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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

Wed, 05 Dec 2007 09:52:01 -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/05/t1196872784hgcunp3qqocsnfp.htm/, Retrieved Mon, 18 May 2026 04:32:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2490, Retrieved Mon, 18 May 2026 04:32:01 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

519

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

-       [(Partial) Autocorrelation Function] [Opdracht 5 Estima...] [2007-12-05 16:52:01] [cb172450b25aceeff04d58e88e905157] [Current]

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Dataseries X:

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Histogram

Boxplots

3,35
3,34
3,39
3,36
3,36
3,49
3,34
3,34
3,42
3,34
3,38
3,44
2,86
2,82
2,66
2,64
2,65
2,38
2,11
2,14
2,1
2,08
2,09
2,32
2,06
2,06
2,06
2,06
2,05
2,13
2,08
2,06
2,09
2,09
2,1
2,21
2,09
2,07
2,12
2,09
2,1
2,17
2,11
2,09
2,15
2,09
2,06
2,42
2,34
2,4
2,62
2,65
2,62
2,89
2,8
3,04
3,1
3,38
3,34
3,69

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2490&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2490&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2490&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.6811	0
1	-0.095461	-0.7333	0.766845
2	0.187205	1.4379	0.077866
3	0.254389	1.954	0.027723
4	0.10533	0.8091	0.210867
5	-0.002483	-0.0191	0.507576
6	0.460825	3.5397	0.000394
7	-0.060315	-0.4633	0.677569
8	0.069881	0.5368	0.296725
9	0.104193	0.8003	0.213368
10	0.04664	0.3582	0.360719
11	-0.167227	-1.2845	0.898005
12	0.320897	2.4649	0.008319
13	-0.060135	-0.4619	0.677077
14	-0.064049	-0.492	0.687717
15	0.078252	0.6011	0.27505
16	-0.024679	-0.1896	0.57485

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & -0.095461 & -0.7333 & 0.766845 \tabularnewline
2 & 0.187205 & 1.4379 & 0.077866 \tabularnewline
3 & 0.254389 & 1.954 & 0.027723 \tabularnewline
4 & 0.10533 & 0.8091 & 0.210867 \tabularnewline
5 & -0.002483 & -0.0191 & 0.507576 \tabularnewline
6 & 0.460825 & 3.5397 & 0.000394 \tabularnewline
7 & -0.060315 & -0.4633 & 0.677569 \tabularnewline
8 & 0.069881 & 0.5368 & 0.296725 \tabularnewline
9 & 0.104193 & 0.8003 & 0.213368 \tabularnewline
10 & 0.04664 & 0.3582 & 0.360719 \tabularnewline
11 & -0.167227 & -1.2845 & 0.898005 \tabularnewline
12 & 0.320897 & 2.4649 & 0.008319 \tabularnewline
13 & -0.060135 & -0.4619 & 0.677077 \tabularnewline
14 & -0.064049 & -0.492 & 0.687717 \tabularnewline
15 & 0.078252 & 0.6011 & 0.27505 \tabularnewline
16 & -0.024679 & -0.1896 & 0.57485 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2490&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]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.095461[/C][C]-0.7333[/C][C]0.766845[/C][/ROW]
[ROW][C]2[/C][C]0.187205[/C][C]1.4379[/C][C]0.077866[/C][/ROW]
[ROW][C]3[/C][C]0.254389[/C][C]1.954[/C][C]0.027723[/C][/ROW]
[ROW][C]4[/C][C]0.10533[/C][C]0.8091[/C][C]0.210867[/C][/ROW]
[ROW][C]5[/C][C]-0.002483[/C][C]-0.0191[/C][C]0.507576[/C][/ROW]
[ROW][C]6[/C][C]0.460825[/C][C]3.5397[/C][C]0.000394[/C][/ROW]
[ROW][C]7[/C][C]-0.060315[/C][C]-0.4633[/C][C]0.677569[/C][/ROW]
[ROW][C]8[/C][C]0.069881[/C][C]0.5368[/C][C]0.296725[/C][/ROW]
[ROW][C]9[/C][C]0.104193[/C][C]0.8003[/C][C]0.213368[/C][/ROW]
[ROW][C]10[/C][C]0.04664[/C][C]0.3582[/C][C]0.360719[/C][/ROW]
[ROW][C]11[/C][C]-0.167227[/C][C]-1.2845[/C][C]0.898005[/C][/ROW]
[ROW][C]12[/C][C]0.320897[/C][C]2.4649[/C][C]0.008319[/C][/ROW]
[ROW][C]13[/C][C]-0.060135[/C][C]-0.4619[/C][C]0.677077[/C][/ROW]
[ROW][C]14[/C][C]-0.064049[/C][C]-0.492[/C][C]0.687717[/C][/ROW]
[ROW][C]15[/C][C]0.078252[/C][C]0.6011[/C][C]0.27505[/C][/ROW]
[ROW][C]16[/C][C]-0.024679[/C][C]-0.1896[/C][C]0.57485[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2490&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2490&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	7.6811	0
1	-0.095461	-0.7333	0.766845
2	0.187205	1.4379	0.077866
3	0.254389	1.954	0.027723
4	0.10533	0.8091	0.210867
5	-0.002483	-0.0191	0.507576
6	0.460825	3.5397	0.000394
7	-0.060315	-0.4633	0.677569
8	0.069881	0.5368	0.296725
9	0.104193	0.8003	0.213368
10	0.04664	0.3582	0.360719
11	-0.167227	-1.2845	0.898005
12	0.320897	2.4649	0.008319
13	-0.060135	-0.4619	0.677077
14	-0.064049	-0.492	0.687717
15	0.078252	0.6011	0.27505
16	-0.024679	-0.1896	0.57485

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.095461	-0.7333	0.766845
1	0.17973	1.3805	0.086315
2	0.298479	2.2927	0.012725
3	0.148111	1.1377	0.12993
4	-0.085848	-0.6594	0.743902
5	0.379185	2.9126	0.002527
6	0.006565	0.0504	0.479976
7	-0.105862	-0.8131	0.790296
8	-0.108434	-0.8329	0.795869
9	-0.000161	-0.0012	0.500491
10	-0.204286	-1.5691	0.939019
11	0.124989	0.9601	0.170472
12	0.100638	0.773	0.221299
13	-0.076626	-0.5886	0.720804
14	-0.025907	-0.199	0.578526
15	-0.017443	-0.134	0.553063
16	-0.002346	-0.018	0.507158

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.095461 & -0.7333 & 0.766845 \tabularnewline
1 & 0.17973 & 1.3805 & 0.086315 \tabularnewline
2 & 0.298479 & 2.2927 & 0.012725 \tabularnewline
3 & 0.148111 & 1.1377 & 0.12993 \tabularnewline
4 & -0.085848 & -0.6594 & 0.743902 \tabularnewline
5 & 0.379185 & 2.9126 & 0.002527 \tabularnewline
6 & 0.006565 & 0.0504 & 0.479976 \tabularnewline
7 & -0.105862 & -0.8131 & 0.790296 \tabularnewline
8 & -0.108434 & -0.8329 & 0.795869 \tabularnewline
9 & -0.000161 & -0.0012 & 0.500491 \tabularnewline
10 & -0.204286 & -1.5691 & 0.939019 \tabularnewline
11 & 0.124989 & 0.9601 & 0.170472 \tabularnewline
12 & 0.100638 & 0.773 & 0.221299 \tabularnewline
13 & -0.076626 & -0.5886 & 0.720804 \tabularnewline
14 & -0.025907 & -0.199 & 0.578526 \tabularnewline
15 & -0.017443 & -0.134 & 0.553063 \tabularnewline
16 & -0.002346 & -0.018 & 0.507158 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2490&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]-0.095461[/C][C]-0.7333[/C][C]0.766845[/C][/ROW]
[ROW][C]1[/C][C]0.17973[/C][C]1.3805[/C][C]0.086315[/C][/ROW]
[ROW][C]2[/C][C]0.298479[/C][C]2.2927[/C][C]0.012725[/C][/ROW]
[ROW][C]3[/C][C]0.148111[/C][C]1.1377[/C][C]0.12993[/C][/ROW]
[ROW][C]4[/C][C]-0.085848[/C][C]-0.6594[/C][C]0.743902[/C][/ROW]
[ROW][C]5[/C][C]0.379185[/C][C]2.9126[/C][C]0.002527[/C][/ROW]
[ROW][C]6[/C][C]0.006565[/C][C]0.0504[/C][C]0.479976[/C][/ROW]
[ROW][C]7[/C][C]-0.105862[/C][C]-0.8131[/C][C]0.790296[/C][/ROW]
[ROW][C]8[/C][C]-0.108434[/C][C]-0.8329[/C][C]0.795869[/C][/ROW]
[ROW][C]9[/C][C]-0.000161[/C][C]-0.0012[/C][C]0.500491[/C][/ROW]
[ROW][C]10[/C][C]-0.204286[/C][C]-1.5691[/C][C]0.939019[/C][/ROW]
[ROW][C]11[/C][C]0.124989[/C][C]0.9601[/C][C]0.170472[/C][/ROW]
[ROW][C]12[/C][C]0.100638[/C][C]0.773[/C][C]0.221299[/C][/ROW]
[ROW][C]13[/C][C]-0.076626[/C][C]-0.5886[/C][C]0.720804[/C][/ROW]
[ROW][C]14[/C][C]-0.025907[/C][C]-0.199[/C][C]0.578526[/C][/ROW]
[ROW][C]15[/C][C]-0.017443[/C][C]-0.134[/C][C]0.553063[/C][/ROW]
[ROW][C]16[/C][C]-0.002346[/C][C]-0.018[/C][C]0.507158[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2490&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2490&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	-0.095461	-0.7333	0.766845
1	0.17973	1.3805	0.086315
2	0.298479	2.2927	0.012725
3	0.148111	1.1377	0.12993
4	-0.085848	-0.6594	0.743902
5	0.379185	2.9126	0.002527
6	0.006565	0.0504	0.479976
7	-0.105862	-0.8131	0.790296
8	-0.108434	-0.8329	0.795869
9	-0.000161	-0.0012	0.500491
10	-0.204286	-1.5691	0.939019
11	0.124989	0.9601	0.170472
12	0.100638	0.773	0.221299
13	-0.076626	-0.5886	0.720804
14	-0.025907	-0.199	0.578526
15	-0.017443	-0.134	0.553063
16	-0.002346	-0.018	0.507158

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code