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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 04 Dec 2009 08:15:19 -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/2009/Dec/04/t1259939756b13zt5jju1pvifl.htm/, Retrieved Wed, 05 Nov 2025 15:54:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63738, Retrieved Wed, 05 Nov 2025 15:54:41 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

402

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       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:19:56] [b98453cac15ba1066b407e146608df68]
-    D        [(Partial) Autocorrelation Function] [] [2009-11-23 15:21:31] [5d885a68c2332cc44f6191ec94766bfa]
- R PD            [(Partial) Autocorrelation Function] [AutoCF d=0,D=1] [2009-12-04 15:15:19] [18c0746232b29e9668aa6bedcb8dd698] [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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63738&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]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=63738&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63738&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.882393	6.1134	0
2	0.692114	4.7951	8e-06
3	0.441398	3.0581	0.001818
4	0.28379	1.9662	0.027539
5	0.180747	1.2523	0.108273
6	0.131267	0.9094	0.18383
7	0.06502	0.4505	0.3272
8	-0.029151	-0.202	0.420398
9	-0.163522	-1.1329	0.131439
10	-0.319137	-2.211	0.015915
11	-0.445069	-3.0835	0.001693
12	-0.51712	-3.5827	0.000396
13	-0.485822	-3.3659	0.000754
14	-0.393309	-2.7249	0.004474
15	-0.260426	-1.8043	0.038732
16	-0.14468	-1.0024	0.160595
17	-0.044025	-0.305	0.380837

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.882393 & 6.1134 & 0 \tabularnewline
2 & 0.692114 & 4.7951 & 8e-06 \tabularnewline
3 & 0.441398 & 3.0581 & 0.001818 \tabularnewline
4 & 0.28379 & 1.9662 & 0.027539 \tabularnewline
5 & 0.180747 & 1.2523 & 0.108273 \tabularnewline
6 & 0.131267 & 0.9094 & 0.18383 \tabularnewline
7 & 0.06502 & 0.4505 & 0.3272 \tabularnewline
8 & -0.029151 & -0.202 & 0.420398 \tabularnewline
9 & -0.163522 & -1.1329 & 0.131439 \tabularnewline
10 & -0.319137 & -2.211 & 0.015915 \tabularnewline
11 & -0.445069 & -3.0835 & 0.001693 \tabularnewline
12 & -0.51712 & -3.5827 & 0.000396 \tabularnewline
13 & -0.485822 & -3.3659 & 0.000754 \tabularnewline
14 & -0.393309 & -2.7249 & 0.004474 \tabularnewline
15 & -0.260426 & -1.8043 & 0.038732 \tabularnewline
16 & -0.14468 & -1.0024 & 0.160595 \tabularnewline
17 & -0.044025 & -0.305 & 0.380837 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63738&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]0.882393[/C][C]6.1134[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.692114[/C][C]4.7951[/C][C]8e-06[/C][/ROW]
[ROW][C]3[/C][C]0.441398[/C][C]3.0581[/C][C]0.001818[/C][/ROW]
[ROW][C]4[/C][C]0.28379[/C][C]1.9662[/C][C]0.027539[/C][/ROW]
[ROW][C]5[/C][C]0.180747[/C][C]1.2523[/C][C]0.108273[/C][/ROW]
[ROW][C]6[/C][C]0.131267[/C][C]0.9094[/C][C]0.18383[/C][/ROW]
[ROW][C]7[/C][C]0.06502[/C][C]0.4505[/C][C]0.3272[/C][/ROW]
[ROW][C]8[/C][C]-0.029151[/C][C]-0.202[/C][C]0.420398[/C][/ROW]
[ROW][C]9[/C][C]-0.163522[/C][C]-1.1329[/C][C]0.131439[/C][/ROW]
[ROW][C]10[/C][C]-0.319137[/C][C]-2.211[/C][C]0.015915[/C][/ROW]
[ROW][C]11[/C][C]-0.445069[/C][C]-3.0835[/C][C]0.001693[/C][/ROW]
[ROW][C]12[/C][C]-0.51712[/C][C]-3.5827[/C][C]0.000396[/C][/ROW]
[ROW][C]13[/C][C]-0.485822[/C][C]-3.3659[/C][C]0.000754[/C][/ROW]
[ROW][C]14[/C][C]-0.393309[/C][C]-2.7249[/C][C]0.004474[/C][/ROW]
[ROW][C]15[/C][C]-0.260426[/C][C]-1.8043[/C][C]0.038732[/C][/ROW]
[ROW][C]16[/C][C]-0.14468[/C][C]-1.0024[/C][C]0.160595[/C][/ROW]
[ROW][C]17[/C][C]-0.044025[/C][C]-0.305[/C][C]0.380837[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63738&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63738&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	0.882393	6.1134	0
2	0.692114	4.7951	8e-06
3	0.441398	3.0581	0.001818
4	0.28379	1.9662	0.027539
5	0.180747	1.2523	0.108273
6	0.131267	0.9094	0.18383
7	0.06502	0.4505	0.3272
8	-0.029151	-0.202	0.420398
9	-0.163522	-1.1329	0.131439
10	-0.319137	-2.211	0.015915
11	-0.445069	-3.0835	0.001693
12	-0.51712	-3.5827	0.000396
13	-0.485822	-3.3659	0.000754
14	-0.393309	-2.7249	0.004474
15	-0.260426	-1.8043	0.038732
16	-0.14468	-1.0024	0.160595
17	-0.044025	-0.305	0.380837

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.882393	6.1134	0
2	-0.390739	-2.7071	0.004686
3	-0.336725	-2.3329	0.011946
4	0.491565	3.4057	0.000671
5	-0.080464	-0.5575	0.289898
6	-0.323928	-2.2442	0.014732
7	-0.011186	-0.0775	0.469274
8	-0.069624	-0.4824	0.315868
9	-0.255056	-1.7671	0.041786
10	-0.249474	-1.7284	0.045172
11	0.152203	1.0545	0.148469
12	0.019674	0.1363	0.446074
13	0.09166	0.635	0.264209
14	0.064937	0.4499	0.327405
15	0.002372	0.0164	0.493478
16	0.159608	1.1058	0.137162
17	0.155488	1.0773	0.143376

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.882393 & 6.1134 & 0 \tabularnewline
2 & -0.390739 & -2.7071 & 0.004686 \tabularnewline
3 & -0.336725 & -2.3329 & 0.011946 \tabularnewline
4 & 0.491565 & 3.4057 & 0.000671 \tabularnewline
5 & -0.080464 & -0.5575 & 0.289898 \tabularnewline
6 & -0.323928 & -2.2442 & 0.014732 \tabularnewline
7 & -0.011186 & -0.0775 & 0.469274 \tabularnewline
8 & -0.069624 & -0.4824 & 0.315868 \tabularnewline
9 & -0.255056 & -1.7671 & 0.041786 \tabularnewline
10 & -0.249474 & -1.7284 & 0.045172 \tabularnewline
11 & 0.152203 & 1.0545 & 0.148469 \tabularnewline
12 & 0.019674 & 0.1363 & 0.446074 \tabularnewline
13 & 0.09166 & 0.635 & 0.264209 \tabularnewline
14 & 0.064937 & 0.4499 & 0.327405 \tabularnewline
15 & 0.002372 & 0.0164 & 0.493478 \tabularnewline
16 & 0.159608 & 1.1058 & 0.137162 \tabularnewline
17 & 0.155488 & 1.0773 & 0.143376 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63738&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]0.882393[/C][C]6.1134[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.390739[/C][C]-2.7071[/C][C]0.004686[/C][/ROW]
[ROW][C]3[/C][C]-0.336725[/C][C]-2.3329[/C][C]0.011946[/C][/ROW]
[ROW][C]4[/C][C]0.491565[/C][C]3.4057[/C][C]0.000671[/C][/ROW]
[ROW][C]5[/C][C]-0.080464[/C][C]-0.5575[/C][C]0.289898[/C][/ROW]
[ROW][C]6[/C][C]-0.323928[/C][C]-2.2442[/C][C]0.014732[/C][/ROW]
[ROW][C]7[/C][C]-0.011186[/C][C]-0.0775[/C][C]0.469274[/C][/ROW]
[ROW][C]8[/C][C]-0.069624[/C][C]-0.4824[/C][C]0.315868[/C][/ROW]
[ROW][C]9[/C][C]-0.255056[/C][C]-1.7671[/C][C]0.041786[/C][/ROW]
[ROW][C]10[/C][C]-0.249474[/C][C]-1.7284[/C][C]0.045172[/C][/ROW]
[ROW][C]11[/C][C]0.152203[/C][C]1.0545[/C][C]0.148469[/C][/ROW]
[ROW][C]12[/C][C]0.019674[/C][C]0.1363[/C][C]0.446074[/C][/ROW]
[ROW][C]13[/C][C]0.09166[/C][C]0.635[/C][C]0.264209[/C][/ROW]
[ROW][C]14[/C][C]0.064937[/C][C]0.4499[/C][C]0.327405[/C][/ROW]
[ROW][C]15[/C][C]0.002372[/C][C]0.0164[/C][C]0.493478[/C][/ROW]
[ROW][C]16[/C][C]0.159608[/C][C]1.1058[/C][C]0.137162[/C][/ROW]
[ROW][C]17[/C][C]0.155488[/C][C]1.0773[/C][C]0.143376[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63738&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63738&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	0.882393	6.1134	0
2	-0.390739	-2.7071	0.004686
3	-0.336725	-2.3329	0.011946
4	0.491565	3.4057	0.000671
5	-0.080464	-0.5575	0.289898
6	-0.323928	-2.2442	0.014732
7	-0.011186	-0.0775	0.469274
8	-0.069624	-0.4824	0.315868
9	-0.255056	-1.7671	0.041786
10	-0.249474	-1.7284	0.045172
11	0.152203	1.0545	0.148469
12	0.019674	0.1363	0.446074
13	0.09166	0.635	0.264209
14	0.064937	0.4499	0.327405
15	0.002372	0.0164	0.493478
16	0.159608	1.1058	0.137162
17	0.155488	1.0773	0.143376

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 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

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