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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 20 Dec 2007 06:29:27 -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/20/t11981563221xmloqx88x6ac17.htm/, Retrieved Tue, 10 Feb 2026 18:40:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4714, Retrieved Tue, 10 Feb 2026 18:40:32 +0000

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No (this computation is public)

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Estimated Impact

495

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-       [(Partial) Autocorrelation Function] [Q1] [2007-12-20 13:29:27] [157a0cf3c12a7482b4e6935b4c49d48f] [Current]

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Dataseries X:

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Histogram

Boxplots

1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,43
1,44
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,48
1,57
1,58
1,58
1,58
1,58
1,59
1,6
1,6
1,61
1,61
1,61
1,62
1,63
1,63
1,64
1,64
1,64
1,64
1,64
1,65
1,65
1,65
1,65

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=4714&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=4714&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4714&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	8.4261	0
1	0.081537	0.687	0.247147
2	-0.050502	-0.4255	0.664133
3	-0.041387	-0.3487	0.635841
4	-0.049314	-0.4155	0.660495
5	0.050542	0.4259	0.335744
6	0.049574	0.4177	0.338708
7	-0.042136	-0.355	0.638194
8	0.037555	0.3164	0.376296
9	-0.061112	-0.5149	0.695903
10	-0.06208	-0.5231	0.698732
11	0.040899	0.3446	0.365697
12	0.022891	0.1929	0.423801
13	-0.048654	-0.41	0.658467
14	0.031037	0.2615	0.397223
15	-0.06763	-0.5699	0.714716
16	-0.068598	-0.578	0.717461
17	-0.066442	-0.5599	0.711329

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4261 & 0 \tabularnewline
1 & 0.081537 & 0.687 & 0.247147 \tabularnewline
2 & -0.050502 & -0.4255 & 0.664133 \tabularnewline
3 & -0.041387 & -0.3487 & 0.635841 \tabularnewline
4 & -0.049314 & -0.4155 & 0.660495 \tabularnewline
5 & 0.050542 & 0.4259 & 0.335744 \tabularnewline
6 & 0.049574 & 0.4177 & 0.338708 \tabularnewline
7 & -0.042136 & -0.355 & 0.638194 \tabularnewline
8 & 0.037555 & 0.3164 & 0.376296 \tabularnewline
9 & -0.061112 & -0.5149 & 0.695903 \tabularnewline
10 & -0.06208 & -0.5231 & 0.698732 \tabularnewline
11 & 0.040899 & 0.3446 & 0.365697 \tabularnewline
12 & 0.022891 & 0.1929 & 0.423801 \tabularnewline
13 & -0.048654 & -0.41 & 0.658467 \tabularnewline
14 & 0.031037 & 0.2615 & 0.397223 \tabularnewline
15 & -0.06763 & -0.5699 & 0.714716 \tabularnewline
16 & -0.068598 & -0.578 & 0.717461 \tabularnewline
17 & -0.066442 & -0.5599 & 0.711329 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4714&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]8.4261[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.081537[/C][C]0.687[/C][C]0.247147[/C][/ROW]
[ROW][C]2[/C][C]-0.050502[/C][C]-0.4255[/C][C]0.664133[/C][/ROW]
[ROW][C]3[/C][C]-0.041387[/C][C]-0.3487[/C][C]0.635841[/C][/ROW]
[ROW][C]4[/C][C]-0.049314[/C][C]-0.4155[/C][C]0.660495[/C][/ROW]
[ROW][C]5[/C][C]0.050542[/C][C]0.4259[/C][C]0.335744[/C][/ROW]
[ROW][C]6[/C][C]0.049574[/C][C]0.4177[/C][C]0.338708[/C][/ROW]
[ROW][C]7[/C][C]-0.042136[/C][C]-0.355[/C][C]0.638194[/C][/ROW]
[ROW][C]8[/C][C]0.037555[/C][C]0.3164[/C][C]0.376296[/C][/ROW]
[ROW][C]9[/C][C]-0.061112[/C][C]-0.5149[/C][C]0.695903[/C][/ROW]
[ROW][C]10[/C][C]-0.06208[/C][C]-0.5231[/C][C]0.698732[/C][/ROW]
[ROW][C]11[/C][C]0.040899[/C][C]0.3446[/C][C]0.365697[/C][/ROW]
[ROW][C]12[/C][C]0.022891[/C][C]0.1929[/C][C]0.423801[/C][/ROW]
[ROW][C]13[/C][C]-0.048654[/C][C]-0.41[/C][C]0.658467[/C][/ROW]
[ROW][C]14[/C][C]0.031037[/C][C]0.2615[/C][C]0.397223[/C][/ROW]
[ROW][C]15[/C][C]-0.06763[/C][C]-0.5699[/C][C]0.714716[/C][/ROW]
[ROW][C]16[/C][C]-0.068598[/C][C]-0.578[/C][C]0.717461[/C][/ROW]
[ROW][C]17[/C][C]-0.066442[/C][C]-0.5599[/C][C]0.711329[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4714&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4714&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	8.4261	0
1	0.081537	0.687	0.247147
2	-0.050502	-0.4255	0.664133
3	-0.041387	-0.3487	0.635841
4	-0.049314	-0.4155	0.660495
5	0.050542	0.4259	0.335744
6	0.049574	0.4177	0.338708
7	-0.042136	-0.355	0.638194
8	0.037555	0.3164	0.376296
9	-0.061112	-0.5149	0.695903
10	-0.06208	-0.5231	0.698732
11	0.040899	0.3446	0.365697
12	0.022891	0.1929	0.423801
13	-0.048654	-0.41	0.658467
14	0.031037	0.2615	0.397223
15	-0.06763	-0.5699	0.714716
16	-0.068598	-0.578	0.717461
17	-0.066442	-0.5599	0.711329

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.081537	0.687	0.247147
1	-0.057533	-0.4848	0.685337
2	-0.032666	-0.2753	0.608039
3	-0.046433	-0.3913	0.651608
4	0.055317	0.4661	0.321282
5	0.034931	0.2943	0.384681
6	-0.047833	-0.403	0.655939
7	0.051513	0.4341	0.332783
8	-0.066854	-0.5633	0.712504
9	-0.049052	-0.4133	0.659692
10	0.039417	0.3321	0.370382
11	0.013487	0.1136	0.45492
12	-0.059565	-0.5019	0.691357
13	0.041162	0.3468	0.36487
14	-0.061001	-0.514	0.695576
15	-0.065883	-0.5551	0.709728
16	-0.07032	-0.5925	0.72231
17	-0.039544	-0.3332	0.63002

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.081537 & 0.687 & 0.247147 \tabularnewline
1 & -0.057533 & -0.4848 & 0.685337 \tabularnewline
2 & -0.032666 & -0.2753 & 0.608039 \tabularnewline
3 & -0.046433 & -0.3913 & 0.651608 \tabularnewline
4 & 0.055317 & 0.4661 & 0.321282 \tabularnewline
5 & 0.034931 & 0.2943 & 0.384681 \tabularnewline
6 & -0.047833 & -0.403 & 0.655939 \tabularnewline
7 & 0.051513 & 0.4341 & 0.332783 \tabularnewline
8 & -0.066854 & -0.5633 & 0.712504 \tabularnewline
9 & -0.049052 & -0.4133 & 0.659692 \tabularnewline
10 & 0.039417 & 0.3321 & 0.370382 \tabularnewline
11 & 0.013487 & 0.1136 & 0.45492 \tabularnewline
12 & -0.059565 & -0.5019 & 0.691357 \tabularnewline
13 & 0.041162 & 0.3468 & 0.36487 \tabularnewline
14 & -0.061001 & -0.514 & 0.695576 \tabularnewline
15 & -0.065883 & -0.5551 & 0.709728 \tabularnewline
16 & -0.07032 & -0.5925 & 0.72231 \tabularnewline
17 & -0.039544 & -0.3332 & 0.63002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4714&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]0.081537[/C][C]0.687[/C][C]0.247147[/C][/ROW]
[ROW][C]1[/C][C]-0.057533[/C][C]-0.4848[/C][C]0.685337[/C][/ROW]
[ROW][C]2[/C][C]-0.032666[/C][C]-0.2753[/C][C]0.608039[/C][/ROW]
[ROW][C]3[/C][C]-0.046433[/C][C]-0.3913[/C][C]0.651608[/C][/ROW]
[ROW][C]4[/C][C]0.055317[/C][C]0.4661[/C][C]0.321282[/C][/ROW]
[ROW][C]5[/C][C]0.034931[/C][C]0.2943[/C][C]0.384681[/C][/ROW]
[ROW][C]6[/C][C]-0.047833[/C][C]-0.403[/C][C]0.655939[/C][/ROW]
[ROW][C]7[/C][C]0.051513[/C][C]0.4341[/C][C]0.332783[/C][/ROW]
[ROW][C]8[/C][C]-0.066854[/C][C]-0.5633[/C][C]0.712504[/C][/ROW]
[ROW][C]9[/C][C]-0.049052[/C][C]-0.4133[/C][C]0.659692[/C][/ROW]
[ROW][C]10[/C][C]0.039417[/C][C]0.3321[/C][C]0.370382[/C][/ROW]
[ROW][C]11[/C][C]0.013487[/C][C]0.1136[/C][C]0.45492[/C][/ROW]
[ROW][C]12[/C][C]-0.059565[/C][C]-0.5019[/C][C]0.691357[/C][/ROW]
[ROW][C]13[/C][C]0.041162[/C][C]0.3468[/C][C]0.36487[/C][/ROW]
[ROW][C]14[/C][C]-0.061001[/C][C]-0.514[/C][C]0.695576[/C][/ROW]
[ROW][C]15[/C][C]-0.065883[/C][C]-0.5551[/C][C]0.709728[/C][/ROW]
[ROW][C]16[/C][C]-0.07032[/C][C]-0.5925[/C][C]0.72231[/C][/ROW]
[ROW][C]17[/C][C]-0.039544[/C][C]-0.3332[/C][C]0.63002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4714&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4714&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	0.081537	0.687	0.247147
1	-0.057533	-0.4848	0.685337
2	-0.032666	-0.2753	0.608039
3	-0.046433	-0.3913	0.651608
4	0.055317	0.4661	0.321282
5	0.034931	0.2943	0.384681
6	-0.047833	-0.403	0.655939
7	0.051513	0.4341	0.332783
8	-0.066854	-0.5633	0.712504
9	-0.049052	-0.4133	0.659692
10	0.039417	0.3321	0.370382
11	0.013487	0.1136	0.45492
12	-0.059565	-0.5019	0.691357
13	0.041162	0.3468	0.36487
14	-0.061001	-0.514	0.695576
15	-0.065883	-0.5551	0.709728
16	-0.07032	-0.5925	0.72231
17	-0.039544	-0.3332	0.63002

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