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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 26 Dec 2010 11:23:56 +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/Dec/26/t1293362516nhodt61bqo3vpwv.htm/, Retrieved Tue, 07 May 2024 00:30:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115525, Retrieved Tue, 07 May 2024 00:30:39 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Autocorrelatie functie met d=1 en D=0

Estimated Impact

148

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

-     [Variance Reduction Matrix] [Unemployment] [2010-11-29 09:29:57] [b98453cac15ba1066b407e146608df68]
- RMPD  [(Partial) Autocorrelation Function] [Workshop 9 (ACF p=0)] [2010-12-15 13:59:06] [845827b7f02503df17c96f445745fee7]
-         [(Partial) Autocorrelation Function] [] [2010-12-16 16:02:02] [24bb5b06bd1854f48aebec8f44957ed0]
-   PD        [(Partial) Autocorrelation Function] [Paper] [2010-12-26 11:23:56] [e247a0a17f1c9a5b89239760575ef468] [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=115525&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=115525&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115525&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	0.262275	2.0316	0.023316
2	-0.312024	-2.4169	0.009355
3	-0.344637	-2.6695	0.004879
4	-0.210416	-1.6299	0.054184
5	0.116471	0.9022	0.185285
6	0.293228	2.2713	0.013364
7	0.138137	1.07	0.144452
8	-0.150183	-1.1633	0.124655
9	-0.304596	-2.3594	0.010788
10	-0.303488	-2.3508	0.011018
11	0.216295	1.6754	0.049529
12	0.707335	5.479	0
13	0.130437	1.0104	0.158189
14	-0.295308	-2.2874	0.012855
15	-0.255187	-1.9767	0.02634
16	-0.167141	-1.2947	0.100198
17	0.10845	0.8401	0.202107

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.262275 & 2.0316 & 0.023316 \tabularnewline
2 & -0.312024 & -2.4169 & 0.009355 \tabularnewline
3 & -0.344637 & -2.6695 & 0.004879 \tabularnewline
4 & -0.210416 & -1.6299 & 0.054184 \tabularnewline
5 & 0.116471 & 0.9022 & 0.185285 \tabularnewline
6 & 0.293228 & 2.2713 & 0.013364 \tabularnewline
7 & 0.138137 & 1.07 & 0.144452 \tabularnewline
8 & -0.150183 & -1.1633 & 0.124655 \tabularnewline
9 & -0.304596 & -2.3594 & 0.010788 \tabularnewline
10 & -0.303488 & -2.3508 & 0.011018 \tabularnewline
11 & 0.216295 & 1.6754 & 0.049529 \tabularnewline
12 & 0.707335 & 5.479 & 0 \tabularnewline
13 & 0.130437 & 1.0104 & 0.158189 \tabularnewline
14 & -0.295308 & -2.2874 & 0.012855 \tabularnewline
15 & -0.255187 & -1.9767 & 0.02634 \tabularnewline
16 & -0.167141 & -1.2947 & 0.100198 \tabularnewline
17 & 0.10845 & 0.8401 & 0.202107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115525&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]0.262275[/C][C]2.0316[/C][C]0.023316[/C][/ROW]
[ROW][C]2[/C][C]-0.312024[/C][C]-2.4169[/C][C]0.009355[/C][/ROW]
[ROW][C]3[/C][C]-0.344637[/C][C]-2.6695[/C][C]0.004879[/C][/ROW]
[ROW][C]4[/C][C]-0.210416[/C][C]-1.6299[/C][C]0.054184[/C][/ROW]
[ROW][C]5[/C][C]0.116471[/C][C]0.9022[/C][C]0.185285[/C][/ROW]
[ROW][C]6[/C][C]0.293228[/C][C]2.2713[/C][C]0.013364[/C][/ROW]
[ROW][C]7[/C][C]0.138137[/C][C]1.07[/C][C]0.144452[/C][/ROW]
[ROW][C]8[/C][C]-0.150183[/C][C]-1.1633[/C][C]0.124655[/C][/ROW]
[ROW][C]9[/C][C]-0.304596[/C][C]-2.3594[/C][C]0.010788[/C][/ROW]
[ROW][C]10[/C][C]-0.303488[/C][C]-2.3508[/C][C]0.011018[/C][/ROW]
[ROW][C]11[/C][C]0.216295[/C][C]1.6754[/C][C]0.049529[/C][/ROW]
[ROW][C]12[/C][C]0.707335[/C][C]5.479[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.130437[/C][C]1.0104[/C][C]0.158189[/C][/ROW]
[ROW][C]14[/C][C]-0.295308[/C][C]-2.2874[/C][C]0.012855[/C][/ROW]
[ROW][C]15[/C][C]-0.255187[/C][C]-1.9767[/C][C]0.02634[/C][/ROW]
[ROW][C]16[/C][C]-0.167141[/C][C]-1.2947[/C][C]0.100198[/C][/ROW]
[ROW][C]17[/C][C]0.10845[/C][C]0.8401[/C][C]0.202107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115525&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115525&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	0.262275	2.0316	0.023316
2	-0.312024	-2.4169	0.009355
3	-0.344637	-2.6695	0.004879
4	-0.210416	-1.6299	0.054184
5	0.116471	0.9022	0.185285
6	0.293228	2.2713	0.013364
7	0.138137	1.07	0.144452
8	-0.150183	-1.1633	0.124655
9	-0.304596	-2.3594	0.010788
10	-0.303488	-2.3508	0.011018
11	0.216295	1.6754	0.049529
12	0.707335	5.479	0
13	0.130437	1.0104	0.158189
14	-0.295308	-2.2874	0.012855
15	-0.255187	-1.9767	0.02634
16	-0.167141	-1.2947	0.100198
17	0.10845	0.8401	0.202107

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.262275	2.0316	0.023316
2	-0.408943	-3.1677	0.001209
3	-0.157424	-1.2194	0.113732
4	-0.229298	-1.7761	0.040391
5	0.080011	0.6198	0.268881
6	0.074443	0.5766	0.283172
7	0.022223	0.1721	0.431953
8	-0.101106	-0.7832	0.218305
9	-0.147324	-1.1412	0.129167
10	-0.277726	-2.1513	0.017746
11	0.267011	2.0683	0.021467
12	0.512928	3.9731	9.6e-05
13	-0.269329	-2.0862	0.020609
14	0.03066	0.2375	0.406542
15	0.14381	1.1139	0.134872
16	-0.037819	-0.2929	0.385288
17	-0.015815	-0.1225	0.451456

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.262275 & 2.0316 & 0.023316 \tabularnewline
2 & -0.408943 & -3.1677 & 0.001209 \tabularnewline
3 & -0.157424 & -1.2194 & 0.113732 \tabularnewline
4 & -0.229298 & -1.7761 & 0.040391 \tabularnewline
5 & 0.080011 & 0.6198 & 0.268881 \tabularnewline
6 & 0.074443 & 0.5766 & 0.283172 \tabularnewline
7 & 0.022223 & 0.1721 & 0.431953 \tabularnewline
8 & -0.101106 & -0.7832 & 0.218305 \tabularnewline
9 & -0.147324 & -1.1412 & 0.129167 \tabularnewline
10 & -0.277726 & -2.1513 & 0.017746 \tabularnewline
11 & 0.267011 & 2.0683 & 0.021467 \tabularnewline
12 & 0.512928 & 3.9731 & 9.6e-05 \tabularnewline
13 & -0.269329 & -2.0862 & 0.020609 \tabularnewline
14 & 0.03066 & 0.2375 & 0.406542 \tabularnewline
15 & 0.14381 & 1.1139 & 0.134872 \tabularnewline
16 & -0.037819 & -0.2929 & 0.385288 \tabularnewline
17 & -0.015815 & -0.1225 & 0.451456 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115525&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]0.262275[/C][C]2.0316[/C][C]0.023316[/C][/ROW]
[ROW][C]2[/C][C]-0.408943[/C][C]-3.1677[/C][C]0.001209[/C][/ROW]
[ROW][C]3[/C][C]-0.157424[/C][C]-1.2194[/C][C]0.113732[/C][/ROW]
[ROW][C]4[/C][C]-0.229298[/C][C]-1.7761[/C][C]0.040391[/C][/ROW]
[ROW][C]5[/C][C]0.080011[/C][C]0.6198[/C][C]0.268881[/C][/ROW]
[ROW][C]6[/C][C]0.074443[/C][C]0.5766[/C][C]0.283172[/C][/ROW]
[ROW][C]7[/C][C]0.022223[/C][C]0.1721[/C][C]0.431953[/C][/ROW]
[ROW][C]8[/C][C]-0.101106[/C][C]-0.7832[/C][C]0.218305[/C][/ROW]
[ROW][C]9[/C][C]-0.147324[/C][C]-1.1412[/C][C]0.129167[/C][/ROW]
[ROW][C]10[/C][C]-0.277726[/C][C]-2.1513[/C][C]0.017746[/C][/ROW]
[ROW][C]11[/C][C]0.267011[/C][C]2.0683[/C][C]0.021467[/C][/ROW]
[ROW][C]12[/C][C]0.512928[/C][C]3.9731[/C][C]9.6e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.269329[/C][C]-2.0862[/C][C]0.020609[/C][/ROW]
[ROW][C]14[/C][C]0.03066[/C][C]0.2375[/C][C]0.406542[/C][/ROW]
[ROW][C]15[/C][C]0.14381[/C][C]1.1139[/C][C]0.134872[/C][/ROW]
[ROW][C]16[/C][C]-0.037819[/C][C]-0.2929[/C][C]0.385288[/C][/ROW]
[ROW][C]17[/C][C]-0.015815[/C][C]-0.1225[/C][C]0.451456[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115525&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115525&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	0.262275	2.0316	0.023316
2	-0.408943	-3.1677	0.001209
3	-0.157424	-1.2194	0.113732
4	-0.229298	-1.7761	0.040391
5	0.080011	0.6198	0.268881
6	0.074443	0.5766	0.283172
7	0.022223	0.1721	0.431953
8	-0.101106	-0.7832	0.218305
9	-0.147324	-1.1412	0.129167
10	-0.277726	-2.1513	0.017746
11	0.267011	2.0683	0.021467
12	0.512928	3.9731	9.6e-05
13	-0.269329	-2.0862	0.020609
14	0.03066	0.2375	0.406542
15	0.14381	1.1139	0.134872
16	-0.037819	-0.2929	0.385288
17	-0.015815	-0.1225	0.451456

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')

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Input Parameters & R Code