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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 26 Nov 2010 17:45:24 +0000

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/2010/Nov/26/t1290793489bnpcuo5bp7ee8cc.htm/, Retrieved Wed, 11 Feb 2026 22:39:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102120, Retrieved Wed, 11 Feb 2026 22:39:47 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

314

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

-       [(Partial) Autocorrelation Function] [] [2010-11-26 17:45:24] [465c6c9df074117d1de4b3f3c25f0c87] [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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102120&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102120&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102120&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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.894927	9.8034	0
2	0.789258	8.6459	0
3	0.675842	7.4035	0
4	0.567827	6.2202	0
5	0.480785	5.2667	0
6	0.411253	4.505	8e-06
7	0.403956	4.4251	1.1e-05
8	0.387585	4.2458	2.2e-05
9	0.371695	4.0717	4.2e-05
10	0.361732	3.9626	6.3e-05
11	0.341656	3.7427	0.00014
12	0.342622	3.7532	0.000135
13	0.27681	3.0323	0.001487
14	0.23	2.5195	0.006533
15	0.173012	1.8952	0.030233
16	0.119489	1.3089	0.096528
17	0.081428	0.892	0.187088
18	0.038231	0.4188	0.338056
19	0.017507	0.1918	0.42412
20	-0.014138	-0.1549	0.438592

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.894927 & 9.8034 & 0 \tabularnewline
2 & 0.789258 & 8.6459 & 0 \tabularnewline
3 & 0.675842 & 7.4035 & 0 \tabularnewline
4 & 0.567827 & 6.2202 & 0 \tabularnewline
5 & 0.480785 & 5.2667 & 0 \tabularnewline
6 & 0.411253 & 4.505 & 8e-06 \tabularnewline
7 & 0.403956 & 4.4251 & 1.1e-05 \tabularnewline
8 & 0.387585 & 4.2458 & 2.2e-05 \tabularnewline
9 & 0.371695 & 4.0717 & 4.2e-05 \tabularnewline
10 & 0.361732 & 3.9626 & 6.3e-05 \tabularnewline
11 & 0.341656 & 3.7427 & 0.00014 \tabularnewline
12 & 0.342622 & 3.7532 & 0.000135 \tabularnewline
13 & 0.27681 & 3.0323 & 0.001487 \tabularnewline
14 & 0.23 & 2.5195 & 0.006533 \tabularnewline
15 & 0.173012 & 1.8952 & 0.030233 \tabularnewline
16 & 0.119489 & 1.3089 & 0.096528 \tabularnewline
17 & 0.081428 & 0.892 & 0.187088 \tabularnewline
18 & 0.038231 & 0.4188 & 0.338056 \tabularnewline
19 & 0.017507 & 0.1918 & 0.42412 \tabularnewline
20 & -0.014138 & -0.1549 & 0.438592 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102120&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]0.894927[/C][C]9.8034[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.789258[/C][C]8.6459[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.675842[/C][C]7.4035[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.567827[/C][C]6.2202[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.480785[/C][C]5.2667[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.411253[/C][C]4.505[/C][C]8e-06[/C][/ROW]
[ROW][C]7[/C][C]0.403956[/C][C]4.4251[/C][C]1.1e-05[/C][/ROW]
[ROW][C]8[/C][C]0.387585[/C][C]4.2458[/C][C]2.2e-05[/C][/ROW]
[ROW][C]9[/C][C]0.371695[/C][C]4.0717[/C][C]4.2e-05[/C][/ROW]
[ROW][C]10[/C][C]0.361732[/C][C]3.9626[/C][C]6.3e-05[/C][/ROW]
[ROW][C]11[/C][C]0.341656[/C][C]3.7427[/C][C]0.00014[/C][/ROW]
[ROW][C]12[/C][C]0.342622[/C][C]3.7532[/C][C]0.000135[/C][/ROW]
[ROW][C]13[/C][C]0.27681[/C][C]3.0323[/C][C]0.001487[/C][/ROW]
[ROW][C]14[/C][C]0.23[/C][C]2.5195[/C][C]0.006533[/C][/ROW]
[ROW][C]15[/C][C]0.173012[/C][C]1.8952[/C][C]0.030233[/C][/ROW]
[ROW][C]16[/C][C]0.119489[/C][C]1.3089[/C][C]0.096528[/C][/ROW]
[ROW][C]17[/C][C]0.081428[/C][C]0.892[/C][C]0.187088[/C][/ROW]
[ROW][C]18[/C][C]0.038231[/C][C]0.4188[/C][C]0.338056[/C][/ROW]
[ROW][C]19[/C][C]0.017507[/C][C]0.1918[/C][C]0.42412[/C][/ROW]
[ROW][C]20[/C][C]-0.014138[/C][C]-0.1549[/C][C]0.438592[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102120&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102120&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	0.894927	9.8034	0
2	0.789258	8.6459	0
3	0.675842	7.4035	0
4	0.567827	6.2202	0
5	0.480785	5.2667	0
6	0.411253	4.505	8e-06
7	0.403956	4.4251	1.1e-05
8	0.387585	4.2458	2.2e-05
9	0.371695	4.0717	4.2e-05
10	0.361732	3.9626	6.3e-05
11	0.341656	3.7427	0.00014
12	0.342622	3.7532	0.000135
13	0.27681	3.0323	0.001487
14	0.23	2.5195	0.006533
15	0.173012	1.8952	0.030233
16	0.119489	1.3089	0.096528
17	0.081428	0.892	0.187088
18	0.038231	0.4188	0.338056
19	0.017507	0.1918	0.42412
20	-0.014138	-0.1549	0.438592

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.894927	9.8034	0
2	-0.058442	-0.6402	0.261631
3	-0.098094	-1.0746	0.142363
4	-0.040194	-0.4403	0.330254
5	0.039277	0.4303	0.333891
6	0.027235	0.2983	0.382978
7	0.257553	2.8213	0.002799
8	-0.068212	-0.7472	0.228196
9	-0.032879	-0.3602	0.359677
10	0.036247	0.3971	0.346013
11	-0.014402	-0.1578	0.437453
12	0.131582	1.4414	0.076037
13	-0.291453	-3.1927	9e-04
14	0.048358	0.5297	0.298638
15	-0.073261	-0.8025	0.211914
16	0.018799	0.2059	0.418597
17	0.011443	0.1254	0.450226
18	-0.050768	-0.5561	0.289577
19	-0.082436	-0.903	0.184156
20	-0.030758	-0.3369	0.368377

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.894927 & 9.8034 & 0 \tabularnewline
2 & -0.058442 & -0.6402 & 0.261631 \tabularnewline
3 & -0.098094 & -1.0746 & 0.142363 \tabularnewline
4 & -0.040194 & -0.4403 & 0.330254 \tabularnewline
5 & 0.039277 & 0.4303 & 0.333891 \tabularnewline
6 & 0.027235 & 0.2983 & 0.382978 \tabularnewline
7 & 0.257553 & 2.8213 & 0.002799 \tabularnewline
8 & -0.068212 & -0.7472 & 0.228196 \tabularnewline
9 & -0.032879 & -0.3602 & 0.359677 \tabularnewline
10 & 0.036247 & 0.3971 & 0.346013 \tabularnewline
11 & -0.014402 & -0.1578 & 0.437453 \tabularnewline
12 & 0.131582 & 1.4414 & 0.076037 \tabularnewline
13 & -0.291453 & -3.1927 & 9e-04 \tabularnewline
14 & 0.048358 & 0.5297 & 0.298638 \tabularnewline
15 & -0.073261 & -0.8025 & 0.211914 \tabularnewline
16 & 0.018799 & 0.2059 & 0.418597 \tabularnewline
17 & 0.011443 & 0.1254 & 0.450226 \tabularnewline
18 & -0.050768 & -0.5561 & 0.289577 \tabularnewline
19 & -0.082436 & -0.903 & 0.184156 \tabularnewline
20 & -0.030758 & -0.3369 & 0.368377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102120&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]0.894927[/C][C]9.8034[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.058442[/C][C]-0.6402[/C][C]0.261631[/C][/ROW]
[ROW][C]3[/C][C]-0.098094[/C][C]-1.0746[/C][C]0.142363[/C][/ROW]
[ROW][C]4[/C][C]-0.040194[/C][C]-0.4403[/C][C]0.330254[/C][/ROW]
[ROW][C]5[/C][C]0.039277[/C][C]0.4303[/C][C]0.333891[/C][/ROW]
[ROW][C]6[/C][C]0.027235[/C][C]0.2983[/C][C]0.382978[/C][/ROW]
[ROW][C]7[/C][C]0.257553[/C][C]2.8213[/C][C]0.002799[/C][/ROW]
[ROW][C]8[/C][C]-0.068212[/C][C]-0.7472[/C][C]0.228196[/C][/ROW]
[ROW][C]9[/C][C]-0.032879[/C][C]-0.3602[/C][C]0.359677[/C][/ROW]
[ROW][C]10[/C][C]0.036247[/C][C]0.3971[/C][C]0.346013[/C][/ROW]
[ROW][C]11[/C][C]-0.014402[/C][C]-0.1578[/C][C]0.437453[/C][/ROW]
[ROW][C]12[/C][C]0.131582[/C][C]1.4414[/C][C]0.076037[/C][/ROW]
[ROW][C]13[/C][C]-0.291453[/C][C]-3.1927[/C][C]9e-04[/C][/ROW]
[ROW][C]14[/C][C]0.048358[/C][C]0.5297[/C][C]0.298638[/C][/ROW]
[ROW][C]15[/C][C]-0.073261[/C][C]-0.8025[/C][C]0.211914[/C][/ROW]
[ROW][C]16[/C][C]0.018799[/C][C]0.2059[/C][C]0.418597[/C][/ROW]
[ROW][C]17[/C][C]0.011443[/C][C]0.1254[/C][C]0.450226[/C][/ROW]
[ROW][C]18[/C][C]-0.050768[/C][C]-0.5561[/C][C]0.289577[/C][/ROW]
[ROW][C]19[/C][C]-0.082436[/C][C]-0.903[/C][C]0.184156[/C][/ROW]
[ROW][C]20[/C][C]-0.030758[/C][C]-0.3369[/C][C]0.368377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102120&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102120&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	0.894927	9.8034	0
2	-0.058442	-0.6402	0.261631
3	-0.098094	-1.0746	0.142363
4	-0.040194	-0.4403	0.330254
5	0.039277	0.4303	0.333891
6	0.027235	0.2983	0.382978
7	0.257553	2.8213	0.002799
8	-0.068212	-0.7472	0.228196
9	-0.032879	-0.3602	0.359677
10	0.036247	0.3971	0.346013
11	-0.014402	-0.1578	0.437453
12	0.131582	1.4414	0.076037
13	-0.291453	-3.1927	9e-04
14	0.048358	0.5297	0.298638
15	-0.073261	-0.8025	0.211914
16	0.018799	0.2059	0.418597
17	0.011443	0.1254	0.450226
18	-0.050768	-0.5561	0.289577
19	-0.082436	-0.903	0.184156
20	-0.030758	-0.3369	0.368377

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code