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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 07 Aug 2015 18:15:39 +0100

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/2015/Aug/07/t1438967792ob19zxfm74gfyrn.htm/, Retrieved Wed, 15 May 2024 11:41:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279924, Retrieved Wed, 15 May 2024 11:41:49 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

113

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

-       [(Partial) Autocorrelation Function] [] [2015-08-07 17:15:39] [70e23d918d09c907c02097a361cd6415] [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	'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279924&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279924&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279924&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.083714	0.9654	0.16804
2	-0.132507	-1.5281	0.064426
3	0.002133	0.0246	0.490207
4	-0.018075	-0.2085	0.417597
5	-0.064558	-0.7445	0.228936
6	0.045491	0.5246	0.300357
7	-0.002013	-0.0232	0.490756
8	-0.029642	-0.3419	0.366501
9	0.046982	0.5418	0.294423
10	-0.011745	-0.1354	0.446231
11	0.001425	0.0164	0.493454
12	0.052813	0.6091	0.27176
13	0.123913	1.429	0.077669
14	-0.068361	-0.7884	0.215939
15	-0.121476	-1.4009	0.081782
16	0.108727	1.2539	0.106039
17	0.047792	0.5512	0.291222
18	-0.143976	-1.6604	0.049593
19	-0.081451	-0.9393	0.174629
20	0.141613	1.6332	0.0524
21	0.131396	1.5153	0.066031

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.083714 & 0.9654 & 0.16804 \tabularnewline
2 & -0.132507 & -1.5281 & 0.064426 \tabularnewline
3 & 0.002133 & 0.0246 & 0.490207 \tabularnewline
4 & -0.018075 & -0.2085 & 0.417597 \tabularnewline
5 & -0.064558 & -0.7445 & 0.228936 \tabularnewline
6 & 0.045491 & 0.5246 & 0.300357 \tabularnewline
7 & -0.002013 & -0.0232 & 0.490756 \tabularnewline
8 & -0.029642 & -0.3419 & 0.366501 \tabularnewline
9 & 0.046982 & 0.5418 & 0.294423 \tabularnewline
10 & -0.011745 & -0.1354 & 0.446231 \tabularnewline
11 & 0.001425 & 0.0164 & 0.493454 \tabularnewline
12 & 0.052813 & 0.6091 & 0.27176 \tabularnewline
13 & 0.123913 & 1.429 & 0.077669 \tabularnewline
14 & -0.068361 & -0.7884 & 0.215939 \tabularnewline
15 & -0.121476 & -1.4009 & 0.081782 \tabularnewline
16 & 0.108727 & 1.2539 & 0.106039 \tabularnewline
17 & 0.047792 & 0.5512 & 0.291222 \tabularnewline
18 & -0.143976 & -1.6604 & 0.049593 \tabularnewline
19 & -0.081451 & -0.9393 & 0.174629 \tabularnewline
20 & 0.141613 & 1.6332 & 0.0524 \tabularnewline
21 & 0.131396 & 1.5153 & 0.066031 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279924&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]0.083714[/C][C]0.9654[/C][C]0.16804[/C][/ROW]
[ROW][C]2[/C][C]-0.132507[/C][C]-1.5281[/C][C]0.064426[/C][/ROW]
[ROW][C]3[/C][C]0.002133[/C][C]0.0246[/C][C]0.490207[/C][/ROW]
[ROW][C]4[/C][C]-0.018075[/C][C]-0.2085[/C][C]0.417597[/C][/ROW]
[ROW][C]5[/C][C]-0.064558[/C][C]-0.7445[/C][C]0.228936[/C][/ROW]
[ROW][C]6[/C][C]0.045491[/C][C]0.5246[/C][C]0.300357[/C][/ROW]
[ROW][C]7[/C][C]-0.002013[/C][C]-0.0232[/C][C]0.490756[/C][/ROW]
[ROW][C]8[/C][C]-0.029642[/C][C]-0.3419[/C][C]0.366501[/C][/ROW]
[ROW][C]9[/C][C]0.046982[/C][C]0.5418[/C][C]0.294423[/C][/ROW]
[ROW][C]10[/C][C]-0.011745[/C][C]-0.1354[/C][C]0.446231[/C][/ROW]
[ROW][C]11[/C][C]0.001425[/C][C]0.0164[/C][C]0.493454[/C][/ROW]
[ROW][C]12[/C][C]0.052813[/C][C]0.6091[/C][C]0.27176[/C][/ROW]
[ROW][C]13[/C][C]0.123913[/C][C]1.429[/C][C]0.077669[/C][/ROW]
[ROW][C]14[/C][C]-0.068361[/C][C]-0.7884[/C][C]0.215939[/C][/ROW]
[ROW][C]15[/C][C]-0.121476[/C][C]-1.4009[/C][C]0.081782[/C][/ROW]
[ROW][C]16[/C][C]0.108727[/C][C]1.2539[/C][C]0.106039[/C][/ROW]
[ROW][C]17[/C][C]0.047792[/C][C]0.5512[/C][C]0.291222[/C][/ROW]
[ROW][C]18[/C][C]-0.143976[/C][C]-1.6604[/C][C]0.049593[/C][/ROW]
[ROW][C]19[/C][C]-0.081451[/C][C]-0.9393[/C][C]0.174629[/C][/ROW]
[ROW][C]20[/C][C]0.141613[/C][C]1.6332[/C][C]0.0524[/C][/ROW]
[ROW][C]21[/C][C]0.131396[/C][C]1.5153[/C][C]0.066031[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279924&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279924&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	0.083714	0.9654	0.16804
2	-0.132507	-1.5281	0.064426
3	0.002133	0.0246	0.490207
4	-0.018075	-0.2085	0.417597
5	-0.064558	-0.7445	0.228936
6	0.045491	0.5246	0.300357
7	-0.002013	-0.0232	0.490756
8	-0.029642	-0.3419	0.366501
9	0.046982	0.5418	0.294423
10	-0.011745	-0.1354	0.446231
11	0.001425	0.0164	0.493454
12	0.052813	0.6091	0.27176
13	0.123913	1.429	0.077669
14	-0.068361	-0.7884	0.215939
15	-0.121476	-1.4009	0.081782
16	0.108727	1.2539	0.106039
17	0.047792	0.5512	0.291222
18	-0.143976	-1.6604	0.049593
19	-0.081451	-0.9393	0.174629
20	0.141613	1.6332	0.0524
21	0.131396	1.5153	0.066031

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.083714	0.9654	0.16804
2	-0.1405	-1.6203	0.053766
3	0.027271	0.3145	0.376813
4	-0.040643	-0.4687	0.320019
5	-0.05651	-0.6517	0.257857
6	0.050843	0.5864	0.279317
7	-0.028946	-0.3338	0.369518
8	-0.012635	-0.1457	0.442185
9	0.044732	0.5159	0.303401
10	-0.030062	-0.3467	0.364684
11	0.025725	0.2967	0.383587
12	0.040224	0.4639	0.321744
13	0.122807	1.4163	0.079516
14	-0.075998	-0.8765	0.191181
15	-0.086012	-0.9919	0.161514
16	0.122898	1.4173	0.079363
17	0.008252	0.0952	0.462164
18	-0.124028	-1.4304	0.077479
19	-0.073894	-0.8522	0.197821
20	0.142035	1.638	0.05189
21	0.127185	1.4668	0.0724

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.083714 & 0.9654 & 0.16804 \tabularnewline
2 & -0.1405 & -1.6203 & 0.053766 \tabularnewline
3 & 0.027271 & 0.3145 & 0.376813 \tabularnewline
4 & -0.040643 & -0.4687 & 0.320019 \tabularnewline
5 & -0.05651 & -0.6517 & 0.257857 \tabularnewline
6 & 0.050843 & 0.5864 & 0.279317 \tabularnewline
7 & -0.028946 & -0.3338 & 0.369518 \tabularnewline
8 & -0.012635 & -0.1457 & 0.442185 \tabularnewline
9 & 0.044732 & 0.5159 & 0.303401 \tabularnewline
10 & -0.030062 & -0.3467 & 0.364684 \tabularnewline
11 & 0.025725 & 0.2967 & 0.383587 \tabularnewline
12 & 0.040224 & 0.4639 & 0.321744 \tabularnewline
13 & 0.122807 & 1.4163 & 0.079516 \tabularnewline
14 & -0.075998 & -0.8765 & 0.191181 \tabularnewline
15 & -0.086012 & -0.9919 & 0.161514 \tabularnewline
16 & 0.122898 & 1.4173 & 0.079363 \tabularnewline
17 & 0.008252 & 0.0952 & 0.462164 \tabularnewline
18 & -0.124028 & -1.4304 & 0.077479 \tabularnewline
19 & -0.073894 & -0.8522 & 0.197821 \tabularnewline
20 & 0.142035 & 1.638 & 0.05189 \tabularnewline
21 & 0.127185 & 1.4668 & 0.0724 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279924&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]0.083714[/C][C]0.9654[/C][C]0.16804[/C][/ROW]
[ROW][C]2[/C][C]-0.1405[/C][C]-1.6203[/C][C]0.053766[/C][/ROW]
[ROW][C]3[/C][C]0.027271[/C][C]0.3145[/C][C]0.376813[/C][/ROW]
[ROW][C]4[/C][C]-0.040643[/C][C]-0.4687[/C][C]0.320019[/C][/ROW]
[ROW][C]5[/C][C]-0.05651[/C][C]-0.6517[/C][C]0.257857[/C][/ROW]
[ROW][C]6[/C][C]0.050843[/C][C]0.5864[/C][C]0.279317[/C][/ROW]
[ROW][C]7[/C][C]-0.028946[/C][C]-0.3338[/C][C]0.369518[/C][/ROW]
[ROW][C]8[/C][C]-0.012635[/C][C]-0.1457[/C][C]0.442185[/C][/ROW]
[ROW][C]9[/C][C]0.044732[/C][C]0.5159[/C][C]0.303401[/C][/ROW]
[ROW][C]10[/C][C]-0.030062[/C][C]-0.3467[/C][C]0.364684[/C][/ROW]
[ROW][C]11[/C][C]0.025725[/C][C]0.2967[/C][C]0.383587[/C][/ROW]
[ROW][C]12[/C][C]0.040224[/C][C]0.4639[/C][C]0.321744[/C][/ROW]
[ROW][C]13[/C][C]0.122807[/C][C]1.4163[/C][C]0.079516[/C][/ROW]
[ROW][C]14[/C][C]-0.075998[/C][C]-0.8765[/C][C]0.191181[/C][/ROW]
[ROW][C]15[/C][C]-0.086012[/C][C]-0.9919[/C][C]0.161514[/C][/ROW]
[ROW][C]16[/C][C]0.122898[/C][C]1.4173[/C][C]0.079363[/C][/ROW]
[ROW][C]17[/C][C]0.008252[/C][C]0.0952[/C][C]0.462164[/C][/ROW]
[ROW][C]18[/C][C]-0.124028[/C][C]-1.4304[/C][C]0.077479[/C][/ROW]
[ROW][C]19[/C][C]-0.073894[/C][C]-0.8522[/C][C]0.197821[/C][/ROW]
[ROW][C]20[/C][C]0.142035[/C][C]1.638[/C][C]0.05189[/C][/ROW]
[ROW][C]21[/C][C]0.127185[/C][C]1.4668[/C][C]0.0724[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279924&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279924&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	0.083714	0.9654	0.16804
2	-0.1405	-1.6203	0.053766
3	0.027271	0.3145	0.376813
4	-0.040643	-0.4687	0.320019
5	-0.05651	-0.6517	0.257857
6	0.050843	0.5864	0.279317
7	-0.028946	-0.3338	0.369518
8	-0.012635	-0.1457	0.442185
9	0.044732	0.5159	0.303401
10	-0.030062	-0.3467	0.364684
11	0.025725	0.2967	0.383587
12	0.040224	0.4639	0.321744
13	0.122807	1.4163	0.079516
14	-0.075998	-0.8765	0.191181
15	-0.086012	-0.9919	0.161514
16	0.122898	1.4173	0.079363
17	0.008252	0.0952	0.462164
18	-0.124028	-1.4304	0.077479
19	-0.073894	-0.8522	0.197821
20	0.142035	1.638	0.05189
21	0.127185	1.4668	0.0724

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 0.1 ; par2 = 0.9 ; par3 = 0.01 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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