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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 08 Aug 2013 09:16:26 -0400

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/2013/Aug/08/t1375967810mtcy7xthk1f5gf7.htm/, Retrieved Mon, 29 Apr 2024 16:37:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211002, Retrieved Mon, 29 Apr 2024 16:37:08 +0000

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User-defined keywords

Estimated Impact

192

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

-       [(Partial) Autocorrelation Function] [Bezoekers mus�e J...] [2013-08-08 13:16:26] [a5e81fc5b84eaf53b9dc73271fe36a59] [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	3 seconds
R Server	'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211002&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211002&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211002&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	3 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.38501	-3.9826	6.2e-05
2	-0.212872	-2.202	0.014907
3	0.212128	2.1943	0.015189
4	0.000674	0.007	0.497225
5	0.031008	0.3207	0.374514
6	-0.246642	-2.5513	0.006073
7	0.052549	0.5436	0.293935
8	-0.041054	-0.4247	0.335967
9	0.231	2.3895	0.009311
10	-0.246997	-2.555	0.006013
11	-0.263431	-2.7249	0.003757
12	0.754434	7.8039	0
13	-0.309997	-3.2066	0.000886
14	-0.129642	-1.341	0.091375
15	0.141646	1.4652	0.0729
16	0.030771	0.3183	0.375439
17	-0.003644	-0.0377	0.485001
18	-0.17617	-1.8223	0.0356
19	0.014091	0.1458	0.442195
20	-0.064027	-0.6623	0.254601

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.38501 & -3.9826 & 6.2e-05 \tabularnewline
2 & -0.212872 & -2.202 & 0.014907 \tabularnewline
3 & 0.212128 & 2.1943 & 0.015189 \tabularnewline
4 & 0.000674 & 0.007 & 0.497225 \tabularnewline
5 & 0.031008 & 0.3207 & 0.374514 \tabularnewline
6 & -0.246642 & -2.5513 & 0.006073 \tabularnewline
7 & 0.052549 & 0.5436 & 0.293935 \tabularnewline
8 & -0.041054 & -0.4247 & 0.335967 \tabularnewline
9 & 0.231 & 2.3895 & 0.009311 \tabularnewline
10 & -0.246997 & -2.555 & 0.006013 \tabularnewline
11 & -0.263431 & -2.7249 & 0.003757 \tabularnewline
12 & 0.754434 & 7.8039 & 0 \tabularnewline
13 & -0.309997 & -3.2066 & 0.000886 \tabularnewline
14 & -0.129642 & -1.341 & 0.091375 \tabularnewline
15 & 0.141646 & 1.4652 & 0.0729 \tabularnewline
16 & 0.030771 & 0.3183 & 0.375439 \tabularnewline
17 & -0.003644 & -0.0377 & 0.485001 \tabularnewline
18 & -0.17617 & -1.8223 & 0.0356 \tabularnewline
19 & 0.014091 & 0.1458 & 0.442195 \tabularnewline
20 & -0.064027 & -0.6623 & 0.254601 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211002&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]-0.38501[/C][C]-3.9826[/C][C]6.2e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.212872[/C][C]-2.202[/C][C]0.014907[/C][/ROW]
[ROW][C]3[/C][C]0.212128[/C][C]2.1943[/C][C]0.015189[/C][/ROW]
[ROW][C]4[/C][C]0.000674[/C][C]0.007[/C][C]0.497225[/C][/ROW]
[ROW][C]5[/C][C]0.031008[/C][C]0.3207[/C][C]0.374514[/C][/ROW]
[ROW][C]6[/C][C]-0.246642[/C][C]-2.5513[/C][C]0.006073[/C][/ROW]
[ROW][C]7[/C][C]0.052549[/C][C]0.5436[/C][C]0.293935[/C][/ROW]
[ROW][C]8[/C][C]-0.041054[/C][C]-0.4247[/C][C]0.335967[/C][/ROW]
[ROW][C]9[/C][C]0.231[/C][C]2.3895[/C][C]0.009311[/C][/ROW]
[ROW][C]10[/C][C]-0.246997[/C][C]-2.555[/C][C]0.006013[/C][/ROW]
[ROW][C]11[/C][C]-0.263431[/C][C]-2.7249[/C][C]0.003757[/C][/ROW]
[ROW][C]12[/C][C]0.754434[/C][C]7.8039[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.309997[/C][C]-3.2066[/C][C]0.000886[/C][/ROW]
[ROW][C]14[/C][C]-0.129642[/C][C]-1.341[/C][C]0.091375[/C][/ROW]
[ROW][C]15[/C][C]0.141646[/C][C]1.4652[/C][C]0.0729[/C][/ROW]
[ROW][C]16[/C][C]0.030771[/C][C]0.3183[/C][C]0.375439[/C][/ROW]
[ROW][C]17[/C][C]-0.003644[/C][C]-0.0377[/C][C]0.485001[/C][/ROW]
[ROW][C]18[/C][C]-0.17617[/C][C]-1.8223[/C][C]0.0356[/C][/ROW]
[ROW][C]19[/C][C]0.014091[/C][C]0.1458[/C][C]0.442195[/C][/ROW]
[ROW][C]20[/C][C]-0.064027[/C][C]-0.6623[/C][C]0.254601[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211002&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211002&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	-0.38501	-3.9826	6.2e-05
2	-0.212872	-2.202	0.014907
3	0.212128	2.1943	0.015189
4	0.000674	0.007	0.497225
5	0.031008	0.3207	0.374514
6	-0.246642	-2.5513	0.006073
7	0.052549	0.5436	0.293935
8	-0.041054	-0.4247	0.335967
9	0.231	2.3895	0.009311
10	-0.246997	-2.555	0.006013
11	-0.263431	-2.7249	0.003757
12	0.754434	7.8039	0
13	-0.309997	-3.2066	0.000886
14	-0.129642	-1.341	0.091375
15	0.141646	1.4652	0.0729
16	0.030771	0.3183	0.375439
17	-0.003644	-0.0377	0.485001
18	-0.17617	-1.8223	0.0356
19	0.014091	0.1458	0.442195
20	-0.064027	-0.6623	0.254601

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.38501	-3.9826	6.2e-05
2	-0.423948	-4.3853	1.4e-05
3	-0.09704	-1.0038	0.158872
4	-0.019125	-0.1978	0.421778
5	0.150523	1.557	0.061209
6	-0.218594	-2.2612	0.012886
7	-0.221857	-2.2949	0.011845
8	-0.424908	-4.3953	1.3e-05
9	0.12464	1.2893	0.10004
10	-0.133181	-1.3776	0.085595
11	-0.508864	-5.2637	0
12	0.379812	3.9288	7.6e-05
13	0.144072	1.4903	0.069544
14	0.172278	1.7821	0.038788
15	0.052758	0.5457	0.293191
16	-0.014605	-0.1511	0.440099
17	-0.104172	-1.0776	0.141826
18	0.004806	0.0497	0.480222
19	-0.088342	-0.9138	0.181434
20	-0.099045	-1.0245	0.153949

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.38501 & -3.9826 & 6.2e-05 \tabularnewline
2 & -0.423948 & -4.3853 & 1.4e-05 \tabularnewline
3 & -0.09704 & -1.0038 & 0.158872 \tabularnewline
4 & -0.019125 & -0.1978 & 0.421778 \tabularnewline
5 & 0.150523 & 1.557 & 0.061209 \tabularnewline
6 & -0.218594 & -2.2612 & 0.012886 \tabularnewline
7 & -0.221857 & -2.2949 & 0.011845 \tabularnewline
8 & -0.424908 & -4.3953 & 1.3e-05 \tabularnewline
9 & 0.12464 & 1.2893 & 0.10004 \tabularnewline
10 & -0.133181 & -1.3776 & 0.085595 \tabularnewline
11 & -0.508864 & -5.2637 & 0 \tabularnewline
12 & 0.379812 & 3.9288 & 7.6e-05 \tabularnewline
13 & 0.144072 & 1.4903 & 0.069544 \tabularnewline
14 & 0.172278 & 1.7821 & 0.038788 \tabularnewline
15 & 0.052758 & 0.5457 & 0.293191 \tabularnewline
16 & -0.014605 & -0.1511 & 0.440099 \tabularnewline
17 & -0.104172 & -1.0776 & 0.141826 \tabularnewline
18 & 0.004806 & 0.0497 & 0.480222 \tabularnewline
19 & -0.088342 & -0.9138 & 0.181434 \tabularnewline
20 & -0.099045 & -1.0245 & 0.153949 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211002&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]-0.38501[/C][C]-3.9826[/C][C]6.2e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.423948[/C][C]-4.3853[/C][C]1.4e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.09704[/C][C]-1.0038[/C][C]0.158872[/C][/ROW]
[ROW][C]4[/C][C]-0.019125[/C][C]-0.1978[/C][C]0.421778[/C][/ROW]
[ROW][C]5[/C][C]0.150523[/C][C]1.557[/C][C]0.061209[/C][/ROW]
[ROW][C]6[/C][C]-0.218594[/C][C]-2.2612[/C][C]0.012886[/C][/ROW]
[ROW][C]7[/C][C]-0.221857[/C][C]-2.2949[/C][C]0.011845[/C][/ROW]
[ROW][C]8[/C][C]-0.424908[/C][C]-4.3953[/C][C]1.3e-05[/C][/ROW]
[ROW][C]9[/C][C]0.12464[/C][C]1.2893[/C][C]0.10004[/C][/ROW]
[ROW][C]10[/C][C]-0.133181[/C][C]-1.3776[/C][C]0.085595[/C][/ROW]
[ROW][C]11[/C][C]-0.508864[/C][C]-5.2637[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.379812[/C][C]3.9288[/C][C]7.6e-05[/C][/ROW]
[ROW][C]13[/C][C]0.144072[/C][C]1.4903[/C][C]0.069544[/C][/ROW]
[ROW][C]14[/C][C]0.172278[/C][C]1.7821[/C][C]0.038788[/C][/ROW]
[ROW][C]15[/C][C]0.052758[/C][C]0.5457[/C][C]0.293191[/C][/ROW]
[ROW][C]16[/C][C]-0.014605[/C][C]-0.1511[/C][C]0.440099[/C][/ROW]
[ROW][C]17[/C][C]-0.104172[/C][C]-1.0776[/C][C]0.141826[/C][/ROW]
[ROW][C]18[/C][C]0.004806[/C][C]0.0497[/C][C]0.480222[/C][/ROW]
[ROW][C]19[/C][C]-0.088342[/C][C]-0.9138[/C][C]0.181434[/C][/ROW]
[ROW][C]20[/C][C]-0.099045[/C][C]-1.0245[/C][C]0.153949[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211002&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211002&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	-0.38501	-3.9826	6.2e-05
2	-0.423948	-4.3853	1.4e-05
3	-0.09704	-1.0038	0.158872
4	-0.019125	-0.1978	0.421778
5	0.150523	1.557	0.061209
6	-0.218594	-2.2612	0.012886
7	-0.221857	-2.2949	0.011845
8	-0.424908	-4.3953	1.3e-05
9	0.12464	1.2893	0.10004
10	-0.133181	-1.3776	0.085595
11	-0.508864	-5.2637	0
12	0.379812	3.9288	7.6e-05
13	0.144072	1.4903	0.069544
14	0.172278	1.7821	0.038788
15	0.052758	0.5457	0.293191
16	-0.014605	-0.1511	0.440099
17	-0.104172	-1.0776	0.141826
18	0.004806	0.0497	0.480222
19	-0.088342	-0.9138	0.181434
20	-0.099045	-1.0245	0.153949

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 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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):

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