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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 24 Oct 2015 20:19:42 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/24/t144571461810r16jlm4nktbz2.htm/, Retrieved Wed, 15 May 2024 15:17:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283061, Retrieved Wed, 15 May 2024 15:17:39 +0000

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-       [(Partial) Autocorrelation Function] [Gedifferentieerd ...] [2015-10-24 19:19:42] [ad5e328aab07d5d247de986d4dfd18ff] [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	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=283061&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=283061&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283061&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	0.020505	0.1575	0.437693
2	0.095423	0.733	0.233244
3	-0.150589	-1.1567	0.12603
4	0.21497	1.6512	0.052004
5	-0.165525	-1.2714	0.104285
6	-0.059896	-0.4601	0.323577
7	-0.173109	-1.3297	0.094371
8	0.253323	1.9458	0.028223
9	-0.214429	-1.6471	0.052431
10	-0.013406	-0.103	0.459168
11	-0.082288	-0.6321	0.264893
12	0.657916	5.0536	2e-06
13	-0.072509	-0.557	0.289833
14	0.050838	0.3905	0.348789
15	-0.189588	-1.4563	0.075312
16	0.097712	0.7505	0.227956
17	-0.176981	-1.3594	0.089594

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.020505 & 0.1575 & 0.437693 \tabularnewline
2 & 0.095423 & 0.733 & 0.233244 \tabularnewline
3 & -0.150589 & -1.1567 & 0.12603 \tabularnewline
4 & 0.21497 & 1.6512 & 0.052004 \tabularnewline
5 & -0.165525 & -1.2714 & 0.104285 \tabularnewline
6 & -0.059896 & -0.4601 & 0.323577 \tabularnewline
7 & -0.173109 & -1.3297 & 0.094371 \tabularnewline
8 & 0.253323 & 1.9458 & 0.028223 \tabularnewline
9 & -0.214429 & -1.6471 & 0.052431 \tabularnewline
10 & -0.013406 & -0.103 & 0.459168 \tabularnewline
11 & -0.082288 & -0.6321 & 0.264893 \tabularnewline
12 & 0.657916 & 5.0536 & 2e-06 \tabularnewline
13 & -0.072509 & -0.557 & 0.289833 \tabularnewline
14 & 0.050838 & 0.3905 & 0.348789 \tabularnewline
15 & -0.189588 & -1.4563 & 0.075312 \tabularnewline
16 & 0.097712 & 0.7505 & 0.227956 \tabularnewline
17 & -0.176981 & -1.3594 & 0.089594 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283061&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]0.020505[/C][C]0.1575[/C][C]0.437693[/C][/ROW]
[ROW][C]2[/C][C]0.095423[/C][C]0.733[/C][C]0.233244[/C][/ROW]
[ROW][C]3[/C][C]-0.150589[/C][C]-1.1567[/C][C]0.12603[/C][/ROW]
[ROW][C]4[/C][C]0.21497[/C][C]1.6512[/C][C]0.052004[/C][/ROW]
[ROW][C]5[/C][C]-0.165525[/C][C]-1.2714[/C][C]0.104285[/C][/ROW]
[ROW][C]6[/C][C]-0.059896[/C][C]-0.4601[/C][C]0.323577[/C][/ROW]
[ROW][C]7[/C][C]-0.173109[/C][C]-1.3297[/C][C]0.094371[/C][/ROW]
[ROW][C]8[/C][C]0.253323[/C][C]1.9458[/C][C]0.028223[/C][/ROW]
[ROW][C]9[/C][C]-0.214429[/C][C]-1.6471[/C][C]0.052431[/C][/ROW]
[ROW][C]10[/C][C]-0.013406[/C][C]-0.103[/C][C]0.459168[/C][/ROW]
[ROW][C]11[/C][C]-0.082288[/C][C]-0.6321[/C][C]0.264893[/C][/ROW]
[ROW][C]12[/C][C]0.657916[/C][C]5.0536[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.072509[/C][C]-0.557[/C][C]0.289833[/C][/ROW]
[ROW][C]14[/C][C]0.050838[/C][C]0.3905[/C][C]0.348789[/C][/ROW]
[ROW][C]15[/C][C]-0.189588[/C][C]-1.4563[/C][C]0.075312[/C][/ROW]
[ROW][C]16[/C][C]0.097712[/C][C]0.7505[/C][C]0.227956[/C][/ROW]
[ROW][C]17[/C][C]-0.176981[/C][C]-1.3594[/C][C]0.089594[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283061&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283061&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	0.020505	0.1575	0.437693
2	0.095423	0.733	0.233244
3	-0.150589	-1.1567	0.12603
4	0.21497	1.6512	0.052004
5	-0.165525	-1.2714	0.104285
6	-0.059896	-0.4601	0.323577
7	-0.173109	-1.3297	0.094371
8	0.253323	1.9458	0.028223
9	-0.214429	-1.6471	0.052431
10	-0.013406	-0.103	0.459168
11	-0.082288	-0.6321	0.264893
12	0.657916	5.0536	2e-06
13	-0.072509	-0.557	0.289833
14	0.050838	0.3905	0.348789
15	-0.189588	-1.4563	0.075312
16	0.097712	0.7505	0.227956
17	-0.176981	-1.3594	0.089594

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.020505	0.1575	0.437693
2	0.095042	0.73	0.23413
3	-0.15578	-1.1966	0.11813
4	0.221253	1.6995	0.047248
5	-0.171441	-1.3169	0.096488
6	-0.105449	-0.81	0.210606
7	-0.075759	-0.5819	0.281421
8	0.211465	1.6243	0.054822
9	-0.2241	-1.7213	0.045214
10	-0.03334	-0.2561	0.399386
11	0.05338	0.41	0.341639
12	0.605995	4.6547	9e-06
13	-0.213492	-1.6399	0.053177
14	-0.088028	-0.6762	0.250792
15	-0.090134	-0.6923	0.245723
16	-0.163556	-1.2563	0.10698
17	0.0676	0.5192	0.302767

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.020505 & 0.1575 & 0.437693 \tabularnewline
2 & 0.095042 & 0.73 & 0.23413 \tabularnewline
3 & -0.15578 & -1.1966 & 0.11813 \tabularnewline
4 & 0.221253 & 1.6995 & 0.047248 \tabularnewline
5 & -0.171441 & -1.3169 & 0.096488 \tabularnewline
6 & -0.105449 & -0.81 & 0.210606 \tabularnewline
7 & -0.075759 & -0.5819 & 0.281421 \tabularnewline
8 & 0.211465 & 1.6243 & 0.054822 \tabularnewline
9 & -0.2241 & -1.7213 & 0.045214 \tabularnewline
10 & -0.03334 & -0.2561 & 0.399386 \tabularnewline
11 & 0.05338 & 0.41 & 0.341639 \tabularnewline
12 & 0.605995 & 4.6547 & 9e-06 \tabularnewline
13 & -0.213492 & -1.6399 & 0.053177 \tabularnewline
14 & -0.088028 & -0.6762 & 0.250792 \tabularnewline
15 & -0.090134 & -0.6923 & 0.245723 \tabularnewline
16 & -0.163556 & -1.2563 & 0.10698 \tabularnewline
17 & 0.0676 & 0.5192 & 0.302767 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283061&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]0.020505[/C][C]0.1575[/C][C]0.437693[/C][/ROW]
[ROW][C]2[/C][C]0.095042[/C][C]0.73[/C][C]0.23413[/C][/ROW]
[ROW][C]3[/C][C]-0.15578[/C][C]-1.1966[/C][C]0.11813[/C][/ROW]
[ROW][C]4[/C][C]0.221253[/C][C]1.6995[/C][C]0.047248[/C][/ROW]
[ROW][C]5[/C][C]-0.171441[/C][C]-1.3169[/C][C]0.096488[/C][/ROW]
[ROW][C]6[/C][C]-0.105449[/C][C]-0.81[/C][C]0.210606[/C][/ROW]
[ROW][C]7[/C][C]-0.075759[/C][C]-0.5819[/C][C]0.281421[/C][/ROW]
[ROW][C]8[/C][C]0.211465[/C][C]1.6243[/C][C]0.054822[/C][/ROW]
[ROW][C]9[/C][C]-0.2241[/C][C]-1.7213[/C][C]0.045214[/C][/ROW]
[ROW][C]10[/C][C]-0.03334[/C][C]-0.2561[/C][C]0.399386[/C][/ROW]
[ROW][C]11[/C][C]0.05338[/C][C]0.41[/C][C]0.341639[/C][/ROW]
[ROW][C]12[/C][C]0.605995[/C][C]4.6547[/C][C]9e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.213492[/C][C]-1.6399[/C][C]0.053177[/C][/ROW]
[ROW][C]14[/C][C]-0.088028[/C][C]-0.6762[/C][C]0.250792[/C][/ROW]
[ROW][C]15[/C][C]-0.090134[/C][C]-0.6923[/C][C]0.245723[/C][/ROW]
[ROW][C]16[/C][C]-0.163556[/C][C]-1.2563[/C][C]0.10698[/C][/ROW]
[ROW][C]17[/C][C]0.0676[/C][C]0.5192[/C][C]0.302767[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283061&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283061&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	0.020505	0.1575	0.437693
2	0.095042	0.73	0.23413
3	-0.15578	-1.1966	0.11813
4	0.221253	1.6995	0.047248
5	-0.171441	-1.3169	0.096488
6	-0.105449	-0.81	0.210606
7	-0.075759	-0.5819	0.281421
8	0.211465	1.6243	0.054822
9	-0.2241	-1.7213	0.045214
10	-0.03334	-0.2561	0.399386
11	0.05338	0.41	0.341639
12	0.605995	4.6547	9e-06
13	-0.213492	-1.6399	0.053177
14	-0.088028	-0.6762	0.250792
15	-0.090134	-0.6923	0.245723
16	-0.163556	-1.2563	0.10698
17	0.0676	0.5192	0.302767

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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