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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 04 Dec 2012 04:41:18 -0500

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/2012/Dec/04/t1354614132cu0ayksqgmbxish.htm/, Retrieved Tue, 10 Feb 2026 02:22:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=196141, Retrieved Tue, 10 Feb 2026 02:22:58 +0000

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User-defined keywords

Estimated Impact

318

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=1, D=1] [2010-12-07 10:36:00] [afe9379cca749d06b3d6872e02cc47ed]
- R P               [(Partial) Autocorrelation Function] [Workshop 9: Stati...] [2012-12-04 09:41:18] [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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196141&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196141&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196141&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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.552421	-5.0024	2e-06
2	0.09587	0.8681	0.193925
3	-0.07985	-0.7231	0.235846
4	0.142357	1.2891	0.100495
5	-0.158806	-1.4381	0.077113
6	-0.001953	-0.0177	0.492966
7	0.167402	1.5159	0.066696
8	-0.202822	-1.8366	0.034944
9	0.139564	1.2638	0.10494
10	0.037016	0.3352	0.369166
11	0.056532	0.5119	0.305041
12	-0.308132	-2.7903	0.003274
13	0.1328	1.2026	0.116305
14	0.118798	1.0758	0.142594
15	-0.120941	-1.0952	0.138326
16	0.063067	0.5711	0.284748
17	0.035743	0.3237	0.373506
18	-0.044799	-0.4057	0.34302
19	0.007775	0.0704	0.472021

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.552421 & -5.0024 & 2e-06 \tabularnewline
2 & 0.09587 & 0.8681 & 0.193925 \tabularnewline
3 & -0.07985 & -0.7231 & 0.235846 \tabularnewline
4 & 0.142357 & 1.2891 & 0.100495 \tabularnewline
5 & -0.158806 & -1.4381 & 0.077113 \tabularnewline
6 & -0.001953 & -0.0177 & 0.492966 \tabularnewline
7 & 0.167402 & 1.5159 & 0.066696 \tabularnewline
8 & -0.202822 & -1.8366 & 0.034944 \tabularnewline
9 & 0.139564 & 1.2638 & 0.10494 \tabularnewline
10 & 0.037016 & 0.3352 & 0.369166 \tabularnewline
11 & 0.056532 & 0.5119 & 0.305041 \tabularnewline
12 & -0.308132 & -2.7903 & 0.003274 \tabularnewline
13 & 0.1328 & 1.2026 & 0.116305 \tabularnewline
14 & 0.118798 & 1.0758 & 0.142594 \tabularnewline
15 & -0.120941 & -1.0952 & 0.138326 \tabularnewline
16 & 0.063067 & 0.5711 & 0.284748 \tabularnewline
17 & 0.035743 & 0.3237 & 0.373506 \tabularnewline
18 & -0.044799 & -0.4057 & 0.34302 \tabularnewline
19 & 0.007775 & 0.0704 & 0.472021 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196141&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]-0.552421[/C][C]-5.0024[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]0.09587[/C][C]0.8681[/C][C]0.193925[/C][/ROW]
[ROW][C]3[/C][C]-0.07985[/C][C]-0.7231[/C][C]0.235846[/C][/ROW]
[ROW][C]4[/C][C]0.142357[/C][C]1.2891[/C][C]0.100495[/C][/ROW]
[ROW][C]5[/C][C]-0.158806[/C][C]-1.4381[/C][C]0.077113[/C][/ROW]
[ROW][C]6[/C][C]-0.001953[/C][C]-0.0177[/C][C]0.492966[/C][/ROW]
[ROW][C]7[/C][C]0.167402[/C][C]1.5159[/C][C]0.066696[/C][/ROW]
[ROW][C]8[/C][C]-0.202822[/C][C]-1.8366[/C][C]0.034944[/C][/ROW]
[ROW][C]9[/C][C]0.139564[/C][C]1.2638[/C][C]0.10494[/C][/ROW]
[ROW][C]10[/C][C]0.037016[/C][C]0.3352[/C][C]0.369166[/C][/ROW]
[ROW][C]11[/C][C]0.056532[/C][C]0.5119[/C][C]0.305041[/C][/ROW]
[ROW][C]12[/C][C]-0.308132[/C][C]-2.7903[/C][C]0.003274[/C][/ROW]
[ROW][C]13[/C][C]0.1328[/C][C]1.2026[/C][C]0.116305[/C][/ROW]
[ROW][C]14[/C][C]0.118798[/C][C]1.0758[/C][C]0.142594[/C][/ROW]
[ROW][C]15[/C][C]-0.120941[/C][C]-1.0952[/C][C]0.138326[/C][/ROW]
[ROW][C]16[/C][C]0.063067[/C][C]0.5711[/C][C]0.284748[/C][/ROW]
[ROW][C]17[/C][C]0.035743[/C][C]0.3237[/C][C]0.373506[/C][/ROW]
[ROW][C]18[/C][C]-0.044799[/C][C]-0.4057[/C][C]0.34302[/C][/ROW]
[ROW][C]19[/C][C]0.007775[/C][C]0.0704[/C][C]0.472021[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196141&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196141&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	-0.552421	-5.0024	2e-06
2	0.09587	0.8681	0.193925
3	-0.07985	-0.7231	0.235846
4	0.142357	1.2891	0.100495
5	-0.158806	-1.4381	0.077113
6	-0.001953	-0.0177	0.492966
7	0.167402	1.5159	0.066696
8	-0.202822	-1.8366	0.034944
9	0.139564	1.2638	0.10494
10	0.037016	0.3352	0.369166
11	0.056532	0.5119	0.305041
12	-0.308132	-2.7903	0.003274
13	0.1328	1.2026	0.116305
14	0.118798	1.0758	0.142594
15	-0.120941	-1.0952	0.138326
16	0.063067	0.5711	0.284748
17	0.035743	0.3237	0.373506
18	-0.044799	-0.4057	0.34302
19	0.007775	0.0704	0.472021

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.552421	-5.0024	2e-06
2	-0.301221	-2.7277	0.0039
3	-0.280692	-2.5418	0.006456
4	-0.049194	-0.4455	0.328578
5	-0.139668	-1.2647	0.104772
6	-0.253439	-2.295	0.012145
7	0.013724	0.1243	0.450701
8	-0.1726	-1.563	0.060957
9	-0.061174	-0.554	0.29056
10	0.147059	1.3317	0.093328
11	0.287262	2.6013	0.005508
12	-0.083066	-0.7522	0.227044
13	-0.28193	-2.553	0.006267
14	-0.061804	-0.5597	0.28862
15	-0.012666	-0.1147	0.454483
16	0.078652	0.7122	0.239174
17	0.121943	1.1042	0.13636
18	-0.02984	-0.2702	0.393839
19	0.068517	0.6205	0.26834

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.552421 & -5.0024 & 2e-06 \tabularnewline
2 & -0.301221 & -2.7277 & 0.0039 \tabularnewline
3 & -0.280692 & -2.5418 & 0.006456 \tabularnewline
4 & -0.049194 & -0.4455 & 0.328578 \tabularnewline
5 & -0.139668 & -1.2647 & 0.104772 \tabularnewline
6 & -0.253439 & -2.295 & 0.012145 \tabularnewline
7 & 0.013724 & 0.1243 & 0.450701 \tabularnewline
8 & -0.1726 & -1.563 & 0.060957 \tabularnewline
9 & -0.061174 & -0.554 & 0.29056 \tabularnewline
10 & 0.147059 & 1.3317 & 0.093328 \tabularnewline
11 & 0.287262 & 2.6013 & 0.005508 \tabularnewline
12 & -0.083066 & -0.7522 & 0.227044 \tabularnewline
13 & -0.28193 & -2.553 & 0.006267 \tabularnewline
14 & -0.061804 & -0.5597 & 0.28862 \tabularnewline
15 & -0.012666 & -0.1147 & 0.454483 \tabularnewline
16 & 0.078652 & 0.7122 & 0.239174 \tabularnewline
17 & 0.121943 & 1.1042 & 0.13636 \tabularnewline
18 & -0.02984 & -0.2702 & 0.393839 \tabularnewline
19 & 0.068517 & 0.6205 & 0.26834 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=196141&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]-0.552421[/C][C]-5.0024[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.301221[/C][C]-2.7277[/C][C]0.0039[/C][/ROW]
[ROW][C]3[/C][C]-0.280692[/C][C]-2.5418[/C][C]0.006456[/C][/ROW]
[ROW][C]4[/C][C]-0.049194[/C][C]-0.4455[/C][C]0.328578[/C][/ROW]
[ROW][C]5[/C][C]-0.139668[/C][C]-1.2647[/C][C]0.104772[/C][/ROW]
[ROW][C]6[/C][C]-0.253439[/C][C]-2.295[/C][C]0.012145[/C][/ROW]
[ROW][C]7[/C][C]0.013724[/C][C]0.1243[/C][C]0.450701[/C][/ROW]
[ROW][C]8[/C][C]-0.1726[/C][C]-1.563[/C][C]0.060957[/C][/ROW]
[ROW][C]9[/C][C]-0.061174[/C][C]-0.554[/C][C]0.29056[/C][/ROW]
[ROW][C]10[/C][C]0.147059[/C][C]1.3317[/C][C]0.093328[/C][/ROW]
[ROW][C]11[/C][C]0.287262[/C][C]2.6013[/C][C]0.005508[/C][/ROW]
[ROW][C]12[/C][C]-0.083066[/C][C]-0.7522[/C][C]0.227044[/C][/ROW]
[ROW][C]13[/C][C]-0.28193[/C][C]-2.553[/C][C]0.006267[/C][/ROW]
[ROW][C]14[/C][C]-0.061804[/C][C]-0.5597[/C][C]0.28862[/C][/ROW]
[ROW][C]15[/C][C]-0.012666[/C][C]-0.1147[/C][C]0.454483[/C][/ROW]
[ROW][C]16[/C][C]0.078652[/C][C]0.7122[/C][C]0.239174[/C][/ROW]
[ROW][C]17[/C][C]0.121943[/C][C]1.1042[/C][C]0.13636[/C][/ROW]
[ROW][C]18[/C][C]-0.02984[/C][C]-0.2702[/C][C]0.393839[/C][/ROW]
[ROW][C]19[/C][C]0.068517[/C][C]0.6205[/C][C]0.26834[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=196141&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=196141&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	-0.552421	-5.0024	2e-06
2	-0.301221	-2.7277	0.0039
3	-0.280692	-2.5418	0.006456
4	-0.049194	-0.4455	0.328578
5	-0.139668	-1.2647	0.104772
6	-0.253439	-2.295	0.012145
7	0.013724	0.1243	0.450701
8	-0.1726	-1.563	0.060957
9	-0.061174	-0.554	0.29056
10	0.147059	1.3317	0.093328
11	0.287262	2.6013	0.005508
12	-0.083066	-0.7522	0.227044
13	-0.28193	-2.553	0.006267
14	-0.061804	-0.5597	0.28862
15	-0.012666	-0.1147	0.454483
16	0.078652	0.7122	0.239174
17	0.121943	1.1042	0.13636
18	-0.02984	-0.2702	0.393839
19	0.068517	0.6205	0.26834

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code