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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 06 Dec 2007 01:43:28 -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/06/t11969305581aj13ydf4u2n6yv.htm/, Retrieved Tue, 10 Feb 2026 13:24:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2551, Retrieved Tue, 10 Feb 2026 13:24:49 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

s0650532

Estimated Impact

439

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

-       [(Partial) Autocorrelation Function] [PACF ACF indexcij...] [2007-12-06 08:43:28] [246ad84e93fbdd1336f5cbee368cde93] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2551&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]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=2551&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2551&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.3666	0
1	-0.475617	-3.9793	0.999917
2	-0.020099	-0.1682	0.566528
3	-0.000647	-0.0054	0.502151
4	-0.076451	-0.6396	0.737751
5	0.101943	0.8529	0.198308
6	-0.019322	-0.1617	0.56398
7	0.012387	0.1036	0.458877
8	-0.01196	-0.1001	0.539711
9	-0.00876	-0.0733	0.52911
10	-0.037922	-0.3173	0.624011
11	0.034539	0.289	0.386727
12	0.010163	0.085	0.466242
13	0.012507	0.1046	0.458479
14	-0.005969	-0.0499	0.519842
15	-0.024709	-0.2067	0.581588
16	0.017333	0.145	0.442557
17	-0.017238	-0.1442	0.557132

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.3666 & 0 \tabularnewline
1 & -0.475617 & -3.9793 & 0.999917 \tabularnewline
2 & -0.020099 & -0.1682 & 0.566528 \tabularnewline
3 & -0.000647 & -0.0054 & 0.502151 \tabularnewline
4 & -0.076451 & -0.6396 & 0.737751 \tabularnewline
5 & 0.101943 & 0.8529 & 0.198308 \tabularnewline
6 & -0.019322 & -0.1617 & 0.56398 \tabularnewline
7 & 0.012387 & 0.1036 & 0.458877 \tabularnewline
8 & -0.01196 & -0.1001 & 0.539711 \tabularnewline
9 & -0.00876 & -0.0733 & 0.52911 \tabularnewline
10 & -0.037922 & -0.3173 & 0.624011 \tabularnewline
11 & 0.034539 & 0.289 & 0.386727 \tabularnewline
12 & 0.010163 & 0.085 & 0.466242 \tabularnewline
13 & 0.012507 & 0.1046 & 0.458479 \tabularnewline
14 & -0.005969 & -0.0499 & 0.519842 \tabularnewline
15 & -0.024709 & -0.2067 & 0.581588 \tabularnewline
16 & 0.017333 & 0.145 & 0.442557 \tabularnewline
17 & -0.017238 & -0.1442 & 0.557132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2551&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]8.3666[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.475617[/C][C]-3.9793[/C][C]0.999917[/C][/ROW]
[ROW][C]2[/C][C]-0.020099[/C][C]-0.1682[/C][C]0.566528[/C][/ROW]
[ROW][C]3[/C][C]-0.000647[/C][C]-0.0054[/C][C]0.502151[/C][/ROW]
[ROW][C]4[/C][C]-0.076451[/C][C]-0.6396[/C][C]0.737751[/C][/ROW]
[ROW][C]5[/C][C]0.101943[/C][C]0.8529[/C][C]0.198308[/C][/ROW]
[ROW][C]6[/C][C]-0.019322[/C][C]-0.1617[/C][C]0.56398[/C][/ROW]
[ROW][C]7[/C][C]0.012387[/C][C]0.1036[/C][C]0.458877[/C][/ROW]
[ROW][C]8[/C][C]-0.01196[/C][C]-0.1001[/C][C]0.539711[/C][/ROW]
[ROW][C]9[/C][C]-0.00876[/C][C]-0.0733[/C][C]0.52911[/C][/ROW]
[ROW][C]10[/C][C]-0.037922[/C][C]-0.3173[/C][C]0.624011[/C][/ROW]
[ROW][C]11[/C][C]0.034539[/C][C]0.289[/C][C]0.386727[/C][/ROW]
[ROW][C]12[/C][C]0.010163[/C][C]0.085[/C][C]0.466242[/C][/ROW]
[ROW][C]13[/C][C]0.012507[/C][C]0.1046[/C][C]0.458479[/C][/ROW]
[ROW][C]14[/C][C]-0.005969[/C][C]-0.0499[/C][C]0.519842[/C][/ROW]
[ROW][C]15[/C][C]-0.024709[/C][C]-0.2067[/C][C]0.581588[/C][/ROW]
[ROW][C]16[/C][C]0.017333[/C][C]0.145[/C][C]0.442557[/C][/ROW]
[ROW][C]17[/C][C]-0.017238[/C][C]-0.1442[/C][C]0.557132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2551&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2551&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	8.3666	0
1	-0.475617	-3.9793	0.999917
2	-0.020099	-0.1682	0.566528
3	-0.000647	-0.0054	0.502151
4	-0.076451	-0.6396	0.737751
5	0.101943	0.8529	0.198308
6	-0.019322	-0.1617	0.56398
7	0.012387	0.1036	0.458877
8	-0.01196	-0.1001	0.539711
9	-0.00876	-0.0733	0.52911
10	-0.037922	-0.3173	0.624011
11	0.034539	0.289	0.386727
12	0.010163	0.085	0.466242
13	0.012507	0.1046	0.458479
14	-0.005969	-0.0499	0.519842
15	-0.024709	-0.2067	0.581588
16	0.017333	0.145	0.442557
17	-0.017238	-0.1442	0.557132

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.475617	-3.9793	0.999917
1	-0.318316	-2.6632	0.995202
2	-0.236769	-1.981	0.974237
3	-0.303013	-2.5352	0.993262
4	-0.185843	-1.5549	0.937757
5	-0.148184	-1.2398	0.890405
6	-0.094776	-0.793	0.784758
7	-0.074974	-0.6273	0.733742
8	-0.051574	-0.4315	0.666285
9	-0.115155	-0.9635	0.830681
10	-0.101625	-0.8503	0.80096
11	-0.08621	-0.7213	0.763431
12	-0.049526	-0.4144	0.660061
13	-0.030722	-0.257	0.601048
14	-0.035904	-0.3004	0.617617
15	-0.012407	-0.1038	0.541191
16	-0.028636	-0.2396	0.594325
17	-0.070636	-0.591	0.721781

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.475617 & -3.9793 & 0.999917 \tabularnewline
1 & -0.318316 & -2.6632 & 0.995202 \tabularnewline
2 & -0.236769 & -1.981 & 0.974237 \tabularnewline
3 & -0.303013 & -2.5352 & 0.993262 \tabularnewline
4 & -0.185843 & -1.5549 & 0.937757 \tabularnewline
5 & -0.148184 & -1.2398 & 0.890405 \tabularnewline
6 & -0.094776 & -0.793 & 0.784758 \tabularnewline
7 & -0.074974 & -0.6273 & 0.733742 \tabularnewline
8 & -0.051574 & -0.4315 & 0.666285 \tabularnewline
9 & -0.115155 & -0.9635 & 0.830681 \tabularnewline
10 & -0.101625 & -0.8503 & 0.80096 \tabularnewline
11 & -0.08621 & -0.7213 & 0.763431 \tabularnewline
12 & -0.049526 & -0.4144 & 0.660061 \tabularnewline
13 & -0.030722 & -0.257 & 0.601048 \tabularnewline
14 & -0.035904 & -0.3004 & 0.617617 \tabularnewline
15 & -0.012407 & -0.1038 & 0.541191 \tabularnewline
16 & -0.028636 & -0.2396 & 0.594325 \tabularnewline
17 & -0.070636 & -0.591 & 0.721781 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2551&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]-0.475617[/C][C]-3.9793[/C][C]0.999917[/C][/ROW]
[ROW][C]1[/C][C]-0.318316[/C][C]-2.6632[/C][C]0.995202[/C][/ROW]
[ROW][C]2[/C][C]-0.236769[/C][C]-1.981[/C][C]0.974237[/C][/ROW]
[ROW][C]3[/C][C]-0.303013[/C][C]-2.5352[/C][C]0.993262[/C][/ROW]
[ROW][C]4[/C][C]-0.185843[/C][C]-1.5549[/C][C]0.937757[/C][/ROW]
[ROW][C]5[/C][C]-0.148184[/C][C]-1.2398[/C][C]0.890405[/C][/ROW]
[ROW][C]6[/C][C]-0.094776[/C][C]-0.793[/C][C]0.784758[/C][/ROW]
[ROW][C]7[/C][C]-0.074974[/C][C]-0.6273[/C][C]0.733742[/C][/ROW]
[ROW][C]8[/C][C]-0.051574[/C][C]-0.4315[/C][C]0.666285[/C][/ROW]
[ROW][C]9[/C][C]-0.115155[/C][C]-0.9635[/C][C]0.830681[/C][/ROW]
[ROW][C]10[/C][C]-0.101625[/C][C]-0.8503[/C][C]0.80096[/C][/ROW]
[ROW][C]11[/C][C]-0.08621[/C][C]-0.7213[/C][C]0.763431[/C][/ROW]
[ROW][C]12[/C][C]-0.049526[/C][C]-0.4144[/C][C]0.660061[/C][/ROW]
[ROW][C]13[/C][C]-0.030722[/C][C]-0.257[/C][C]0.601048[/C][/ROW]
[ROW][C]14[/C][C]-0.035904[/C][C]-0.3004[/C][C]0.617617[/C][/ROW]
[ROW][C]15[/C][C]-0.012407[/C][C]-0.1038[/C][C]0.541191[/C][/ROW]
[ROW][C]16[/C][C]-0.028636[/C][C]-0.2396[/C][C]0.594325[/C][/ROW]
[ROW][C]17[/C][C]-0.070636[/C][C]-0.591[/C][C]0.721781[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2551&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2551&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	-0.475617	-3.9793	0.999917
1	-0.318316	-2.6632	0.995202
2	-0.236769	-1.981	0.974237
3	-0.303013	-2.5352	0.993262
4	-0.185843	-1.5549	0.937757
5	-0.148184	-1.2398	0.890405
6	-0.094776	-0.793	0.784758
7	-0.074974	-0.6273	0.733742
8	-0.051574	-0.4315	0.666285
9	-0.115155	-0.9635	0.830681
10	-0.101625	-0.8503	0.80096
11	-0.08621	-0.7213	0.763431
12	-0.049526	-0.4144	0.660061
13	-0.030722	-0.257	0.601048
14	-0.035904	-0.3004	0.617617
15	-0.012407	-0.1038	0.541191
16	-0.028636	-0.2396	0.594325
17	-0.070636	-0.591	0.721781

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 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; 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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