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Author's title

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

Wed, 17 Dec 2008 04:25:15 -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/2008/Dec/17/t1229513161qvujasdxwhnlj50.htm/, Retrieved Sat, 23 May 2026 17:48:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34303, Retrieved Sat, 23 May 2026 17:48:40 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

499

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

-     [(Partial) Autocorrelation Function] [VAC (Parti�le) au...] [2008-12-14 13:47:12] [379d6c32f73e3218fd773d79e4063d07]
-    D  [(Partial) Autocorrelation Function] [VAC (Parti�le) au...] [2008-12-14 14:18:58] [379d6c32f73e3218fd773d79e4063d07]
-   P       [(Partial) Autocorrelation Function] [VAC (Parti�le) au...] [2008-12-17 11:25:15] [490fee4f334e2e025c95681783e3fd0b] [Current]
-   P         [(Partial) Autocorrelation Function] [VAC (Parti�le) au...] [2008-12-23 15:15:29] [379d6c32f73e3218fd773d79e4063d07] 
-  MP           [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2010-01-23 19:23:21] [f1bd7399181c649098ca7b814ee0e027] 
-   P         [(Partial) Autocorrelation Function] [VAC (Parti�le) au...] [2008-12-23 15:59:09] [379d6c32f73e3218fd773d79e4063d07] 

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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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34303&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34303&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34303&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.343419	2.0317	0.024915
2	-0.065236	-0.3859	0.350939
3	-0.256777	-1.5191	0.068858
4	-0.118048	-0.6984	0.244776
5	0.298867	1.7681	0.042879
6	0.239299	1.4157	0.082848
7	0.015625	0.0924	0.463439
8	-0.188959	-1.1179	0.135613
9	-0.115462	-0.6831	0.249526
10	0.134716	0.797	0.215415
11	0.098756	0.5842	0.2814
12	-0.139071	-0.8228	0.208108
13	-0.288196	-1.705	0.048529
14	-0.192786	-1.1405	0.130903
15	0.055969	0.3311	0.371265
16	0.178094	1.0536	0.149639
17	0.023982	0.1419	0.443995
18	-0.241136	-1.4266	0.081281
19	-0.187162	-1.1073	0.137866
20	-0.077228	-0.4569	0.325288
21	0.082439	0.4877	0.314397
22	0.101699	0.6017	0.275638
23	0.027012	0.1598	0.436977
24	-0.004481	-0.0265	0.4895

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.343419 & 2.0317 & 0.024915 \tabularnewline
2 & -0.065236 & -0.3859 & 0.350939 \tabularnewline
3 & -0.256777 & -1.5191 & 0.068858 \tabularnewline
4 & -0.118048 & -0.6984 & 0.244776 \tabularnewline
5 & 0.298867 & 1.7681 & 0.042879 \tabularnewline
6 & 0.239299 & 1.4157 & 0.082848 \tabularnewline
7 & 0.015625 & 0.0924 & 0.463439 \tabularnewline
8 & -0.188959 & -1.1179 & 0.135613 \tabularnewline
9 & -0.115462 & -0.6831 & 0.249526 \tabularnewline
10 & 0.134716 & 0.797 & 0.215415 \tabularnewline
11 & 0.098756 & 0.5842 & 0.2814 \tabularnewline
12 & -0.139071 & -0.8228 & 0.208108 \tabularnewline
13 & -0.288196 & -1.705 & 0.048529 \tabularnewline
14 & -0.192786 & -1.1405 & 0.130903 \tabularnewline
15 & 0.055969 & 0.3311 & 0.371265 \tabularnewline
16 & 0.178094 & 1.0536 & 0.149639 \tabularnewline
17 & 0.023982 & 0.1419 & 0.443995 \tabularnewline
18 & -0.241136 & -1.4266 & 0.081281 \tabularnewline
19 & -0.187162 & -1.1073 & 0.137866 \tabularnewline
20 & -0.077228 & -0.4569 & 0.325288 \tabularnewline
21 & 0.082439 & 0.4877 & 0.314397 \tabularnewline
22 & 0.101699 & 0.6017 & 0.275638 \tabularnewline
23 & 0.027012 & 0.1598 & 0.436977 \tabularnewline
24 & -0.004481 & -0.0265 & 0.4895 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34303&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]0.343419[/C][C]2.0317[/C][C]0.024915[/C][/ROW]
[ROW][C]2[/C][C]-0.065236[/C][C]-0.3859[/C][C]0.350939[/C][/ROW]
[ROW][C]3[/C][C]-0.256777[/C][C]-1.5191[/C][C]0.068858[/C][/ROW]
[ROW][C]4[/C][C]-0.118048[/C][C]-0.6984[/C][C]0.244776[/C][/ROW]
[ROW][C]5[/C][C]0.298867[/C][C]1.7681[/C][C]0.042879[/C][/ROW]
[ROW][C]6[/C][C]0.239299[/C][C]1.4157[/C][C]0.082848[/C][/ROW]
[ROW][C]7[/C][C]0.015625[/C][C]0.0924[/C][C]0.463439[/C][/ROW]
[ROW][C]8[/C][C]-0.188959[/C][C]-1.1179[/C][C]0.135613[/C][/ROW]
[ROW][C]9[/C][C]-0.115462[/C][C]-0.6831[/C][C]0.249526[/C][/ROW]
[ROW][C]10[/C][C]0.134716[/C][C]0.797[/C][C]0.215415[/C][/ROW]
[ROW][C]11[/C][C]0.098756[/C][C]0.5842[/C][C]0.2814[/C][/ROW]
[ROW][C]12[/C][C]-0.139071[/C][C]-0.8228[/C][C]0.208108[/C][/ROW]
[ROW][C]13[/C][C]-0.288196[/C][C]-1.705[/C][C]0.048529[/C][/ROW]
[ROW][C]14[/C][C]-0.192786[/C][C]-1.1405[/C][C]0.130903[/C][/ROW]
[ROW][C]15[/C][C]0.055969[/C][C]0.3311[/C][C]0.371265[/C][/ROW]
[ROW][C]16[/C][C]0.178094[/C][C]1.0536[/C][C]0.149639[/C][/ROW]
[ROW][C]17[/C][C]0.023982[/C][C]0.1419[/C][C]0.443995[/C][/ROW]
[ROW][C]18[/C][C]-0.241136[/C][C]-1.4266[/C][C]0.081281[/C][/ROW]
[ROW][C]19[/C][C]-0.187162[/C][C]-1.1073[/C][C]0.137866[/C][/ROW]
[ROW][C]20[/C][C]-0.077228[/C][C]-0.4569[/C][C]0.325288[/C][/ROW]
[ROW][C]21[/C][C]0.082439[/C][C]0.4877[/C][C]0.314397[/C][/ROW]
[ROW][C]22[/C][C]0.101699[/C][C]0.6017[/C][C]0.275638[/C][/ROW]
[ROW][C]23[/C][C]0.027012[/C][C]0.1598[/C][C]0.436977[/C][/ROW]
[ROW][C]24[/C][C]-0.004481[/C][C]-0.0265[/C][C]0.4895[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34303&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34303&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	0.343419	2.0317	0.024915
2	-0.065236	-0.3859	0.350939
3	-0.256777	-1.5191	0.068858
4	-0.118048	-0.6984	0.244776
5	0.298867	1.7681	0.042879
6	0.239299	1.4157	0.082848
7	0.015625	0.0924	0.463439
8	-0.188959	-1.1179	0.135613
9	-0.115462	-0.6831	0.249526
10	0.134716	0.797	0.215415
11	0.098756	0.5842	0.2814
12	-0.139071	-0.8228	0.208108
13	-0.288196	-1.705	0.048529
14	-0.192786	-1.1405	0.130903
15	0.055969	0.3311	0.371265
16	0.178094	1.0536	0.149639
17	0.023982	0.1419	0.443995
18	-0.241136	-1.4266	0.081281
19	-0.187162	-1.1073	0.137866
20	-0.077228	-0.4569	0.325288
21	0.082439	0.4877	0.314397
22	0.101699	0.6017	0.275638
23	0.027012	0.1598	0.436977
24	-0.004481	-0.0265	0.4895

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.343419	2.0317	0.024915
2	-0.207663	-1.2286	0.113718
3	-0.18768	-1.1103	0.137214
4	0.042272	0.2501	0.401992
5	0.349931	2.0702	0.022937
6	-0.062378	-0.369	0.357162
7	-0.083156	-0.492	0.312911
8	-0.038181	-0.2259	0.411304
9	0.104701	0.6194	0.269826
10	0.06164	0.3647	0.358777
11	-0.153082	-0.9056	0.185658
12	-0.223572	-1.3227	0.097262
13	-0.048488	-0.2869	0.387957
14	0.02403	0.1422	0.443882
15	-0.029956	-0.1772	0.430177
16	-0.011066	-0.0655	0.474088
17	-0.016651	-0.0985	0.461046
18	-0.100631	-0.5953	0.277723
19	0.079516	0.4704	0.320486
20	-0.112643	-0.6664	0.254762
21	-0.052964	-0.3133	0.377941
22	0.052825	0.3125	0.37825
23	0.15813	0.9355	0.177967
24	-0.005972	-0.0353	0.486008

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.343419 & 2.0317 & 0.024915 \tabularnewline
2 & -0.207663 & -1.2286 & 0.113718 \tabularnewline
3 & -0.18768 & -1.1103 & 0.137214 \tabularnewline
4 & 0.042272 & 0.2501 & 0.401992 \tabularnewline
5 & 0.349931 & 2.0702 & 0.022937 \tabularnewline
6 & -0.062378 & -0.369 & 0.357162 \tabularnewline
7 & -0.083156 & -0.492 & 0.312911 \tabularnewline
8 & -0.038181 & -0.2259 & 0.411304 \tabularnewline
9 & 0.104701 & 0.6194 & 0.269826 \tabularnewline
10 & 0.06164 & 0.3647 & 0.358777 \tabularnewline
11 & -0.153082 & -0.9056 & 0.185658 \tabularnewline
12 & -0.223572 & -1.3227 & 0.097262 \tabularnewline
13 & -0.048488 & -0.2869 & 0.387957 \tabularnewline
14 & 0.02403 & 0.1422 & 0.443882 \tabularnewline
15 & -0.029956 & -0.1772 & 0.430177 \tabularnewline
16 & -0.011066 & -0.0655 & 0.474088 \tabularnewline
17 & -0.016651 & -0.0985 & 0.461046 \tabularnewline
18 & -0.100631 & -0.5953 & 0.277723 \tabularnewline
19 & 0.079516 & 0.4704 & 0.320486 \tabularnewline
20 & -0.112643 & -0.6664 & 0.254762 \tabularnewline
21 & -0.052964 & -0.3133 & 0.377941 \tabularnewline
22 & 0.052825 & 0.3125 & 0.37825 \tabularnewline
23 & 0.15813 & 0.9355 & 0.177967 \tabularnewline
24 & -0.005972 & -0.0353 & 0.486008 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34303&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]0.343419[/C][C]2.0317[/C][C]0.024915[/C][/ROW]
[ROW][C]2[/C][C]-0.207663[/C][C]-1.2286[/C][C]0.113718[/C][/ROW]
[ROW][C]3[/C][C]-0.18768[/C][C]-1.1103[/C][C]0.137214[/C][/ROW]
[ROW][C]4[/C][C]0.042272[/C][C]0.2501[/C][C]0.401992[/C][/ROW]
[ROW][C]5[/C][C]0.349931[/C][C]2.0702[/C][C]0.022937[/C][/ROW]
[ROW][C]6[/C][C]-0.062378[/C][C]-0.369[/C][C]0.357162[/C][/ROW]
[ROW][C]7[/C][C]-0.083156[/C][C]-0.492[/C][C]0.312911[/C][/ROW]
[ROW][C]8[/C][C]-0.038181[/C][C]-0.2259[/C][C]0.411304[/C][/ROW]
[ROW][C]9[/C][C]0.104701[/C][C]0.6194[/C][C]0.269826[/C][/ROW]
[ROW][C]10[/C][C]0.06164[/C][C]0.3647[/C][C]0.358777[/C][/ROW]
[ROW][C]11[/C][C]-0.153082[/C][C]-0.9056[/C][C]0.185658[/C][/ROW]
[ROW][C]12[/C][C]-0.223572[/C][C]-1.3227[/C][C]0.097262[/C][/ROW]
[ROW][C]13[/C][C]-0.048488[/C][C]-0.2869[/C][C]0.387957[/C][/ROW]
[ROW][C]14[/C][C]0.02403[/C][C]0.1422[/C][C]0.443882[/C][/ROW]
[ROW][C]15[/C][C]-0.029956[/C][C]-0.1772[/C][C]0.430177[/C][/ROW]
[ROW][C]16[/C][C]-0.011066[/C][C]-0.0655[/C][C]0.474088[/C][/ROW]
[ROW][C]17[/C][C]-0.016651[/C][C]-0.0985[/C][C]0.461046[/C][/ROW]
[ROW][C]18[/C][C]-0.100631[/C][C]-0.5953[/C][C]0.277723[/C][/ROW]
[ROW][C]19[/C][C]0.079516[/C][C]0.4704[/C][C]0.320486[/C][/ROW]
[ROW][C]20[/C][C]-0.112643[/C][C]-0.6664[/C][C]0.254762[/C][/ROW]
[ROW][C]21[/C][C]-0.052964[/C][C]-0.3133[/C][C]0.377941[/C][/ROW]
[ROW][C]22[/C][C]0.052825[/C][C]0.3125[/C][C]0.37825[/C][/ROW]
[ROW][C]23[/C][C]0.15813[/C][C]0.9355[/C][C]0.177967[/C][/ROW]
[ROW][C]24[/C][C]-0.005972[/C][C]-0.0353[/C][C]0.486008[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34303&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34303&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	0.343419	2.0317	0.024915
2	-0.207663	-1.2286	0.113718
3	-0.18768	-1.1103	0.137214
4	0.042272	0.2501	0.401992
5	0.349931	2.0702	0.022937
6	-0.062378	-0.369	0.357162
7	-0.083156	-0.492	0.312911
8	-0.038181	-0.2259	0.411304
9	0.104701	0.6194	0.269826
10	0.06164	0.3647	0.358777
11	-0.153082	-0.9056	0.185658
12	-0.223572	-1.3227	0.097262
13	-0.048488	-0.2869	0.387957
14	0.02403	0.1422	0.443882
15	-0.029956	-0.1772	0.430177
16	-0.011066	-0.0655	0.474088
17	-0.016651	-0.0985	0.461046
18	-0.100631	-0.5953	0.277723
19	0.079516	0.4704	0.320486
20	-0.112643	-0.6664	0.254762
21	-0.052964	-0.3133	0.377941
22	0.052825	0.3125	0.37825
23	0.15813	0.9355	0.177967
24	-0.005972	-0.0353	0.486008

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1.1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ;

Parameters (R input):

par1 = 24 ; par2 = 1.1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ;

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 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