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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Mar 2017 18:35:51 +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/2017/Mar/19/t1489948593ytx57y5n1lz5v24.htm/, Retrieved Wed, 15 May 2024 05:09:43 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 05:09:43 +0200

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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	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.113023	-0.9523	0.172076
2	0.133372	1.1238	0.132439
3	0.201574	1.6985	0.046897
4	-0.159061	-1.3403	0.092215
5	0.127132	1.0712	0.143847
6	-0.114145	-0.9618	0.169707
7	0.036538	0.3079	0.379541
8	-0.240615	-2.0275	0.023185
9	0.132551	1.1169	0.133903
10	-0.094511	-0.7964	0.214237
11	-0.111343	-0.9382	0.175664
12	0.192594	1.6228	0.05453
13	-0.295633	-2.491	0.007538
14	0.013395	0.1129	0.455228
15	-0.017963	-0.1514	0.440062
16	-0.178169	-1.5013	0.068859
17	-0.041184	-0.347	0.364802
18	-0.077123	-0.6499	0.258943

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.113023 & -0.9523 & 0.172076 \tabularnewline
2 & 0.133372 & 1.1238 & 0.132439 \tabularnewline
3 & 0.201574 & 1.6985 & 0.046897 \tabularnewline
4 & -0.159061 & -1.3403 & 0.092215 \tabularnewline
5 & 0.127132 & 1.0712 & 0.143847 \tabularnewline
6 & -0.114145 & -0.9618 & 0.169707 \tabularnewline
7 & 0.036538 & 0.3079 & 0.379541 \tabularnewline
8 & -0.240615 & -2.0275 & 0.023185 \tabularnewline
9 & 0.132551 & 1.1169 & 0.133903 \tabularnewline
10 & -0.094511 & -0.7964 & 0.214237 \tabularnewline
11 & -0.111343 & -0.9382 & 0.175664 \tabularnewline
12 & 0.192594 & 1.6228 & 0.05453 \tabularnewline
13 & -0.295633 & -2.491 & 0.007538 \tabularnewline
14 & 0.013395 & 0.1129 & 0.455228 \tabularnewline
15 & -0.017963 & -0.1514 & 0.440062 \tabularnewline
16 & -0.178169 & -1.5013 & 0.068859 \tabularnewline
17 & -0.041184 & -0.347 & 0.364802 \tabularnewline
18 & -0.077123 & -0.6499 & 0.258943 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.113023[/C][C]-0.9523[/C][C]0.172076[/C][/ROW]
[ROW][C]2[/C][C]0.133372[/C][C]1.1238[/C][C]0.132439[/C][/ROW]
[ROW][C]3[/C][C]0.201574[/C][C]1.6985[/C][C]0.046897[/C][/ROW]
[ROW][C]4[/C][C]-0.159061[/C][C]-1.3403[/C][C]0.092215[/C][/ROW]
[ROW][C]5[/C][C]0.127132[/C][C]1.0712[/C][C]0.143847[/C][/ROW]
[ROW][C]6[/C][C]-0.114145[/C][C]-0.9618[/C][C]0.169707[/C][/ROW]
[ROW][C]7[/C][C]0.036538[/C][C]0.3079[/C][C]0.379541[/C][/ROW]
[ROW][C]8[/C][C]-0.240615[/C][C]-2.0275[/C][C]0.023185[/C][/ROW]
[ROW][C]9[/C][C]0.132551[/C][C]1.1169[/C][C]0.133903[/C][/ROW]
[ROW][C]10[/C][C]-0.094511[/C][C]-0.7964[/C][C]0.214237[/C][/ROW]
[ROW][C]11[/C][C]-0.111343[/C][C]-0.9382[/C][C]0.175664[/C][/ROW]
[ROW][C]12[/C][C]0.192594[/C][C]1.6228[/C][C]0.05453[/C][/ROW]
[ROW][C]13[/C][C]-0.295633[/C][C]-2.491[/C][C]0.007538[/C][/ROW]
[ROW][C]14[/C][C]0.013395[/C][C]0.1129[/C][C]0.455228[/C][/ROW]
[ROW][C]15[/C][C]-0.017963[/C][C]-0.1514[/C][C]0.440062[/C][/ROW]
[ROW][C]16[/C][C]-0.178169[/C][C]-1.5013[/C][C]0.068859[/C][/ROW]
[ROW][C]17[/C][C]-0.041184[/C][C]-0.347[/C][C]0.364802[/C][/ROW]
[ROW][C]18[/C][C]-0.077123[/C][C]-0.6499[/C][C]0.258943[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.113023	-0.9523	0.172076
2	0.133372	1.1238	0.132439
3	0.201574	1.6985	0.046897
4	-0.159061	-1.3403	0.092215
5	0.127132	1.0712	0.143847
6	-0.114145	-0.9618	0.169707
7	0.036538	0.3079	0.379541
8	-0.240615	-2.0275	0.023185
9	0.132551	1.1169	0.133903
10	-0.094511	-0.7964	0.214237
11	-0.111343	-0.9382	0.175664
12	0.192594	1.6228	0.05453
13	-0.295633	-2.491	0.007538
14	0.013395	0.1129	0.455228
15	-0.017963	-0.1514	0.440062
16	-0.178169	-1.5013	0.068859
17	-0.041184	-0.347	0.364802
18	-0.077123	-0.6499	0.258943

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.113023	-0.9523	0.172076
2	0.122158	1.0293	0.153411
3	0.235079	1.9808	0.025743
4	-0.137259	-1.1566	0.125664
5	0.037762	0.3182	0.375639
6	-0.109009	-0.9185	0.180726
7	0.059872	0.5045	0.307741
8	-0.289219	-2.437	0.008659
9	0.187557	1.5804	0.059232
10	-0.097879	-0.8247	0.20614
11	0.006446	0.0543	0.478418
12	0.035558	0.2996	0.382674
13	-0.147713	-1.2446	0.108677
14	-0.14397	-1.2131	0.114553
15	0.025399	0.214	0.415573
16	-0.145829	-1.2288	0.111606
17	-0.06837	-0.5761	0.283186
18	-0.074752	-0.6299	0.2654

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.113023 & -0.9523 & 0.172076 \tabularnewline
2 & 0.122158 & 1.0293 & 0.153411 \tabularnewline
3 & 0.235079 & 1.9808 & 0.025743 \tabularnewline
4 & -0.137259 & -1.1566 & 0.125664 \tabularnewline
5 & 0.037762 & 0.3182 & 0.375639 \tabularnewline
6 & -0.109009 & -0.9185 & 0.180726 \tabularnewline
7 & 0.059872 & 0.5045 & 0.307741 \tabularnewline
8 & -0.289219 & -2.437 & 0.008659 \tabularnewline
9 & 0.187557 & 1.5804 & 0.059232 \tabularnewline
10 & -0.097879 & -0.8247 & 0.20614 \tabularnewline
11 & 0.006446 & 0.0543 & 0.478418 \tabularnewline
12 & 0.035558 & 0.2996 & 0.382674 \tabularnewline
13 & -0.147713 & -1.2446 & 0.108677 \tabularnewline
14 & -0.14397 & -1.2131 & 0.114553 \tabularnewline
15 & 0.025399 & 0.214 & 0.415573 \tabularnewline
16 & -0.145829 & -1.2288 & 0.111606 \tabularnewline
17 & -0.06837 & -0.5761 & 0.283186 \tabularnewline
18 & -0.074752 & -0.6299 & 0.2654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]-0.113023[/C][C]-0.9523[/C][C]0.172076[/C][/ROW]
[ROW][C]2[/C][C]0.122158[/C][C]1.0293[/C][C]0.153411[/C][/ROW]
[ROW][C]3[/C][C]0.235079[/C][C]1.9808[/C][C]0.025743[/C][/ROW]
[ROW][C]4[/C][C]-0.137259[/C][C]-1.1566[/C][C]0.125664[/C][/ROW]
[ROW][C]5[/C][C]0.037762[/C][C]0.3182[/C][C]0.375639[/C][/ROW]
[ROW][C]6[/C][C]-0.109009[/C][C]-0.9185[/C][C]0.180726[/C][/ROW]
[ROW][C]7[/C][C]0.059872[/C][C]0.5045[/C][C]0.307741[/C][/ROW]
[ROW][C]8[/C][C]-0.289219[/C][C]-2.437[/C][C]0.008659[/C][/ROW]
[ROW][C]9[/C][C]0.187557[/C][C]1.5804[/C][C]0.059232[/C][/ROW]
[ROW][C]10[/C][C]-0.097879[/C][C]-0.8247[/C][C]0.20614[/C][/ROW]
[ROW][C]11[/C][C]0.006446[/C][C]0.0543[/C][C]0.478418[/C][/ROW]
[ROW][C]12[/C][C]0.035558[/C][C]0.2996[/C][C]0.382674[/C][/ROW]
[ROW][C]13[/C][C]-0.147713[/C][C]-1.2446[/C][C]0.108677[/C][/ROW]
[ROW][C]14[/C][C]-0.14397[/C][C]-1.2131[/C][C]0.114553[/C][/ROW]
[ROW][C]15[/C][C]0.025399[/C][C]0.214[/C][C]0.415573[/C][/ROW]
[ROW][C]16[/C][C]-0.145829[/C][C]-1.2288[/C][C]0.111606[/C][/ROW]
[ROW][C]17[/C][C]-0.06837[/C][C]-0.5761[/C][C]0.283186[/C][/ROW]
[ROW][C]18[/C][C]-0.074752[/C][C]-0.6299[/C][C]0.2654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.113023	-0.9523	0.172076
2	0.122158	1.0293	0.153411
3	0.235079	1.9808	0.025743
4	-0.137259	-1.1566	0.125664
5	0.037762	0.3182	0.375639
6	-0.109009	-0.9185	0.180726
7	0.059872	0.5045	0.307741
8	-0.289219	-2.437	0.008659
9	0.187557	1.5804	0.059232
10	-0.097879	-0.8247	0.20614
11	0.006446	0.0543	0.478418
12	0.035558	0.2996	0.382674
13	-0.147713	-1.2446	0.108677
14	-0.14397	-1.2131	0.114553
15	0.025399	0.214	0.415573
16	-0.145829	-1.2288	0.111606
17	-0.06837	-0.5761	0.283186
18	-0.074752	-0.6299	0.2654

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)
x <- na.omit(x)
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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code