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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

Tue, 27 Nov 2007 14:02:27 -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/t11961968574dneg9uzvyiaso5.htm/, Retrieved Wed, 11 Feb 2026 14:30:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6960, Retrieved Wed, 11 Feb 2026 14:30:27 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

groep MENS

Estimated Impact

426

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

-       [(Partial) Autocorrelation Function] [Transport_Q2] [2007-11-27 21:02:27] [68ccea1ea79fa519d33f2664ba3973dd] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6960&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]2 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=6960&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6960&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.544	0
1	0.807824	6.9021	0
2	0.688723	5.8844	0
3	0.585382	5.0015	2e-06
4	0.531517	4.5413	1.1e-05
5	0.489393	4.1814	4e-05
6	0.446243	3.8127	0.000142
7	0.357638	3.0557	0.001568
8	0.258699	2.2103	0.015109
9	0.153802	1.3141	0.096466
10	0.133913	1.1442	0.128149
11	0.15729	1.3439	0.091574
12	0.159478	1.3626	0.088601
13	0.093685	0.8004	0.213025
14	-0.052178	-0.4458	0.671473
15	-0.126892	-1.0842	0.85907
16	-0.170188	-1.4541	0.924896
17	-0.140312	-1.1988	0.882764

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.544 & 0 \tabularnewline
1 & 0.807824 & 6.9021 & 0 \tabularnewline
2 & 0.688723 & 5.8844 & 0 \tabularnewline
3 & 0.585382 & 5.0015 & 2e-06 \tabularnewline
4 & 0.531517 & 4.5413 & 1.1e-05 \tabularnewline
5 & 0.489393 & 4.1814 & 4e-05 \tabularnewline
6 & 0.446243 & 3.8127 & 0.000142 \tabularnewline
7 & 0.357638 & 3.0557 & 0.001568 \tabularnewline
8 & 0.258699 & 2.2103 & 0.015109 \tabularnewline
9 & 0.153802 & 1.3141 & 0.096466 \tabularnewline
10 & 0.133913 & 1.1442 & 0.128149 \tabularnewline
11 & 0.15729 & 1.3439 & 0.091574 \tabularnewline
12 & 0.159478 & 1.3626 & 0.088601 \tabularnewline
13 & 0.093685 & 0.8004 & 0.213025 \tabularnewline
14 & -0.052178 & -0.4458 & 0.671473 \tabularnewline
15 & -0.126892 & -1.0842 & 0.85907 \tabularnewline
16 & -0.170188 & -1.4541 & 0.924896 \tabularnewline
17 & -0.140312 & -1.1988 & 0.882764 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6960&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]8.544[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.807824[/C][C]6.9021[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.688723[/C][C]5.8844[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.585382[/C][C]5.0015[/C][C]2e-06[/C][/ROW]
[ROW][C]4[/C][C]0.531517[/C][C]4.5413[/C][C]1.1e-05[/C][/ROW]
[ROW][C]5[/C][C]0.489393[/C][C]4.1814[/C][C]4e-05[/C][/ROW]
[ROW][C]6[/C][C]0.446243[/C][C]3.8127[/C][C]0.000142[/C][/ROW]
[ROW][C]7[/C][C]0.357638[/C][C]3.0557[/C][C]0.001568[/C][/ROW]
[ROW][C]8[/C][C]0.258699[/C][C]2.2103[/C][C]0.015109[/C][/ROW]
[ROW][C]9[/C][C]0.153802[/C][C]1.3141[/C][C]0.096466[/C][/ROW]
[ROW][C]10[/C][C]0.133913[/C][C]1.1442[/C][C]0.128149[/C][/ROW]
[ROW][C]11[/C][C]0.15729[/C][C]1.3439[/C][C]0.091574[/C][/ROW]
[ROW][C]12[/C][C]0.159478[/C][C]1.3626[/C][C]0.088601[/C][/ROW]
[ROW][C]13[/C][C]0.093685[/C][C]0.8004[/C][C]0.213025[/C][/ROW]
[ROW][C]14[/C][C]-0.052178[/C][C]-0.4458[/C][C]0.671473[/C][/ROW]
[ROW][C]15[/C][C]-0.126892[/C][C]-1.0842[/C][C]0.85907[/C][/ROW]
[ROW][C]16[/C][C]-0.170188[/C][C]-1.4541[/C][C]0.924896[/C][/ROW]
[ROW][C]17[/C][C]-0.140312[/C][C]-1.1988[/C][C]0.882764[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6960&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6960&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	8.544	0
1	0.807824	6.9021	0
2	0.688723	5.8844	0
3	0.585382	5.0015	2e-06
4	0.531517	4.5413	1.1e-05
5	0.489393	4.1814	4e-05
6	0.446243	3.8127	0.000142
7	0.357638	3.0557	0.001568
8	0.258699	2.2103	0.015109
9	0.153802	1.3141	0.096466
10	0.133913	1.1442	0.128149
11	0.15729	1.3439	0.091574
12	0.159478	1.3626	0.088601
13	0.093685	0.8004	0.213025
14	-0.052178	-0.4458	0.671473
15	-0.126892	-1.0842	0.85907
16	-0.170188	-1.4541	0.924896
17	-0.140312	-1.1988	0.882764

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.807824	6.9021	0
1	0.104031	0.8888	0.188504
2	0.008311	0.071	0.471792
3	0.099267	0.8481	0.199566
4	0.051184	0.4373	0.331586
5	0.006534	0.0558	0.477817
6	-0.130569	-1.1156	0.865869
7	-0.113798	-0.9723	0.832943
8	-0.118382	-1.0115	0.84243
9	0.122804	1.0492	0.148764
10	0.154063	1.3163	0.096093
11	0.011487	0.0981	0.461044
12	-0.152986	-1.3071	0.902362
13	-0.325402	-2.7802	0.996547
14	-0.0118	-0.1008	0.540014
15	-0.003684	-0.0315	0.512511
16	0.149291	1.2755	0.103081
17	0.050395	0.4306	0.334022

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.807824 & 6.9021 & 0 \tabularnewline
1 & 0.104031 & 0.8888 & 0.188504 \tabularnewline
2 & 0.008311 & 0.071 & 0.471792 \tabularnewline
3 & 0.099267 & 0.8481 & 0.199566 \tabularnewline
4 & 0.051184 & 0.4373 & 0.331586 \tabularnewline
5 & 0.006534 & 0.0558 & 0.477817 \tabularnewline
6 & -0.130569 & -1.1156 & 0.865869 \tabularnewline
7 & -0.113798 & -0.9723 & 0.832943 \tabularnewline
8 & -0.118382 & -1.0115 & 0.84243 \tabularnewline
9 & 0.122804 & 1.0492 & 0.148764 \tabularnewline
10 & 0.154063 & 1.3163 & 0.096093 \tabularnewline
11 & 0.011487 & 0.0981 & 0.461044 \tabularnewline
12 & -0.152986 & -1.3071 & 0.902362 \tabularnewline
13 & -0.325402 & -2.7802 & 0.996547 \tabularnewline
14 & -0.0118 & -0.1008 & 0.540014 \tabularnewline
15 & -0.003684 & -0.0315 & 0.512511 \tabularnewline
16 & 0.149291 & 1.2755 & 0.103081 \tabularnewline
17 & 0.050395 & 0.4306 & 0.334022 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6960&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]0.807824[/C][C]6.9021[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.104031[/C][C]0.8888[/C][C]0.188504[/C][/ROW]
[ROW][C]2[/C][C]0.008311[/C][C]0.071[/C][C]0.471792[/C][/ROW]
[ROW][C]3[/C][C]0.099267[/C][C]0.8481[/C][C]0.199566[/C][/ROW]
[ROW][C]4[/C][C]0.051184[/C][C]0.4373[/C][C]0.331586[/C][/ROW]
[ROW][C]5[/C][C]0.006534[/C][C]0.0558[/C][C]0.477817[/C][/ROW]
[ROW][C]6[/C][C]-0.130569[/C][C]-1.1156[/C][C]0.865869[/C][/ROW]
[ROW][C]7[/C][C]-0.113798[/C][C]-0.9723[/C][C]0.832943[/C][/ROW]
[ROW][C]8[/C][C]-0.118382[/C][C]-1.0115[/C][C]0.84243[/C][/ROW]
[ROW][C]9[/C][C]0.122804[/C][C]1.0492[/C][C]0.148764[/C][/ROW]
[ROW][C]10[/C][C]0.154063[/C][C]1.3163[/C][C]0.096093[/C][/ROW]
[ROW][C]11[/C][C]0.011487[/C][C]0.0981[/C][C]0.461044[/C][/ROW]
[ROW][C]12[/C][C]-0.152986[/C][C]-1.3071[/C][C]0.902362[/C][/ROW]
[ROW][C]13[/C][C]-0.325402[/C][C]-2.7802[/C][C]0.996547[/C][/ROW]
[ROW][C]14[/C][C]-0.0118[/C][C]-0.1008[/C][C]0.540014[/C][/ROW]
[ROW][C]15[/C][C]-0.003684[/C][C]-0.0315[/C][C]0.512511[/C][/ROW]
[ROW][C]16[/C][C]0.149291[/C][C]1.2755[/C][C]0.103081[/C][/ROW]
[ROW][C]17[/C][C]0.050395[/C][C]0.4306[/C][C]0.334022[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6960&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6960&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	0.807824	6.9021	0
1	0.104031	0.8888	0.188504
2	0.008311	0.071	0.471792
3	0.099267	0.8481	0.199566
4	0.051184	0.4373	0.331586
5	0.006534	0.0558	0.477817
6	-0.130569	-1.1156	0.865869
7	-0.113798	-0.9723	0.832943
8	-0.118382	-1.0115	0.84243
9	0.122804	1.0492	0.148764
10	0.154063	1.3163	0.096093
11	0.011487	0.0981	0.461044
12	-0.152986	-1.3071	0.902362
13	-0.325402	-2.7802	0.996547
14	-0.0118	-0.1008	0.540014
15	-0.003684	-0.0315	0.512511
16	0.149291	1.2755	0.103081
17	0.050395	0.4306	0.334022

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 ;

Parameters (R input):

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

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code