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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 12 Mar 2016 17:48:38 +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/2016/Mar/12/t1457804940zaerpt2z1yaxf9x.htm/, Retrieved Sun, 05 May 2024 16:43:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293934, Retrieved Sun, 05 May 2024 16:43:40 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-03-12 17:48:38] [4661a511bc27dc3517a7b8e15be46886] [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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293934&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293934&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293934&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.552238	4.2776	3.4e-05
2	0.02331	0.1806	0.428663
3	-0.287581	-2.2276	0.014835
4	-0.317931	-2.4627	0.008339
5	-0.193467	-1.4986	0.069612
6	-0.104035	-0.8058	0.211756
7	-0.156415	-1.2116	0.11521
8	-0.269776	-2.0897	0.020447
9	-0.260255	-2.0159	0.024146
10	0.029448	0.2281	0.41017
11	0.459771	3.5614	0.000365
12	0.675448	5.232	1e-06
13	0.477782	3.7009	0.000234
14	0.030008	0.2324	0.408492
15	-0.236629	-1.8329	0.035889
16	-0.273456	-2.1182	0.019155
17	-0.168838	-1.3078	0.097963

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.552238 & 4.2776 & 3.4e-05 \tabularnewline
2 & 0.02331 & 0.1806 & 0.428663 \tabularnewline
3 & -0.287581 & -2.2276 & 0.014835 \tabularnewline
4 & -0.317931 & -2.4627 & 0.008339 \tabularnewline
5 & -0.193467 & -1.4986 & 0.069612 \tabularnewline
6 & -0.104035 & -0.8058 & 0.211756 \tabularnewline
7 & -0.156415 & -1.2116 & 0.11521 \tabularnewline
8 & -0.269776 & -2.0897 & 0.020447 \tabularnewline
9 & -0.260255 & -2.0159 & 0.024146 \tabularnewline
10 & 0.029448 & 0.2281 & 0.41017 \tabularnewline
11 & 0.459771 & 3.5614 & 0.000365 \tabularnewline
12 & 0.675448 & 5.232 & 1e-06 \tabularnewline
13 & 0.477782 & 3.7009 & 0.000234 \tabularnewline
14 & 0.030008 & 0.2324 & 0.408492 \tabularnewline
15 & -0.236629 & -1.8329 & 0.035889 \tabularnewline
16 & -0.273456 & -2.1182 & 0.019155 \tabularnewline
17 & -0.168838 & -1.3078 & 0.097963 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293934&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]0.552238[/C][C]4.2776[/C][C]3.4e-05[/C][/ROW]
[ROW][C]2[/C][C]0.02331[/C][C]0.1806[/C][C]0.428663[/C][/ROW]
[ROW][C]3[/C][C]-0.287581[/C][C]-2.2276[/C][C]0.014835[/C][/ROW]
[ROW][C]4[/C][C]-0.317931[/C][C]-2.4627[/C][C]0.008339[/C][/ROW]
[ROW][C]5[/C][C]-0.193467[/C][C]-1.4986[/C][C]0.069612[/C][/ROW]
[ROW][C]6[/C][C]-0.104035[/C][C]-0.8058[/C][C]0.211756[/C][/ROW]
[ROW][C]7[/C][C]-0.156415[/C][C]-1.2116[/C][C]0.11521[/C][/ROW]
[ROW][C]8[/C][C]-0.269776[/C][C]-2.0897[/C][C]0.020447[/C][/ROW]
[ROW][C]9[/C][C]-0.260255[/C][C]-2.0159[/C][C]0.024146[/C][/ROW]
[ROW][C]10[/C][C]0.029448[/C][C]0.2281[/C][C]0.41017[/C][/ROW]
[ROW][C]11[/C][C]0.459771[/C][C]3.5614[/C][C]0.000365[/C][/ROW]
[ROW][C]12[/C][C]0.675448[/C][C]5.232[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.477782[/C][C]3.7009[/C][C]0.000234[/C][/ROW]
[ROW][C]14[/C][C]0.030008[/C][C]0.2324[/C][C]0.408492[/C][/ROW]
[ROW][C]15[/C][C]-0.236629[/C][C]-1.8329[/C][C]0.035889[/C][/ROW]
[ROW][C]16[/C][C]-0.273456[/C][C]-2.1182[/C][C]0.019155[/C][/ROW]
[ROW][C]17[/C][C]-0.168838[/C][C]-1.3078[/C][C]0.097963[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293934&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293934&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	0.552238	4.2776	3.4e-05
2	0.02331	0.1806	0.428663
3	-0.287581	-2.2276	0.014835
4	-0.317931	-2.4627	0.008339
5	-0.193467	-1.4986	0.069612
6	-0.104035	-0.8058	0.211756
7	-0.156415	-1.2116	0.11521
8	-0.269776	-2.0897	0.020447
9	-0.260255	-2.0159	0.024146
10	0.029448	0.2281	0.41017
11	0.459771	3.5614	0.000365
12	0.675448	5.232	1e-06
13	0.477782	3.7009	0.000234
14	0.030008	0.2324	0.408492
15	-0.236629	-1.8329	0.035889
16	-0.273456	-2.1182	0.019155
17	-0.168838	-1.3078	0.097963

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.552238	4.2776	3.4e-05
2	-0.405244	-3.139	0.001315
3	-0.140953	-1.0918	0.13964
4	-0.046457	-0.3599	0.36011
5	-0.049038	-0.3799	0.352699
6	-0.131827	-1.0211	0.155647
7	-0.237173	-1.8371	0.035572
8	-0.250534	-1.9406	0.028503
9	-0.147125	-1.1396	0.129486
10	0.153812	1.1914	0.11909
11	0.331011	2.564	0.006435
12	0.275553	2.1344	0.018452
13	0.076678	0.5939	0.277391
14	-0.089669	-0.6946	0.245003
15	0.10601	0.8211	0.207407
16	0.019332	0.1497	0.440734
17	0.020201	0.1565	0.438091

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.552238 & 4.2776 & 3.4e-05 \tabularnewline
2 & -0.405244 & -3.139 & 0.001315 \tabularnewline
3 & -0.140953 & -1.0918 & 0.13964 \tabularnewline
4 & -0.046457 & -0.3599 & 0.36011 \tabularnewline
5 & -0.049038 & -0.3799 & 0.352699 \tabularnewline
6 & -0.131827 & -1.0211 & 0.155647 \tabularnewline
7 & -0.237173 & -1.8371 & 0.035572 \tabularnewline
8 & -0.250534 & -1.9406 & 0.028503 \tabularnewline
9 & -0.147125 & -1.1396 & 0.129486 \tabularnewline
10 & 0.153812 & 1.1914 & 0.11909 \tabularnewline
11 & 0.331011 & 2.564 & 0.006435 \tabularnewline
12 & 0.275553 & 2.1344 & 0.018452 \tabularnewline
13 & 0.076678 & 0.5939 & 0.277391 \tabularnewline
14 & -0.089669 & -0.6946 & 0.245003 \tabularnewline
15 & 0.10601 & 0.8211 & 0.207407 \tabularnewline
16 & 0.019332 & 0.1497 & 0.440734 \tabularnewline
17 & 0.020201 & 0.1565 & 0.438091 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293934&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]0.552238[/C][C]4.2776[/C][C]3.4e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.405244[/C][C]-3.139[/C][C]0.001315[/C][/ROW]
[ROW][C]3[/C][C]-0.140953[/C][C]-1.0918[/C][C]0.13964[/C][/ROW]
[ROW][C]4[/C][C]-0.046457[/C][C]-0.3599[/C][C]0.36011[/C][/ROW]
[ROW][C]5[/C][C]-0.049038[/C][C]-0.3799[/C][C]0.352699[/C][/ROW]
[ROW][C]6[/C][C]-0.131827[/C][C]-1.0211[/C][C]0.155647[/C][/ROW]
[ROW][C]7[/C][C]-0.237173[/C][C]-1.8371[/C][C]0.035572[/C][/ROW]
[ROW][C]8[/C][C]-0.250534[/C][C]-1.9406[/C][C]0.028503[/C][/ROW]
[ROW][C]9[/C][C]-0.147125[/C][C]-1.1396[/C][C]0.129486[/C][/ROW]
[ROW][C]10[/C][C]0.153812[/C][C]1.1914[/C][C]0.11909[/C][/ROW]
[ROW][C]11[/C][C]0.331011[/C][C]2.564[/C][C]0.006435[/C][/ROW]
[ROW][C]12[/C][C]0.275553[/C][C]2.1344[/C][C]0.018452[/C][/ROW]
[ROW][C]13[/C][C]0.076678[/C][C]0.5939[/C][C]0.277391[/C][/ROW]
[ROW][C]14[/C][C]-0.089669[/C][C]-0.6946[/C][C]0.245003[/C][/ROW]
[ROW][C]15[/C][C]0.10601[/C][C]0.8211[/C][C]0.207407[/C][/ROW]
[ROW][C]16[/C][C]0.019332[/C][C]0.1497[/C][C]0.440734[/C][/ROW]
[ROW][C]17[/C][C]0.020201[/C][C]0.1565[/C][C]0.438091[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293934&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293934&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	0.552238	4.2776	3.4e-05
2	-0.405244	-3.139	0.001315
3	-0.140953	-1.0918	0.13964
4	-0.046457	-0.3599	0.36011
5	-0.049038	-0.3799	0.352699
6	-0.131827	-1.0211	0.155647
7	-0.237173	-1.8371	0.035572
8	-0.250534	-1.9406	0.028503
9	-0.147125	-1.1396	0.129486
10	0.153812	1.1914	0.11909
11	0.331011	2.564	0.006435
12	0.275553	2.1344	0.018452
13	0.076678	0.5939	0.277391
14	-0.089669	-0.6946	0.245003
15	0.10601	0.8211	0.207407
16	0.019332	0.1497	0.440734
17	0.020201	0.1565	0.438091

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)
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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