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Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 04 Dec 2012 10:54:33 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/04/t13546364992qvo1fpjcxk1tee.htm/, Retrieved Tue, 10 Feb 2026 13:10:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=196322, Retrieved Tue, 10 Feb 2026 13:10:27 +0000

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User-defined keywords

Estimated Impact

271

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [(Partial) Autocorrelation Function] [Births] [2010-11-29 09:36:27] [b98453cac15ba1066b407e146608df68]
- R PD          [(Partial) Autocorrelation Function] [ws9 3.1 ACF d=0, D=1] [2010-12-07 10:32:56] [afe9379cca749d06b3d6872e02cc47ed]
- RM                [(Partial) Autocorrelation Function] [] [2012-12-04 15:54:33] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational 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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196322&T=0

[TABLE]
[ROW][C]Summary of computational 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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196322&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196322&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 computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.363506	3.3316	0.000643
2	0.044052	0.4037	0.343714
3	-0.12229	-1.1208	0.132782
4	-0.177569	-1.6275	0.053693
5	-0.190564	-1.7465	0.042186
6	-0.073214	-0.671	0.252026
7	0.064547	0.5916	0.277861
8	0.032768	0.3003	0.382338
9	0.099473	0.9117	0.182273
10	-0.087425	-0.8013	0.212619
11	-0.369297	-3.3847	0.000543
12	-0.474287	-4.3469	1.9e-05
13	-0.11077	-1.0152	0.156457
14	0.178515	1.6361	0.052778
15	0.239992	2.1996	0.015293
16	0.323715	2.9669	0.001958
17	0.216099	1.9806	0.025456
18	0.068825	0.6308	0.264944
19	-0.022489	-0.2061	0.418599

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.363506 & 3.3316 & 0.000643 \tabularnewline
2 & 0.044052 & 0.4037 & 0.343714 \tabularnewline
3 & -0.12229 & -1.1208 & 0.132782 \tabularnewline
4 & -0.177569 & -1.6275 & 0.053693 \tabularnewline
5 & -0.190564 & -1.7465 & 0.042186 \tabularnewline
6 & -0.073214 & -0.671 & 0.252026 \tabularnewline
7 & 0.064547 & 0.5916 & 0.277861 \tabularnewline
8 & 0.032768 & 0.3003 & 0.382338 \tabularnewline
9 & 0.099473 & 0.9117 & 0.182273 \tabularnewline
10 & -0.087425 & -0.8013 & 0.212619 \tabularnewline
11 & -0.369297 & -3.3847 & 0.000543 \tabularnewline
12 & -0.474287 & -4.3469 & 1.9e-05 \tabularnewline
13 & -0.11077 & -1.0152 & 0.156457 \tabularnewline
14 & 0.178515 & 1.6361 & 0.052778 \tabularnewline
15 & 0.239992 & 2.1996 & 0.015293 \tabularnewline
16 & 0.323715 & 2.9669 & 0.001958 \tabularnewline
17 & 0.216099 & 1.9806 & 0.025456 \tabularnewline
18 & 0.068825 & 0.6308 & 0.264944 \tabularnewline
19 & -0.022489 & -0.2061 & 0.418599 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196322&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]1[/C][C]0.363506[/C][C]3.3316[/C][C]0.000643[/C][/ROW]
[ROW][C]2[/C][C]0.044052[/C][C]0.4037[/C][C]0.343714[/C][/ROW]
[ROW][C]3[/C][C]-0.12229[/C][C]-1.1208[/C][C]0.132782[/C][/ROW]
[ROW][C]4[/C][C]-0.177569[/C][C]-1.6275[/C][C]0.053693[/C][/ROW]
[ROW][C]5[/C][C]-0.190564[/C][C]-1.7465[/C][C]0.042186[/C][/ROW]
[ROW][C]6[/C][C]-0.073214[/C][C]-0.671[/C][C]0.252026[/C][/ROW]
[ROW][C]7[/C][C]0.064547[/C][C]0.5916[/C][C]0.277861[/C][/ROW]
[ROW][C]8[/C][C]0.032768[/C][C]0.3003[/C][C]0.382338[/C][/ROW]
[ROW][C]9[/C][C]0.099473[/C][C]0.9117[/C][C]0.182273[/C][/ROW]
[ROW][C]10[/C][C]-0.087425[/C][C]-0.8013[/C][C]0.212619[/C][/ROW]
[ROW][C]11[/C][C]-0.369297[/C][C]-3.3847[/C][C]0.000543[/C][/ROW]
[ROW][C]12[/C][C]-0.474287[/C][C]-4.3469[/C][C]1.9e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.11077[/C][C]-1.0152[/C][C]0.156457[/C][/ROW]
[ROW][C]14[/C][C]0.178515[/C][C]1.6361[/C][C]0.052778[/C][/ROW]
[ROW][C]15[/C][C]0.239992[/C][C]2.1996[/C][C]0.015293[/C][/ROW]
[ROW][C]16[/C][C]0.323715[/C][C]2.9669[/C][C]0.001958[/C][/ROW]
[ROW][C]17[/C][C]0.216099[/C][C]1.9806[/C][C]0.025456[/C][/ROW]
[ROW][C]18[/C][C]0.068825[/C][C]0.6308[/C][C]0.264944[/C][/ROW]
[ROW][C]19[/C][C]-0.022489[/C][C]-0.2061[/C][C]0.418599[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196322&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196322&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
1	0.363506	3.3316	0.000643
2	0.044052	0.4037	0.343714
3	-0.12229	-1.1208	0.132782
4	-0.177569	-1.6275	0.053693
5	-0.190564	-1.7465	0.042186
6	-0.073214	-0.671	0.252026
7	0.064547	0.5916	0.277861
8	0.032768	0.3003	0.382338
9	0.099473	0.9117	0.182273
10	-0.087425	-0.8013	0.212619
11	-0.369297	-3.3847	0.000543
12	-0.474287	-4.3469	1.9e-05
13	-0.11077	-1.0152	0.156457
14	0.178515	1.6361	0.052778
15	0.239992	2.1996	0.015293
16	0.323715	2.9669	0.001958
17	0.216099	1.9806	0.025456
18	0.068825	0.6308	0.264944
19	-0.022489	-0.2061	0.418599

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.363506	3.3316	0.000643
2	-0.101496	-0.9302	0.17746
3	-0.119957	-1.0994	0.137362
4	-0.099382	-0.9108	0.182491
5	-0.10883	-0.9974	0.160707
6	0.019107	0.1751	0.430703
7	0.06602	0.6051	0.273377
8	-0.069639	-0.6383	0.262523
9	0.089479	0.8201	0.207242
10	-0.194135	-1.7793	0.039406
11	-0.343827	-3.1512	0.001127
12	-0.302028	-2.7681	0.003467
13	0.142629	1.3072	0.097353
14	0.190639	1.7472	0.042126
15	0.03443	0.3156	0.376561
16	0.107507	0.9853	0.163649
17	0.005908	0.0541	0.478473
18	0.004739	0.0434	0.482728
19	0.072409	0.6636	0.25437

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.363506 & 3.3316 & 0.000643 \tabularnewline
2 & -0.101496 & -0.9302 & 0.17746 \tabularnewline
3 & -0.119957 & -1.0994 & 0.137362 \tabularnewline
4 & -0.099382 & -0.9108 & 0.182491 \tabularnewline
5 & -0.10883 & -0.9974 & 0.160707 \tabularnewline
6 & 0.019107 & 0.1751 & 0.430703 \tabularnewline
7 & 0.06602 & 0.6051 & 0.273377 \tabularnewline
8 & -0.069639 & -0.6383 & 0.262523 \tabularnewline
9 & 0.089479 & 0.8201 & 0.207242 \tabularnewline
10 & -0.194135 & -1.7793 & 0.039406 \tabularnewline
11 & -0.343827 & -3.1512 & 0.001127 \tabularnewline
12 & -0.302028 & -2.7681 & 0.003467 \tabularnewline
13 & 0.142629 & 1.3072 & 0.097353 \tabularnewline
14 & 0.190639 & 1.7472 & 0.042126 \tabularnewline
15 & 0.03443 & 0.3156 & 0.376561 \tabularnewline
16 & 0.107507 & 0.9853 & 0.163649 \tabularnewline
17 & 0.005908 & 0.0541 & 0.478473 \tabularnewline
18 & 0.004739 & 0.0434 & 0.482728 \tabularnewline
19 & 0.072409 & 0.6636 & 0.25437 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196322&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]1[/C][C]0.363506[/C][C]3.3316[/C][C]0.000643[/C][/ROW]
[ROW][C]2[/C][C]-0.101496[/C][C]-0.9302[/C][C]0.17746[/C][/ROW]
[ROW][C]3[/C][C]-0.119957[/C][C]-1.0994[/C][C]0.137362[/C][/ROW]
[ROW][C]4[/C][C]-0.099382[/C][C]-0.9108[/C][C]0.182491[/C][/ROW]
[ROW][C]5[/C][C]-0.10883[/C][C]-0.9974[/C][C]0.160707[/C][/ROW]
[ROW][C]6[/C][C]0.019107[/C][C]0.1751[/C][C]0.430703[/C][/ROW]
[ROW][C]7[/C][C]0.06602[/C][C]0.6051[/C][C]0.273377[/C][/ROW]
[ROW][C]8[/C][C]-0.069639[/C][C]-0.6383[/C][C]0.262523[/C][/ROW]
[ROW][C]9[/C][C]0.089479[/C][C]0.8201[/C][C]0.207242[/C][/ROW]
[ROW][C]10[/C][C]-0.194135[/C][C]-1.7793[/C][C]0.039406[/C][/ROW]
[ROW][C]11[/C][C]-0.343827[/C][C]-3.1512[/C][C]0.001127[/C][/ROW]
[ROW][C]12[/C][C]-0.302028[/C][C]-2.7681[/C][C]0.003467[/C][/ROW]
[ROW][C]13[/C][C]0.142629[/C][C]1.3072[/C][C]0.097353[/C][/ROW]
[ROW][C]14[/C][C]0.190639[/C][C]1.7472[/C][C]0.042126[/C][/ROW]
[ROW][C]15[/C][C]0.03443[/C][C]0.3156[/C][C]0.376561[/C][/ROW]
[ROW][C]16[/C][C]0.107507[/C][C]0.9853[/C][C]0.163649[/C][/ROW]
[ROW][C]17[/C][C]0.005908[/C][C]0.0541[/C][C]0.478473[/C][/ROW]
[ROW][C]18[/C][C]0.004739[/C][C]0.0434[/C][C]0.482728[/C][/ROW]
[ROW][C]19[/C][C]0.072409[/C][C]0.6636[/C][C]0.25437[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196322&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196322&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
1	0.363506	3.3316	0.000643
2	-0.101496	-0.9302	0.17746
3	-0.119957	-1.0994	0.137362
4	-0.099382	-0.9108	0.182491
5	-0.10883	-0.9974	0.160707
6	0.019107	0.1751	0.430703
7	0.06602	0.6051	0.273377
8	-0.069639	-0.6383	0.262523
9	0.089479	0.8201	0.207242
10	-0.194135	-1.7793	0.039406
11	-0.343827	-3.1512	0.001127
12	-0.302028	-2.7681	0.003467
13	0.142629	1.3072	0.097353
14	0.190639	1.7472	0.042126
15	0.03443	0.3156	0.376561
16	0.107507	0.9853	0.163649
17	0.005908	0.0541	0.478473
18	0.004739	0.0434	0.482728
19	0.072409	0.6636	0.25437

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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 2:(par1+1)) {
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(abs(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,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(abs(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