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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 04 Dec 2009 07:24:14 -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/t1259936712e63mdjvk7spiund.htm/, Retrieved Wed, 11 Feb 2026 00:37:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63598, Retrieved Wed, 11 Feb 2026 00:37:41 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

394

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [ARIMA Backward Selection] [] [2009-11-27 14:53:14] [b98453cac15ba1066b407e146608df68]
-    D    [ARIMA Backward Selection] [BBWS9-Arimabackward1] [2009-12-01 20:26:03] [408e92805dcb18620260f240a7fb9d53]
- RM D      [Harrell-Davis Quantiles] [BBWS9-Harolddavis] [2009-12-01 20:39:11] [408e92805dcb18620260f240a7fb9d53]
-   PD        [Harrell-Davis Quantiles] [W9: Harrell Davis] [2009-12-02 10:38:10] [03d5b865e91ca35b5a5d21b8d6da5aba]
- RMPD            [(Partial) Autocorrelation Function] [W9.2] [2009-12-04 14:24:14] [852eae237d08746109043531619a60c9] [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=63598&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=63598&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63598&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	0.05444	0.4619	0.322759
2	0.136876	1.1614	0.124651
3	0.149513	1.2687	0.104325
4	0.03169	0.2689	0.394387
5	0.045593	0.3869	0.349997
6	0.091981	0.7805	0.218832
7	0.015192	0.1289	0.448893
8	0.203558	1.7272	0.044205
9	0.02738	0.2323	0.408472
10	-0.079682	-0.6761	0.250565
11	0.190193	1.6138	0.055469
12	-0.180006	-1.5274	0.065521
13	-0.013888	-0.1178	0.45326
14	0.194659	1.6517	0.051471
15	0.021493	0.1824	0.4279
16	0.005917	0.0502	0.480047
17	-0.074964	-0.6361	0.263368
18	0.016319	0.1385	0.445127
19	0.004458	0.0378	0.484967

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.05444 & 0.4619 & 0.322759 \tabularnewline
2 & 0.136876 & 1.1614 & 0.124651 \tabularnewline
3 & 0.149513 & 1.2687 & 0.104325 \tabularnewline
4 & 0.03169 & 0.2689 & 0.394387 \tabularnewline
5 & 0.045593 & 0.3869 & 0.349997 \tabularnewline
6 & 0.091981 & 0.7805 & 0.218832 \tabularnewline
7 & 0.015192 & 0.1289 & 0.448893 \tabularnewline
8 & 0.203558 & 1.7272 & 0.044205 \tabularnewline
9 & 0.02738 & 0.2323 & 0.408472 \tabularnewline
10 & -0.079682 & -0.6761 & 0.250565 \tabularnewline
11 & 0.190193 & 1.6138 & 0.055469 \tabularnewline
12 & -0.180006 & -1.5274 & 0.065521 \tabularnewline
13 & -0.013888 & -0.1178 & 0.45326 \tabularnewline
14 & 0.194659 & 1.6517 & 0.051471 \tabularnewline
15 & 0.021493 & 0.1824 & 0.4279 \tabularnewline
16 & 0.005917 & 0.0502 & 0.480047 \tabularnewline
17 & -0.074964 & -0.6361 & 0.263368 \tabularnewline
18 & 0.016319 & 0.1385 & 0.445127 \tabularnewline
19 & 0.004458 & 0.0378 & 0.484967 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63598&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]0.05444[/C][C]0.4619[/C][C]0.322759[/C][/ROW]
[ROW][C]2[/C][C]0.136876[/C][C]1.1614[/C][C]0.124651[/C][/ROW]
[ROW][C]3[/C][C]0.149513[/C][C]1.2687[/C][C]0.104325[/C][/ROW]
[ROW][C]4[/C][C]0.03169[/C][C]0.2689[/C][C]0.394387[/C][/ROW]
[ROW][C]5[/C][C]0.045593[/C][C]0.3869[/C][C]0.349997[/C][/ROW]
[ROW][C]6[/C][C]0.091981[/C][C]0.7805[/C][C]0.218832[/C][/ROW]
[ROW][C]7[/C][C]0.015192[/C][C]0.1289[/C][C]0.448893[/C][/ROW]
[ROW][C]8[/C][C]0.203558[/C][C]1.7272[/C][C]0.044205[/C][/ROW]
[ROW][C]9[/C][C]0.02738[/C][C]0.2323[/C][C]0.408472[/C][/ROW]
[ROW][C]10[/C][C]-0.079682[/C][C]-0.6761[/C][C]0.250565[/C][/ROW]
[ROW][C]11[/C][C]0.190193[/C][C]1.6138[/C][C]0.055469[/C][/ROW]
[ROW][C]12[/C][C]-0.180006[/C][C]-1.5274[/C][C]0.065521[/C][/ROW]
[ROW][C]13[/C][C]-0.013888[/C][C]-0.1178[/C][C]0.45326[/C][/ROW]
[ROW][C]14[/C][C]0.194659[/C][C]1.6517[/C][C]0.051471[/C][/ROW]
[ROW][C]15[/C][C]0.021493[/C][C]0.1824[/C][C]0.4279[/C][/ROW]
[ROW][C]16[/C][C]0.005917[/C][C]0.0502[/C][C]0.480047[/C][/ROW]
[ROW][C]17[/C][C]-0.074964[/C][C]-0.6361[/C][C]0.263368[/C][/ROW]
[ROW][C]18[/C][C]0.016319[/C][C]0.1385[/C][C]0.445127[/C][/ROW]
[ROW][C]19[/C][C]0.004458[/C][C]0.0378[/C][C]0.484967[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63598&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63598&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	0.05444	0.4619	0.322759
2	0.136876	1.1614	0.124651
3	0.149513	1.2687	0.104325
4	0.03169	0.2689	0.394387
5	0.045593	0.3869	0.349997
6	0.091981	0.7805	0.218832
7	0.015192	0.1289	0.448893
8	0.203558	1.7272	0.044205
9	0.02738	0.2323	0.408472
10	-0.079682	-0.6761	0.250565
11	0.190193	1.6138	0.055469
12	-0.180006	-1.5274	0.065521
13	-0.013888	-0.1178	0.45326
14	0.194659	1.6517	0.051471
15	0.021493	0.1824	0.4279
16	0.005917	0.0502	0.480047
17	-0.074964	-0.6361	0.263368
18	0.016319	0.1385	0.445127
19	0.004458	0.0378	0.484967

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.05444	0.4619	0.322759
2	0.134311	1.1397	0.129102
3	0.138655	1.1765	0.12163
4	0.00249	0.0211	0.491603
5	0.00681	0.0578	0.477038
6	0.068126	0.5781	0.28251
7	-0.000643	-0.0055	0.49783
8	0.183971	1.561	0.061449
9	-0.007425	-0.063	0.474971
10	-0.140554	-1.1926	0.118463
11	0.15512	1.3162	0.096134
12	-0.199256	-1.6907	0.047605
13	-0.015101	-0.1281	0.4492
14	0.213506	1.8117	0.037104
15	0.03333	0.2828	0.389066
16	-0.071837	-0.6096	0.272036
17	-0.165311	-1.4027	0.0825
18	0.099752	0.8464	0.20006
19	-0.024497	-0.2079	0.41796

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.05444 & 0.4619 & 0.322759 \tabularnewline
2 & 0.134311 & 1.1397 & 0.129102 \tabularnewline
3 & 0.138655 & 1.1765 & 0.12163 \tabularnewline
4 & 0.00249 & 0.0211 & 0.491603 \tabularnewline
5 & 0.00681 & 0.0578 & 0.477038 \tabularnewline
6 & 0.068126 & 0.5781 & 0.28251 \tabularnewline
7 & -0.000643 & -0.0055 & 0.49783 \tabularnewline
8 & 0.183971 & 1.561 & 0.061449 \tabularnewline
9 & -0.007425 & -0.063 & 0.474971 \tabularnewline
10 & -0.140554 & -1.1926 & 0.118463 \tabularnewline
11 & 0.15512 & 1.3162 & 0.096134 \tabularnewline
12 & -0.199256 & -1.6907 & 0.047605 \tabularnewline
13 & -0.015101 & -0.1281 & 0.4492 \tabularnewline
14 & 0.213506 & 1.8117 & 0.037104 \tabularnewline
15 & 0.03333 & 0.2828 & 0.389066 \tabularnewline
16 & -0.071837 & -0.6096 & 0.272036 \tabularnewline
17 & -0.165311 & -1.4027 & 0.0825 \tabularnewline
18 & 0.099752 & 0.8464 & 0.20006 \tabularnewline
19 & -0.024497 & -0.2079 & 0.41796 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63598&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]0.05444[/C][C]0.4619[/C][C]0.322759[/C][/ROW]
[ROW][C]2[/C][C]0.134311[/C][C]1.1397[/C][C]0.129102[/C][/ROW]
[ROW][C]3[/C][C]0.138655[/C][C]1.1765[/C][C]0.12163[/C][/ROW]
[ROW][C]4[/C][C]0.00249[/C][C]0.0211[/C][C]0.491603[/C][/ROW]
[ROW][C]5[/C][C]0.00681[/C][C]0.0578[/C][C]0.477038[/C][/ROW]
[ROW][C]6[/C][C]0.068126[/C][C]0.5781[/C][C]0.28251[/C][/ROW]
[ROW][C]7[/C][C]-0.000643[/C][C]-0.0055[/C][C]0.49783[/C][/ROW]
[ROW][C]8[/C][C]0.183971[/C][C]1.561[/C][C]0.061449[/C][/ROW]
[ROW][C]9[/C][C]-0.007425[/C][C]-0.063[/C][C]0.474971[/C][/ROW]
[ROW][C]10[/C][C]-0.140554[/C][C]-1.1926[/C][C]0.118463[/C][/ROW]
[ROW][C]11[/C][C]0.15512[/C][C]1.3162[/C][C]0.096134[/C][/ROW]
[ROW][C]12[/C][C]-0.199256[/C][C]-1.6907[/C][C]0.047605[/C][/ROW]
[ROW][C]13[/C][C]-0.015101[/C][C]-0.1281[/C][C]0.4492[/C][/ROW]
[ROW][C]14[/C][C]0.213506[/C][C]1.8117[/C][C]0.037104[/C][/ROW]
[ROW][C]15[/C][C]0.03333[/C][C]0.2828[/C][C]0.389066[/C][/ROW]
[ROW][C]16[/C][C]-0.071837[/C][C]-0.6096[/C][C]0.272036[/C][/ROW]
[ROW][C]17[/C][C]-0.165311[/C][C]-1.4027[/C][C]0.0825[/C][/ROW]
[ROW][C]18[/C][C]0.099752[/C][C]0.8464[/C][C]0.20006[/C][/ROW]
[ROW][C]19[/C][C]-0.024497[/C][C]-0.2079[/C][C]0.41796[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63598&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63598&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	0.05444	0.4619	0.322759
2	0.134311	1.1397	0.129102
3	0.138655	1.1765	0.12163
4	0.00249	0.0211	0.491603
5	0.00681	0.0578	0.477038
6	0.068126	0.5781	0.28251
7	-0.000643	-0.0055	0.49783
8	0.183971	1.561	0.061449
9	-0.007425	-0.063	0.474971
10	-0.140554	-1.1926	0.118463
11	0.15512	1.3162	0.096134
12	-0.199256	-1.6907	0.047605
13	-0.015101	-0.1281	0.4492
14	0.213506	1.8117	0.037104
15	0.03333	0.2828	0.389066
16	-0.071837	-0.6096	0.272036
17	-0.165311	-1.4027	0.0825
18	0.099752	0.8464	0.20006
19	-0.024497	-0.2079	0.41796

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; 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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code