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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 06 Dec 2007 08:01:23 -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/Dec/06/t1196952566xpott9cc8wgynug.htm/, Retrieved Tue, 21 Apr 2026 16:37:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2650, Retrieved Tue, 21 Apr 2026 16:37:43 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

autocorrelatie functie:prijs diepvriesfrieten

Estimated Impact

404

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

-       [(Partial) Autocorrelation Function] [workshop 4] [2007-12-06 15:01:23] [011cc8cdd02d5893b5258ac3f5e21d83] [Current]

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Dataseries X:

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Histogram

Boxplots

1,6
1,59
1,6
1,6
1,59
1,59
1,58
1,59
1,59
1,58
1,58
1,58
1,57
1,57
1,57
1,57
1,58
1,58
1,57
1,58
1,57
1,57
1,57
1,57
1,57
1,57
1,59
1,6
1,6
1,6
1,6
1,61
1,61
1,62
1,62
1,62
1,62
1,62
1,62
1,61
1,59
1,58
1,56
1,56
1,54
1,55
1,56
1,57
1,58
1,59
1,6
1,6
1,61
1,61
1,62
1,61
1,6
1,6
1,6
1,61
1,62
1,63
1,63
1,66
1,66
1,66
1,65
1,65
1,64
1,64
1,65
1,64

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=2650&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=2650&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2650&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	7.6158	0
1	-0.580345	-4.4198	0.999978
2	0.237983	1.8124	0.037549
3	-0.140792	-1.0722	0.855974
4	0.042291	0.3221	0.374276
5	0.013183	0.1004	0.460186
6	-0.063118	-0.4807	0.683728
7	0.160883	1.2252	0.112717
8	-0.258448	-1.9683	0.973089
9	0.23749	1.8087	0.037843
10	-0.301213	-2.294	0.987284
11	0.412467	3.1413	0.001324
12	-0.441263	-3.3606	0.99931
13	0.180686	1.3761	0.087046
14	-0.04299	-0.3274	0.627729
15	0.007444	0.0567	0.477493
16	0.055343	0.4215	0.337481
17	0.028408	0.2164	0.414737

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6158 & 0 \tabularnewline
1 & -0.580345 & -4.4198 & 0.999978 \tabularnewline
2 & 0.237983 & 1.8124 & 0.037549 \tabularnewline
3 & -0.140792 & -1.0722 & 0.855974 \tabularnewline
4 & 0.042291 & 0.3221 & 0.374276 \tabularnewline
5 & 0.013183 & 0.1004 & 0.460186 \tabularnewline
6 & -0.063118 & -0.4807 & 0.683728 \tabularnewline
7 & 0.160883 & 1.2252 & 0.112717 \tabularnewline
8 & -0.258448 & -1.9683 & 0.973089 \tabularnewline
9 & 0.23749 & 1.8087 & 0.037843 \tabularnewline
10 & -0.301213 & -2.294 & 0.987284 \tabularnewline
11 & 0.412467 & 3.1413 & 0.001324 \tabularnewline
12 & -0.441263 & -3.3606 & 0.99931 \tabularnewline
13 & 0.180686 & 1.3761 & 0.087046 \tabularnewline
14 & -0.04299 & -0.3274 & 0.627729 \tabularnewline
15 & 0.007444 & 0.0567 & 0.477493 \tabularnewline
16 & 0.055343 & 0.4215 & 0.337481 \tabularnewline
17 & 0.028408 & 0.2164 & 0.414737 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2650&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]7.6158[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.580345[/C][C]-4.4198[/C][C]0.999978[/C][/ROW]
[ROW][C]2[/C][C]0.237983[/C][C]1.8124[/C][C]0.037549[/C][/ROW]
[ROW][C]3[/C][C]-0.140792[/C][C]-1.0722[/C][C]0.855974[/C][/ROW]
[ROW][C]4[/C][C]0.042291[/C][C]0.3221[/C][C]0.374276[/C][/ROW]
[ROW][C]5[/C][C]0.013183[/C][C]0.1004[/C][C]0.460186[/C][/ROW]
[ROW][C]6[/C][C]-0.063118[/C][C]-0.4807[/C][C]0.683728[/C][/ROW]
[ROW][C]7[/C][C]0.160883[/C][C]1.2252[/C][C]0.112717[/C][/ROW]
[ROW][C]8[/C][C]-0.258448[/C][C]-1.9683[/C][C]0.973089[/C][/ROW]
[ROW][C]9[/C][C]0.23749[/C][C]1.8087[/C][C]0.037843[/C][/ROW]
[ROW][C]10[/C][C]-0.301213[/C][C]-2.294[/C][C]0.987284[/C][/ROW]
[ROW][C]11[/C][C]0.412467[/C][C]3.1413[/C][C]0.001324[/C][/ROW]
[ROW][C]12[/C][C]-0.441263[/C][C]-3.3606[/C][C]0.99931[/C][/ROW]
[ROW][C]13[/C][C]0.180686[/C][C]1.3761[/C][C]0.087046[/C][/ROW]
[ROW][C]14[/C][C]-0.04299[/C][C]-0.3274[/C][C]0.627729[/C][/ROW]
[ROW][C]15[/C][C]0.007444[/C][C]0.0567[/C][C]0.477493[/C][/ROW]
[ROW][C]16[/C][C]0.055343[/C][C]0.4215[/C][C]0.337481[/C][/ROW]
[ROW][C]17[/C][C]0.028408[/C][C]0.2164[/C][C]0.414737[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2650&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2650&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	7.6158	0
1	-0.580345	-4.4198	0.999978
2	0.237983	1.8124	0.037549
3	-0.140792	-1.0722	0.855974
4	0.042291	0.3221	0.374276
5	0.013183	0.1004	0.460186
6	-0.063118	-0.4807	0.683728
7	0.160883	1.2252	0.112717
8	-0.258448	-1.9683	0.973089
9	0.23749	1.8087	0.037843
10	-0.301213	-2.294	0.987284
11	0.412467	3.1413	0.001324
12	-0.441263	-3.3606	0.99931
13	0.180686	1.3761	0.087046
14	-0.04299	-0.3274	0.627729
15	0.007444	0.0567	0.477493
16	0.055343	0.4215	0.337481
17	0.028408	0.2164	0.414737

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.580345	-4.4198	0.999978
1	-0.149	-1.1348	0.869426
2	-0.105745	-0.8053	0.78804
3	-0.098153	-0.7475	0.771113
4	-0.011501	-0.0876	0.534747
5	-0.07846	-0.5975	0.72376
6	0.128156	0.976	0.166558
7	-0.144896	-1.1035	0.862815
8	0.004018	0.0306	0.487847
9	-0.233664	-1.7795	0.959804
10	0.21204	1.6148	0.055885
11	-0.20826	-1.5861	0.940918
12	-0.254137	-1.9354	0.971092
13	-0.129308	-0.9848	0.835589
14	-0.027372	-0.2085	0.5822
15	-0.048761	-0.3714	0.644136
16	0.186921	1.4235	0.079967
17	-0.035743	-0.2722	0.606785

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.580345 & -4.4198 & 0.999978 \tabularnewline
1 & -0.149 & -1.1348 & 0.869426 \tabularnewline
2 & -0.105745 & -0.8053 & 0.78804 \tabularnewline
3 & -0.098153 & -0.7475 & 0.771113 \tabularnewline
4 & -0.011501 & -0.0876 & 0.534747 \tabularnewline
5 & -0.07846 & -0.5975 & 0.72376 \tabularnewline
6 & 0.128156 & 0.976 & 0.166558 \tabularnewline
7 & -0.144896 & -1.1035 & 0.862815 \tabularnewline
8 & 0.004018 & 0.0306 & 0.487847 \tabularnewline
9 & -0.233664 & -1.7795 & 0.959804 \tabularnewline
10 & 0.21204 & 1.6148 & 0.055885 \tabularnewline
11 & -0.20826 & -1.5861 & 0.940918 \tabularnewline
12 & -0.254137 & -1.9354 & 0.971092 \tabularnewline
13 & -0.129308 & -0.9848 & 0.835589 \tabularnewline
14 & -0.027372 & -0.2085 & 0.5822 \tabularnewline
15 & -0.048761 & -0.3714 & 0.644136 \tabularnewline
16 & 0.186921 & 1.4235 & 0.079967 \tabularnewline
17 & -0.035743 & -0.2722 & 0.606785 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2650&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]-0.580345[/C][C]-4.4198[/C][C]0.999978[/C][/ROW]
[ROW][C]1[/C][C]-0.149[/C][C]-1.1348[/C][C]0.869426[/C][/ROW]
[ROW][C]2[/C][C]-0.105745[/C][C]-0.8053[/C][C]0.78804[/C][/ROW]
[ROW][C]3[/C][C]-0.098153[/C][C]-0.7475[/C][C]0.771113[/C][/ROW]
[ROW][C]4[/C][C]-0.011501[/C][C]-0.0876[/C][C]0.534747[/C][/ROW]
[ROW][C]5[/C][C]-0.07846[/C][C]-0.5975[/C][C]0.72376[/C][/ROW]
[ROW][C]6[/C][C]0.128156[/C][C]0.976[/C][C]0.166558[/C][/ROW]
[ROW][C]7[/C][C]-0.144896[/C][C]-1.1035[/C][C]0.862815[/C][/ROW]
[ROW][C]8[/C][C]0.004018[/C][C]0.0306[/C][C]0.487847[/C][/ROW]
[ROW][C]9[/C][C]-0.233664[/C][C]-1.7795[/C][C]0.959804[/C][/ROW]
[ROW][C]10[/C][C]0.21204[/C][C]1.6148[/C][C]0.055885[/C][/ROW]
[ROW][C]11[/C][C]-0.20826[/C][C]-1.5861[/C][C]0.940918[/C][/ROW]
[ROW][C]12[/C][C]-0.254137[/C][C]-1.9354[/C][C]0.971092[/C][/ROW]
[ROW][C]13[/C][C]-0.129308[/C][C]-0.9848[/C][C]0.835589[/C][/ROW]
[ROW][C]14[/C][C]-0.027372[/C][C]-0.2085[/C][C]0.5822[/C][/ROW]
[ROW][C]15[/C][C]-0.048761[/C][C]-0.3714[/C][C]0.644136[/C][/ROW]
[ROW][C]16[/C][C]0.186921[/C][C]1.4235[/C][C]0.079967[/C][/ROW]
[ROW][C]17[/C][C]-0.035743[/C][C]-0.2722[/C][C]0.606785[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2650&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2650&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	-0.580345	-4.4198	0.999978
1	-0.149	-1.1348	0.869426
2	-0.105745	-0.8053	0.78804
3	-0.098153	-0.7475	0.771113
4	-0.011501	-0.0876	0.534747
5	-0.07846	-0.5975	0.72376
6	0.128156	0.976	0.166558
7	-0.144896	-1.1035	0.862815
8	0.004018	0.0306	0.487847
9	-0.233664	-1.7795	0.959804
10	0.21204	1.6148	0.055885
11	-0.20826	-1.5861	0.940918
12	-0.254137	-1.9354	0.971092
13	-0.129308	-0.9848	0.835589
14	-0.027372	-0.2085	0.5822
15	-0.048761	-0.3714	0.644136
16	0.186921	1.4235	0.079967
17	-0.035743	-0.2722	0.606785

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 2 ; par3 = 1 ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; 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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code