C][C]0.9855[/C][C]0.163847[/C][/ROW]
[ROW][C]3[/C][C]-0.027539[/C][C]-0.2337[/C][C]0.592051[/C][/ROW]
[ROW][C]4[/C][C]0.028955[/C][C]0.2457[/C][C]0.40331[/C][/ROW]
[ROW][C]5[/C][C]0.017771[/C][C]0.1508[/C][C]0.440282[/C][/ROW]
[ROW][C]6[/C][C]0.179076[/C][C]1.5195[/C][C]0.066507[/C][/ROW]
[ROW][C]7[/C][C]-0.084495[/C][C]-0.717[/C][C]0.762141[/C][/ROW]
[ROW][C]8[/C][C]-0.039837[/C][C]-0.338[/C][C]0.631837[/C][/ROW]
[ROW][C]9[/C][C]-0.060662[/C][C]-0.5147[/C][C]0.695844[/C][/ROW]
[ROW][C]10[/C][C]-0.063351[/C][C]-0.5376[/C][C]0.703728[/C][/ROW]
[ROW][C]11[/C][C]-0.049049[/C][C]-0.4162[/C][C]0.660746[/C][/ROW]
[ROW][C]12[/C][C]0.067201[/C][C]0.5702[/C][C]0.285151[/C][/ROW]
[ROW][C]13[/C][C]-0.104922[/C][C]-0.8903[/C][C]0.811864[/C][/ROW]
[ROW][C]14[/C][C]-0.027428[/C][C]-0.2327[/C][C]0.591685[/C][/ROW]
[ROW][C]15[/C][C]0.011025[/C][C]0.0936[/C][C]0.462862[/C][/ROW]
[ROW][C]16[/C][C]-0.038437[/C][C]-0.3261[/C][C]0.627371[/C][/ROW]
[ROW][C]17[/C][C]0.044499[/C][C]0.3776[/C][C]0.353426[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6882&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6882&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	8.4853	0
1	0.183451	1.5566	0.061971
2	0.116138	0.9855	0.163847
3	-0.027539	-0.2337	0.592051
4	0.028955	0.2457	0.40331
5	0.017771	0.1508	0.440282
6	0.179076	1.5195	0.066507
7	-0.084495	-0.717	0.762141
8	-0.039837	-0.338	0.631837
9	-0.060662	-0.5147	0.695844
10	-0.063351	-0.5376	0.703728
11	-0.049049	-0.4162	0.660746
12	0.067201	0.5702	0.285151
13	-0.104922	-0.8903	0.811864
14	-0.027428	-0.2327	0.591685
15	0.011025	0.0936	0.462862
16	-0.038437	-0.3261	0.627371
17	0.044499	0.3776	0.353426

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.183451	1.5566	0.061971
1	0.085357	0.7243	0.235621
2	-0.065344	-0.5545	0.70951
3	0.03615	0.3067	0.379964
4	0.017741	0.1505	0.44038
5	0.172106	1.4604	0.074269
6	-0.156458	-1.3276	0.905746
7	-0.035521	-0.3014	0.618013
8	-0.005943	-0.0504	0.520038
9	-0.06538	-0.5548	0.709613
10	-0.023249	-0.1973	0.577914
11	0.064878	0.5505	0.291837
12	-0.09176	-0.7786	0.78062
13	-0.005783	-0.0491	0.519501
14	0.055097	0.4675	0.320774
15	-0.049904	-0.4235	0.663386
16	0.058156	0.4935	0.311592
17	-0.036595	-0.3105	0.621468

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.183451 & 1.5566 & 0.061971 \tabularnewline
1 & 0.085357 & 0.7243 & 0.235621 \tabularnewline
2 & -0.065344 & -0.5545 & 0.70951 \tabularnewline
3 & 0.03615 & 0.3067 & 0.379964 \tabularnewline
4 & 0.017741 & 0.1505 & 0.44038 \tabularnewline
5 & 0.172106 & 1.4604 & 0.074269 \tabularnewline
6 & -0.156458 & -1.3276 & 0.905746 \tabularnewline
7 & -0.035521 & -0.3014 & 0.618013 \tabularnewline
8 & -0.005943 & -0.0504 & 0.520038 \tabularnewline
9 & -0.06538 & -0.5548 & 0.709613 \tabularnewline
10 & -0.023249 & -0.1973 & 0.577914 \tabularnewline
11 & 0.064878 & 0.5505 & 0.291837 \tabularnewline
12 & -0.09176 & -0.7786 & 0.78062 \tabularnewline
13 & -0.005783 & -0.0491 & 0.519501 \tabularnewline
14 & 0.055097 & 0.4675 & 0.320774 \tabularnewline
15 & -0.049904 & -0.4235 & 0.663386 \tabularnewline
16 & 0.058156 & 0.4935 & 0.311592 \tabularnewline
17 & -0.036595 & -0.3105 & 0.621468 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6882&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]0.183451[/C][C]1.5566[/C][C]0.061971[/C][/ROW]
[ROW][C]1[/C][C]0.085357[/C][C]0.7243[/C][C]0.235621[/C][/ROW]
[ROW][C]2[/C][C]-0.065344[/C][C]-0.5545[/C][C]0.70951[/C][/ROW]
[ROW][C]3[/C][C]0.03615[/C][C]0.3067[/C][C]0.379964[/C][/ROW]
[ROW][C]4[/C][C]0.017741[/C][C]0.1505[/C][C]0.44038[/C][/ROW]
[ROW][C]5[/C][C]0.172106[/C][C]1.4604[/C][C]0.074269[/C][/ROW]
[ROW][C]6[/C][C]-0.156458[/C][C]-1.3276[/C][C]0.905746[/C][/ROW]
[ROW][C]7[/C][C]-0.035521[/C][C]-0.3014[/C][C]0.618013[/C][/ROW]
[ROW][C]8[/C][C]-0.005943[/C][C]-0.0504[/C][C]0.520038[/C][/ROW]
[ROW][C]9[/C][C]-0.06538[/C][C]-0.5548[/C][C]0.709613[/C][/ROW]
[ROW][C]10[/C][C]-0.023249[/C][C]-0.1973[/C][C]0.577914[/C][/ROW]
[ROW][C]11[/C][C]0.064878[/C][C]0.5505[/C][C]0.291837[/C][/ROW]
[ROW][C]12[/C][C]-0.09176[/C][C]-0.7786[/C][C]0.78062[/C][/ROW]
[ROW][C]13[/C][C]-0.005783[/C][C]-0.0491[/C][C]0.519501[/C][/ROW]
[ROW][C]14[/C][C]0.055097[/C][C]0.4675[/C][C]0.320774[/C][/ROW]
[ROW][C]15[/C][C]-0.049904[/C][C]-0.4235[/C][C]0.663386[/C][/ROW]
[ROW][C]16[/C][C]0.058156[/C][C]0.4935[/C][C]0.311592[/C][/ROW]
[ROW][C]17[/C][C]-0.036595[/C][C]-0.3105[/C][C]0.621468[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6882&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6882&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	0.183451	1.5566	0.061971
1	0.085357	0.7243	0.235621
2	-0.065344	-0.5545	0.70951
3	0.03615	0.3067	0.379964
4	0.017741	0.1505	0.44038
5	0.172106	1.4604	0.074269
6	-0.156458	-1.3276	0.905746
7	-0.035521	-0.3014	0.618013
8	-0.005943	-0.0504	0.520038
9	-0.06538	-0.5548	0.709613
10	-0.023249	-0.1973	0.577914
11	0.064878	0.5505	0.291837
12	-0.09176	-0.7786	0.78062
13	-0.005783	-0.0491	0.519501
14	0.055097	0.4675	0.320774
15	-0.049904	-0.4235	0.663386
16	0.058156	0.4935	0.311592
17	-0.036595	-0.3105	0.621468

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 = 0 ; par5 = 12 ;

Parameters (R input):

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