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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, 03 Dec 2008 06:40:14 -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/2008/Dec/03/t12283116315cwiqoybjpmm0to.htm/, Retrieved Mon, 25 May 2026 19:04:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28704, Retrieved Mon, 25 May 2026 19:04:13 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

461

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

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
- RMPD  [Standard Deviation-Mean Plot] [q5] [2008-12-03 13:15:06] [3ffd109c9e040b1ae7e5dbe576d4698c]
- RMPD    [(Partial) Autocorrelation Function] [q8] [2008-12-03 13:16:51] [3ffd109c9e040b1ae7e5dbe576d4698c]
- RMP       [Variance Reduction Matrix] [q8] [2008-12-03 13:29:02] [3ffd109c9e040b1ae7e5dbe576d4698c]
-    D        [Variance Reduction Matrix] [q8] [2008-12-03 13:37:20] [3ffd109c9e040b1ae7e5dbe576d4698c]
- RM              [(Partial) Autocorrelation Function] [q8] [2008-12-03 13:40:14] [962e6c9020896982bc8283b8971710a9] [Current]
- RM                [Spectral Analysis] [q8] [2008-12-03 13:42:10] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- RM D              [Cross Correlation Function] [q9] [2008-12-03 13:45:45] [3ffd109c9e040b1ae7e5dbe576d4698c] 

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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=28704&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=28704&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28704&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	0.000219	0.0015	0.499398
2	0.020616	0.1428	0.44351
3	0.085714	0.5938	0.277703
4	0.127604	0.8841	0.190534
5	-0.005336	-0.037	0.485332
6	0.017792	0.1233	0.451205
7	-0.015515	-0.1075	0.457424
8	0.057156	0.396	0.346935
9	-0.002827	-0.0196	0.492226
10	-0.106007	-0.7344	0.233128
11	0.177678	1.231	0.112163
12	-0.088972	-0.6164	0.270266
13	-0.180867	-1.2531	0.108123
14	0.149246	1.034	0.153158
15	-0.040161	-0.2782	0.391011
16	-0.12324	-0.8538	0.19872
17	-0.064879	-0.4495	0.327549

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.000219 & 0.0015 & 0.499398 \tabularnewline
2 & 0.020616 & 0.1428 & 0.44351 \tabularnewline
3 & 0.085714 & 0.5938 & 0.277703 \tabularnewline
4 & 0.127604 & 0.8841 & 0.190534 \tabularnewline
5 & -0.005336 & -0.037 & 0.485332 \tabularnewline
6 & 0.017792 & 0.1233 & 0.451205 \tabularnewline
7 & -0.015515 & -0.1075 & 0.457424 \tabularnewline
8 & 0.057156 & 0.396 & 0.346935 \tabularnewline
9 & -0.002827 & -0.0196 & 0.492226 \tabularnewline
10 & -0.106007 & -0.7344 & 0.233128 \tabularnewline
11 & 0.177678 & 1.231 & 0.112163 \tabularnewline
12 & -0.088972 & -0.6164 & 0.270266 \tabularnewline
13 & -0.180867 & -1.2531 & 0.108123 \tabularnewline
14 & 0.149246 & 1.034 & 0.153158 \tabularnewline
15 & -0.040161 & -0.2782 & 0.391011 \tabularnewline
16 & -0.12324 & -0.8538 & 0.19872 \tabularnewline
17 & -0.064879 & -0.4495 & 0.327549 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28704&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]0.000219[/C][C]0.0015[/C][C]0.499398[/C][/ROW]
[ROW][C]2[/C][C]0.020616[/C][C]0.1428[/C][C]0.44351[/C][/ROW]
[ROW][C]3[/C][C]0.085714[/C][C]0.5938[/C][C]0.277703[/C][/ROW]
[ROW][C]4[/C][C]0.127604[/C][C]0.8841[/C][C]0.190534[/C][/ROW]
[ROW][C]5[/C][C]-0.005336[/C][C]-0.037[/C][C]0.485332[/C][/ROW]
[ROW][C]6[/C][C]0.017792[/C][C]0.1233[/C][C]0.451205[/C][/ROW]
[ROW][C]7[/C][C]-0.015515[/C][C]-0.1075[/C][C]0.457424[/C][/ROW]
[ROW][C]8[/C][C]0.057156[/C][C]0.396[/C][C]0.346935[/C][/ROW]
[ROW][C]9[/C][C]-0.002827[/C][C]-0.0196[/C][C]0.492226[/C][/ROW]
[ROW][C]10[/C][C]-0.106007[/C][C]-0.7344[/C][C]0.233128[/C][/ROW]
[ROW][C]11[/C][C]0.177678[/C][C]1.231[/C][C]0.112163[/C][/ROW]
[ROW][C]12[/C][C]-0.088972[/C][C]-0.6164[/C][C]0.270266[/C][/ROW]
[ROW][C]13[/C][C]-0.180867[/C][C]-1.2531[/C][C]0.108123[/C][/ROW]
[ROW][C]14[/C][C]0.149246[/C][C]1.034[/C][C]0.153158[/C][/ROW]
[ROW][C]15[/C][C]-0.040161[/C][C]-0.2782[/C][C]0.391011[/C][/ROW]
[ROW][C]16[/C][C]-0.12324[/C][C]-0.8538[/C][C]0.19872[/C][/ROW]
[ROW][C]17[/C][C]-0.064879[/C][C]-0.4495[/C][C]0.327549[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28704&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28704&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	0.000219	0.0015	0.499398
2	0.020616	0.1428	0.44351
3	0.085714	0.5938	0.277703
4	0.127604	0.8841	0.190534
5	-0.005336	-0.037	0.485332
6	0.017792	0.1233	0.451205
7	-0.015515	-0.1075	0.457424
8	0.057156	0.396	0.346935
9	-0.002827	-0.0196	0.492226
10	-0.106007	-0.7344	0.233128
11	0.177678	1.231	0.112163
12	-0.088972	-0.6164	0.270266
13	-0.180867	-1.2531	0.108123
14	0.149246	1.034	0.153158
15	-0.040161	-0.2782	0.391011
16	-0.12324	-0.8538	0.19872
17	-0.064879	-0.4495	0.327549

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.000219	0.0015	0.499398
2	0.020616	0.1428	0.44351
3	0.085741	0.594	0.277639
4	0.128291	0.8888	0.189265
5	-0.007248	-0.0502	0.480081
6	0.005473	0.0379	0.484955
7	-0.037885	-0.2625	0.397039
8	0.041924	0.2905	0.386359
9	-0.001267	-0.0088	0.496515
10	-0.109112	-0.7559	0.226687
11	0.180853	1.253	0.10814
12	-0.104731	-0.7256	0.235805
13	-0.178333	-1.2355	0.111323
14	0.173611	1.2028	0.117475
15	-0.079812	-0.553	0.291431
16	-0.091063	-0.6309	0.265549
17	-0.037274	-0.2582	0.398663

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.000219 & 0.0015 & 0.499398 \tabularnewline
2 & 0.020616 & 0.1428 & 0.44351 \tabularnewline
3 & 0.085741 & 0.594 & 0.277639 \tabularnewline
4 & 0.128291 & 0.8888 & 0.189265 \tabularnewline
5 & -0.007248 & -0.0502 & 0.480081 \tabularnewline
6 & 0.005473 & 0.0379 & 0.484955 \tabularnewline
7 & -0.037885 & -0.2625 & 0.397039 \tabularnewline
8 & 0.041924 & 0.2905 & 0.386359 \tabularnewline
9 & -0.001267 & -0.0088 & 0.496515 \tabularnewline
10 & -0.109112 & -0.7559 & 0.226687 \tabularnewline
11 & 0.180853 & 1.253 & 0.10814 \tabularnewline
12 & -0.104731 & -0.7256 & 0.235805 \tabularnewline
13 & -0.178333 & -1.2355 & 0.111323 \tabularnewline
14 & 0.173611 & 1.2028 & 0.117475 \tabularnewline
15 & -0.079812 & -0.553 & 0.291431 \tabularnewline
16 & -0.091063 & -0.6309 & 0.265549 \tabularnewline
17 & -0.037274 & -0.2582 & 0.398663 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28704&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]0.000219[/C][C]0.0015[/C][C]0.499398[/C][/ROW]
[ROW][C]2[/C][C]0.020616[/C][C]0.1428[/C][C]0.44351[/C][/ROW]
[ROW][C]3[/C][C]0.085741[/C][C]0.594[/C][C]0.277639[/C][/ROW]
[ROW][C]4[/C][C]0.128291[/C][C]0.8888[/C][C]0.189265[/C][/ROW]
[ROW][C]5[/C][C]-0.007248[/C][C]-0.0502[/C][C]0.480081[/C][/ROW]
[ROW][C]6[/C][C]0.005473[/C][C]0.0379[/C][C]0.484955[/C][/ROW]
[ROW][C]7[/C][C]-0.037885[/C][C]-0.2625[/C][C]0.397039[/C][/ROW]
[ROW][C]8[/C][C]0.041924[/C][C]0.2905[/C][C]0.386359[/C][/ROW]
[ROW][C]9[/C][C]-0.001267[/C][C]-0.0088[/C][C]0.496515[/C][/ROW]
[ROW][C]10[/C][C]-0.109112[/C][C]-0.7559[/C][C]0.226687[/C][/ROW]
[ROW][C]11[/C][C]0.180853[/C][C]1.253[/C][C]0.10814[/C][/ROW]
[ROW][C]12[/C][C]-0.104731[/C][C]-0.7256[/C][C]0.235805[/C][/ROW]
[ROW][C]13[/C][C]-0.178333[/C][C]-1.2355[/C][C]0.111323[/C][/ROW]
[ROW][C]14[/C][C]0.173611[/C][C]1.2028[/C][C]0.117475[/C][/ROW]
[ROW][C]15[/C][C]-0.079812[/C][C]-0.553[/C][C]0.291431[/C][/ROW]
[ROW][C]16[/C][C]-0.091063[/C][C]-0.6309[/C][C]0.265549[/C][/ROW]
[ROW][C]17[/C][C]-0.037274[/C][C]-0.2582[/C][C]0.398663[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28704&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28704&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	0.000219	0.0015	0.499398
2	0.020616	0.1428	0.44351
3	0.085741	0.594	0.277639
4	0.128291	0.8888	0.189265
5	-0.007248	-0.0502	0.480081
6	0.005473	0.0379	0.484955
7	-0.037885	-0.2625	0.397039
8	0.041924	0.2905	0.386359
9	-0.001267	-0.0088	0.496515
10	-0.109112	-0.7559	0.226687
11	0.180853	1.253	0.10814
12	-0.104731	-0.7256	0.235805
13	-0.178333	-1.2355	0.111323
14	0.173611	1.2028	0.117475
15	-0.079812	-0.553	0.291431
16	-0.091063	-0.6309	0.265549
17	-0.037274	-0.2582	0.398663

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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 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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code