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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 19 May 2011 19:15:43 +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/2011/May/19/t1305832349eeg519rdlccik22.htm/, Retrieved Sat, 11 May 2024 16:15:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122206, Retrieved Sat, 11 May 2024 16:15:50 +0000

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No (this computation is public)

User-defined keywords

KDGP2W62

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

-       [(Partial) Autocorrelation Function] [Verbetering opgav...] [2011-05-19 19:15:43] [764118764852521a1756ded753a212d7] [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	'George Udny Yule' @ 216.218.223.82

\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 & 'George Udny Yule' @ 216.218.223.82 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122206&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]'George Udny Yule' @ 216.218.223.82[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122206&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122206&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	'George Udny Yule' @ 216.218.223.82

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.78046	6.6683	0
2	0.431441	3.6862	0.000217
3	0.160049	1.3675	0.087838
4	0.048566	0.4149	0.3397
5	0.064944	0.5549	0.290335
6	0.097178	0.8303	0.20454
7	0.069424	0.5932	0.277454
8	0.024086	0.2058	0.418764
9	0.063655	0.5439	0.294093
10	0.224924	1.9218	0.02927
11	0.458455	3.917	1e-04
12	0.587529	5.0198	2e-06
13	0.387539	3.3111	0.000723
14	0.094066	0.8037	0.21209
15	-0.125138	-1.0692	0.144256
16	-0.209725	-1.7919	0.038647
17	-0.192443	-1.6442	0.052214
18	-0.173853	-1.4854	0.070872

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.78046 & 6.6683 & 0 \tabularnewline
2 & 0.431441 & 3.6862 & 0.000217 \tabularnewline
3 & 0.160049 & 1.3675 & 0.087838 \tabularnewline
4 & 0.048566 & 0.4149 & 0.3397 \tabularnewline
5 & 0.064944 & 0.5549 & 0.290335 \tabularnewline
6 & 0.097178 & 0.8303 & 0.20454 \tabularnewline
7 & 0.069424 & 0.5932 & 0.277454 \tabularnewline
8 & 0.024086 & 0.2058 & 0.418764 \tabularnewline
9 & 0.063655 & 0.5439 & 0.294093 \tabularnewline
10 & 0.224924 & 1.9218 & 0.02927 \tabularnewline
11 & 0.458455 & 3.917 & 1e-04 \tabularnewline
12 & 0.587529 & 5.0198 & 2e-06 \tabularnewline
13 & 0.387539 & 3.3111 & 0.000723 \tabularnewline
14 & 0.094066 & 0.8037 & 0.21209 \tabularnewline
15 & -0.125138 & -1.0692 & 0.144256 \tabularnewline
16 & -0.209725 & -1.7919 & 0.038647 \tabularnewline
17 & -0.192443 & -1.6442 & 0.052214 \tabularnewline
18 & -0.173853 & -1.4854 & 0.070872 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122206&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]0.78046[/C][C]6.6683[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.431441[/C][C]3.6862[/C][C]0.000217[/C][/ROW]
[ROW][C]3[/C][C]0.160049[/C][C]1.3675[/C][C]0.087838[/C][/ROW]
[ROW][C]4[/C][C]0.048566[/C][C]0.4149[/C][C]0.3397[/C][/ROW]
[ROW][C]5[/C][C]0.064944[/C][C]0.5549[/C][C]0.290335[/C][/ROW]
[ROW][C]6[/C][C]0.097178[/C][C]0.8303[/C][C]0.20454[/C][/ROW]
[ROW][C]7[/C][C]0.069424[/C][C]0.5932[/C][C]0.277454[/C][/ROW]
[ROW][C]8[/C][C]0.024086[/C][C]0.2058[/C][C]0.418764[/C][/ROW]
[ROW][C]9[/C][C]0.063655[/C][C]0.5439[/C][C]0.294093[/C][/ROW]
[ROW][C]10[/C][C]0.224924[/C][C]1.9218[/C][C]0.02927[/C][/ROW]
[ROW][C]11[/C][C]0.458455[/C][C]3.917[/C][C]1e-04[/C][/ROW]
[ROW][C]12[/C][C]0.587529[/C][C]5.0198[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]0.387539[/C][C]3.3111[/C][C]0.000723[/C][/ROW]
[ROW][C]14[/C][C]0.094066[/C][C]0.8037[/C][C]0.21209[/C][/ROW]
[ROW][C]15[/C][C]-0.125138[/C][C]-1.0692[/C][C]0.144256[/C][/ROW]
[ROW][C]16[/C][C]-0.209725[/C][C]-1.7919[/C][C]0.038647[/C][/ROW]
[ROW][C]17[/C][C]-0.192443[/C][C]-1.6442[/C][C]0.052214[/C][/ROW]
[ROW][C]18[/C][C]-0.173853[/C][C]-1.4854[/C][C]0.070872[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122206&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122206&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	0.78046	6.6683	0
2	0.431441	3.6862	0.000217
3	0.160049	1.3675	0.087838
4	0.048566	0.4149	0.3397
5	0.064944	0.5549	0.290335
6	0.097178	0.8303	0.20454
7	0.069424	0.5932	0.277454
8	0.024086	0.2058	0.418764
9	0.063655	0.5439	0.294093
10	0.224924	1.9218	0.02927
11	0.458455	3.917	1e-04
12	0.587529	5.0198	2e-06
13	0.387539	3.3111	0.000723
14	0.094066	0.8037	0.21209
15	-0.125138	-1.0692	0.144256
16	-0.209725	-1.7919	0.038647
17	-0.192443	-1.6442	0.052214
18	-0.173853	-1.4854	0.070872

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.78046	6.6683	0
2	-0.454555	-3.8837	0.000112
3	0.080712	0.6896	0.246316
4	0.109234	0.9333	0.176873
5	0.07056	0.6029	0.274234
6	-0.063073	-0.5389	0.2958
7	-0.077813	-0.6648	0.254125
8	0.075962	0.649	0.259182
9	0.227311	1.9421	0.027989
10	0.249525	2.1319	0.018188
11	0.2829	2.4171	0.009072
12	-0.006079	-0.0519	0.47936
13	-0.606574	-5.1826	1e-06
14	0.22904	1.9569	0.027091
15	-0.035079	-0.2997	0.382623
16	-0.167451	-1.4307	0.078391
17	-0.145145	-1.2401	0.109451
18	-0.136872	-1.1694	0.123017

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.78046 & 6.6683 & 0 \tabularnewline
2 & -0.454555 & -3.8837 & 0.000112 \tabularnewline
3 & 0.080712 & 0.6896 & 0.246316 \tabularnewline
4 & 0.109234 & 0.9333 & 0.176873 \tabularnewline
5 & 0.07056 & 0.6029 & 0.274234 \tabularnewline
6 & -0.063073 & -0.5389 & 0.2958 \tabularnewline
7 & -0.077813 & -0.6648 & 0.254125 \tabularnewline
8 & 0.075962 & 0.649 & 0.259182 \tabularnewline
9 & 0.227311 & 1.9421 & 0.027989 \tabularnewline
10 & 0.249525 & 2.1319 & 0.018188 \tabularnewline
11 & 0.2829 & 2.4171 & 0.009072 \tabularnewline
12 & -0.006079 & -0.0519 & 0.47936 \tabularnewline
13 & -0.606574 & -5.1826 & 1e-06 \tabularnewline
14 & 0.22904 & 1.9569 & 0.027091 \tabularnewline
15 & -0.035079 & -0.2997 & 0.382623 \tabularnewline
16 & -0.167451 & -1.4307 & 0.078391 \tabularnewline
17 & -0.145145 & -1.2401 & 0.109451 \tabularnewline
18 & -0.136872 & -1.1694 & 0.123017 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122206&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]0.78046[/C][C]6.6683[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.454555[/C][C]-3.8837[/C][C]0.000112[/C][/ROW]
[ROW][C]3[/C][C]0.080712[/C][C]0.6896[/C][C]0.246316[/C][/ROW]
[ROW][C]4[/C][C]0.109234[/C][C]0.9333[/C][C]0.176873[/C][/ROW]
[ROW][C]5[/C][C]0.07056[/C][C]0.6029[/C][C]0.274234[/C][/ROW]
[ROW][C]6[/C][C]-0.063073[/C][C]-0.5389[/C][C]0.2958[/C][/ROW]
[ROW][C]7[/C][C]-0.077813[/C][C]-0.6648[/C][C]0.254125[/C][/ROW]
[ROW][C]8[/C][C]0.075962[/C][C]0.649[/C][C]0.259182[/C][/ROW]
[ROW][C]9[/C][C]0.227311[/C][C]1.9421[/C][C]0.027989[/C][/ROW]
[ROW][C]10[/C][C]0.249525[/C][C]2.1319[/C][C]0.018188[/C][/ROW]
[ROW][C]11[/C][C]0.2829[/C][C]2.4171[/C][C]0.009072[/C][/ROW]
[ROW][C]12[/C][C]-0.006079[/C][C]-0.0519[/C][C]0.47936[/C][/ROW]
[ROW][C]13[/C][C]-0.606574[/C][C]-5.1826[/C][C]1e-06[/C][/ROW]
[ROW][C]14[/C][C]0.22904[/C][C]1.9569[/C][C]0.027091[/C][/ROW]
[ROW][C]15[/C][C]-0.035079[/C][C]-0.2997[/C][C]0.382623[/C][/ROW]
[ROW][C]16[/C][C]-0.167451[/C][C]-1.4307[/C][C]0.078391[/C][/ROW]
[ROW][C]17[/C][C]-0.145145[/C][C]-1.2401[/C][C]0.109451[/C][/ROW]
[ROW][C]18[/C][C]-0.136872[/C][C]-1.1694[/C][C]0.123017[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122206&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122206&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	0.78046	6.6683	0
2	-0.454555	-3.8837	0.000112
3	0.080712	0.6896	0.246316
4	0.109234	0.9333	0.176873
5	0.07056	0.6029	0.274234
6	-0.063073	-0.5389	0.2958
7	-0.077813	-0.6648	0.254125
8	0.075962	0.649	0.259182
9	0.227311	1.9421	0.027989
10	0.249525	2.1319	0.018188
11	0.2829	2.4171	0.009072
12	-0.006079	-0.0519	0.47936
13	-0.606574	-5.1826	1e-06
14	0.22904	1.9569	0.027091
15	-0.035079	-0.2997	0.382623
16	-0.167451	-1.4307	0.078391
17	-0.145145	-1.2401	0.109451
18	-0.136872	-1.1694	0.123017

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 = 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 ; par8 = ;

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 (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')

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Input Parameters & R Code