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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 22 Dec 2010 16:23:09 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/22/t1293034895pvobncko2cfe325.htm/, Retrieved Sun, 05 May 2024 22:42:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114367, Retrieved Sun, 05 May 2024 22:42:35 +0000

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101

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-       [(Partial) Autocorrelation Function] [ACF] [2010-12-22 16:23:09] [27f38de572a508a633f0ad2411de6a3e] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114367&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114367&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114367&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.92664	7.2373	0
2	0.779303	6.0866	0
3	0.576887	4.5056	1.5e-05
4	0.364048	2.8433	0.003033
5	0.161988	1.2652	0.105311
6	-0.003661	-0.0286	0.488641
7	-0.120454	-0.9408	0.175265
8	-0.20104	-1.5702	0.060774
9	-0.25593	-1.9989	0.025041
10	-0.282131	-2.2035	0.015672
11	-0.295285	-2.3063	0.012255
12	-0.304394	-2.3774	0.010293
13	-0.303277	-2.3687	0.010518
14	-0.290226	-2.2667	0.013482
15	-0.269948	-2.1084	0.019557
16	-0.252076	-1.9688	0.026763
17	-0.223985	-1.7494	0.042628

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.92664 & 7.2373 & 0 \tabularnewline
2 & 0.779303 & 6.0866 & 0 \tabularnewline
3 & 0.576887 & 4.5056 & 1.5e-05 \tabularnewline
4 & 0.364048 & 2.8433 & 0.003033 \tabularnewline
5 & 0.161988 & 1.2652 & 0.105311 \tabularnewline
6 & -0.003661 & -0.0286 & 0.488641 \tabularnewline
7 & -0.120454 & -0.9408 & 0.175265 \tabularnewline
8 & -0.20104 & -1.5702 & 0.060774 \tabularnewline
9 & -0.25593 & -1.9989 & 0.025041 \tabularnewline
10 & -0.282131 & -2.2035 & 0.015672 \tabularnewline
11 & -0.295285 & -2.3063 & 0.012255 \tabularnewline
12 & -0.304394 & -2.3774 & 0.010293 \tabularnewline
13 & -0.303277 & -2.3687 & 0.010518 \tabularnewline
14 & -0.290226 & -2.2667 & 0.013482 \tabularnewline
15 & -0.269948 & -2.1084 & 0.019557 \tabularnewline
16 & -0.252076 & -1.9688 & 0.026763 \tabularnewline
17 & -0.223985 & -1.7494 & 0.042628 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114367&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]0.92664[/C][C]7.2373[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.779303[/C][C]6.0866[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.576887[/C][C]4.5056[/C][C]1.5e-05[/C][/ROW]
[ROW][C]4[/C][C]0.364048[/C][C]2.8433[/C][C]0.003033[/C][/ROW]
[ROW][C]5[/C][C]0.161988[/C][C]1.2652[/C][C]0.105311[/C][/ROW]
[ROW][C]6[/C][C]-0.003661[/C][C]-0.0286[/C][C]0.488641[/C][/ROW]
[ROW][C]7[/C][C]-0.120454[/C][C]-0.9408[/C][C]0.175265[/C][/ROW]
[ROW][C]8[/C][C]-0.20104[/C][C]-1.5702[/C][C]0.060774[/C][/ROW]
[ROW][C]9[/C][C]-0.25593[/C][C]-1.9989[/C][C]0.025041[/C][/ROW]
[ROW][C]10[/C][C]-0.282131[/C][C]-2.2035[/C][C]0.015672[/C][/ROW]
[ROW][C]11[/C][C]-0.295285[/C][C]-2.3063[/C][C]0.012255[/C][/ROW]
[ROW][C]12[/C][C]-0.304394[/C][C]-2.3774[/C][C]0.010293[/C][/ROW]
[ROW][C]13[/C][C]-0.303277[/C][C]-2.3687[/C][C]0.010518[/C][/ROW]
[ROW][C]14[/C][C]-0.290226[/C][C]-2.2667[/C][C]0.013482[/C][/ROW]
[ROW][C]15[/C][C]-0.269948[/C][C]-2.1084[/C][C]0.019557[/C][/ROW]
[ROW][C]16[/C][C]-0.252076[/C][C]-1.9688[/C][C]0.026763[/C][/ROW]
[ROW][C]17[/C][C]-0.223985[/C][C]-1.7494[/C][C]0.042628[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114367&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114367&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	0.92664	7.2373	0
2	0.779303	6.0866	0
3	0.576887	4.5056	1.5e-05
4	0.364048	2.8433	0.003033
5	0.161988	1.2652	0.105311
6	-0.003661	-0.0286	0.488641
7	-0.120454	-0.9408	0.175265
8	-0.20104	-1.5702	0.060774
9	-0.25593	-1.9989	0.025041
10	-0.282131	-2.2035	0.015672
11	-0.295285	-2.3063	0.012255
12	-0.304394	-2.3774	0.010293
13	-0.303277	-2.3687	0.010518
14	-0.290226	-2.2667	0.013482
15	-0.269948	-2.1084	0.019557
16	-0.252076	-1.9688	0.026763
17	-0.223985	-1.7494	0.042628

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.92664	7.2373	0
2	-0.56148	-4.3853	2.3e-05
3	-0.31432	-2.4549	0.008479
4	0.063547	0.4963	0.310726
5	-0.013506	-0.1055	0.458168
6	0.04109	0.3209	0.374684
7	0.055722	0.4352	0.332476
8	-0.175404	-1.3699	0.087862
9	-0.141352	-1.104	0.136965
10	0.10827	0.8456	0.200535
11	-0.100225	-0.7828	0.218391
12	-0.138461	-1.0814	0.141885
13	0.104713	0.8178	0.208318
14	-0.011064	-0.0864	0.465712
15	-0.127982	-0.9996	0.160733
16	-0.081339	-0.6353	0.263812
17	0.096296	0.7521	0.227444

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.92664 & 7.2373 & 0 \tabularnewline
2 & -0.56148 & -4.3853 & 2.3e-05 \tabularnewline
3 & -0.31432 & -2.4549 & 0.008479 \tabularnewline
4 & 0.063547 & 0.4963 & 0.310726 \tabularnewline
5 & -0.013506 & -0.1055 & 0.458168 \tabularnewline
6 & 0.04109 & 0.3209 & 0.374684 \tabularnewline
7 & 0.055722 & 0.4352 & 0.332476 \tabularnewline
8 & -0.175404 & -1.3699 & 0.087862 \tabularnewline
9 & -0.141352 & -1.104 & 0.136965 \tabularnewline
10 & 0.10827 & 0.8456 & 0.200535 \tabularnewline
11 & -0.100225 & -0.7828 & 0.218391 \tabularnewline
12 & -0.138461 & -1.0814 & 0.141885 \tabularnewline
13 & 0.104713 & 0.8178 & 0.208318 \tabularnewline
14 & -0.011064 & -0.0864 & 0.465712 \tabularnewline
15 & -0.127982 & -0.9996 & 0.160733 \tabularnewline
16 & -0.081339 & -0.6353 & 0.263812 \tabularnewline
17 & 0.096296 & 0.7521 & 0.227444 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114367&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]0.92664[/C][C]7.2373[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.56148[/C][C]-4.3853[/C][C]2.3e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.31432[/C][C]-2.4549[/C][C]0.008479[/C][/ROW]
[ROW][C]4[/C][C]0.063547[/C][C]0.4963[/C][C]0.310726[/C][/ROW]
[ROW][C]5[/C][C]-0.013506[/C][C]-0.1055[/C][C]0.458168[/C][/ROW]
[ROW][C]6[/C][C]0.04109[/C][C]0.3209[/C][C]0.374684[/C][/ROW]
[ROW][C]7[/C][C]0.055722[/C][C]0.4352[/C][C]0.332476[/C][/ROW]
[ROW][C]8[/C][C]-0.175404[/C][C]-1.3699[/C][C]0.087862[/C][/ROW]
[ROW][C]9[/C][C]-0.141352[/C][C]-1.104[/C][C]0.136965[/C][/ROW]
[ROW][C]10[/C][C]0.10827[/C][C]0.8456[/C][C]0.200535[/C][/ROW]
[ROW][C]11[/C][C]-0.100225[/C][C]-0.7828[/C][C]0.218391[/C][/ROW]
[ROW][C]12[/C][C]-0.138461[/C][C]-1.0814[/C][C]0.141885[/C][/ROW]
[ROW][C]13[/C][C]0.104713[/C][C]0.8178[/C][C]0.208318[/C][/ROW]
[ROW][C]14[/C][C]-0.011064[/C][C]-0.0864[/C][C]0.465712[/C][/ROW]
[ROW][C]15[/C][C]-0.127982[/C][C]-0.9996[/C][C]0.160733[/C][/ROW]
[ROW][C]16[/C][C]-0.081339[/C][C]-0.6353[/C][C]0.263812[/C][/ROW]
[ROW][C]17[/C][C]0.096296[/C][C]0.7521[/C][C]0.227444[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114367&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114367&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	0.92664	7.2373	0
2	-0.56148	-4.3853	2.3e-05
3	-0.31432	-2.4549	0.008479
4	0.063547	0.4963	0.310726
5	-0.013506	-0.1055	0.458168
6	0.04109	0.3209	0.374684
7	0.055722	0.4352	0.332476
8	-0.175404	-1.3699	0.087862
9	-0.141352	-1.104	0.136965
10	0.10827	0.8456	0.200535
11	-0.100225	-0.7828	0.218391
12	-0.138461	-1.0814	0.141885
13	0.104713	0.8178	0.208318
14	-0.011064	-0.0864	0.465712
15	-0.127982	-0.9996	0.160733
16	-0.081339	-0.6353	0.263812
17	0.096296	0.7521	0.227444

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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