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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 20 Oct 2016 17:46:35 +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/2016/Oct/20/t1476982026msbv9vbavs17bwi.htm/, Retrieved Sat, 04 May 2024 23:56:18 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 04 May 2024 23:56:18 +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	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/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	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.555782	-4.269	3.6e-05
2	0.090877	0.698	0.243948
3	0.030392	0.2334	0.408113
4	0.071985	0.5529	0.2912
5	-0.267752	-2.0566	0.022076
6	0.377524	2.8998	0.002619
7	-0.336608	-2.5855	0.006106
8	0.221844	1.704	0.04682
9	-0.036173	-0.2778	0.39105
10	-0.024913	-0.1914	0.424451
11	-0.03824	-0.2937	0.385
12	0.27183	2.088	0.020563
13	-0.387956	-2.9799	0.002091
14	0.262011	2.0125	0.024367
15	-0.154243	-1.1848	0.12043
16	0.082879	0.6366	0.263423
17	0.047448	0.3645	0.358411

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.555782 & -4.269 & 3.6e-05 \tabularnewline
2 & 0.090877 & 0.698 & 0.243948 \tabularnewline
3 & 0.030392 & 0.2334 & 0.408113 \tabularnewline
4 & 0.071985 & 0.5529 & 0.2912 \tabularnewline
5 & -0.267752 & -2.0566 & 0.022076 \tabularnewline
6 & 0.377524 & 2.8998 & 0.002619 \tabularnewline
7 & -0.336608 & -2.5855 & 0.006106 \tabularnewline
8 & 0.221844 & 1.704 & 0.04682 \tabularnewline
9 & -0.036173 & -0.2778 & 0.39105 \tabularnewline
10 & -0.024913 & -0.1914 & 0.424451 \tabularnewline
11 & -0.03824 & -0.2937 & 0.385 \tabularnewline
12 & 0.27183 & 2.088 & 0.020563 \tabularnewline
13 & -0.387956 & -2.9799 & 0.002091 \tabularnewline
14 & 0.262011 & 2.0125 & 0.024367 \tabularnewline
15 & -0.154243 & -1.1848 & 0.12043 \tabularnewline
16 & 0.082879 & 0.6366 & 0.263423 \tabularnewline
17 & 0.047448 & 0.3645 & 0.358411 \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]-0.555782[/C][C]-4.269[/C][C]3.6e-05[/C][/ROW]
[ROW][C]2[/C][C]0.090877[/C][C]0.698[/C][C]0.243948[/C][/ROW]
[ROW][C]3[/C][C]0.030392[/C][C]0.2334[/C][C]0.408113[/C][/ROW]
[ROW][C]4[/C][C]0.071985[/C][C]0.5529[/C][C]0.2912[/C][/ROW]
[ROW][C]5[/C][C]-0.267752[/C][C]-2.0566[/C][C]0.022076[/C][/ROW]
[ROW][C]6[/C][C]0.377524[/C][C]2.8998[/C][C]0.002619[/C][/ROW]
[ROW][C]7[/C][C]-0.336608[/C][C]-2.5855[/C][C]0.006106[/C][/ROW]
[ROW][C]8[/C][C]0.221844[/C][C]1.704[/C][C]0.04682[/C][/ROW]
[ROW][C]9[/C][C]-0.036173[/C][C]-0.2778[/C][C]0.39105[/C][/ROW]
[ROW][C]10[/C][C]-0.024913[/C][C]-0.1914[/C][C]0.424451[/C][/ROW]
[ROW][C]11[/C][C]-0.03824[/C][C]-0.2937[/C][C]0.385[/C][/ROW]
[ROW][C]12[/C][C]0.27183[/C][C]2.088[/C][C]0.020563[/C][/ROW]
[ROW][C]13[/C][C]-0.387956[/C][C]-2.9799[/C][C]0.002091[/C][/ROW]
[ROW][C]14[/C][C]0.262011[/C][C]2.0125[/C][C]0.024367[/C][/ROW]
[ROW][C]15[/C][C]-0.154243[/C][C]-1.1848[/C][C]0.12043[/C][/ROW]
[ROW][C]16[/C][C]0.082879[/C][C]0.6366[/C][C]0.263423[/C][/ROW]
[ROW][C]17[/C][C]0.047448[/C][C]0.3645[/C][C]0.358411[/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	-0.555782	-4.269	3.6e-05
2	0.090877	0.698	0.243948
3	0.030392	0.2334	0.408113
4	0.071985	0.5529	0.2912
5	-0.267752	-2.0566	0.022076
6	0.377524	2.8998	0.002619
7	-0.336608	-2.5855	0.006106
8	0.221844	1.704	0.04682
9	-0.036173	-0.2778	0.39105
10	-0.024913	-0.1914	0.424451
11	-0.03824	-0.2937	0.385
12	0.27183	2.088	0.020563
13	-0.387956	-2.9799	0.002091
14	0.262011	2.0125	0.024367
15	-0.154243	-1.1848	0.12043
16	0.082879	0.6366	0.263423
17	0.047448	0.3645	0.358411

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.555782	-4.269	3.6e-05
2	-0.315461	-2.4231	0.009238
3	-0.126131	-0.9688	0.168292
4	0.101826	0.7821	0.218629
5	-0.232862	-1.7886	0.039403
6	0.156077	1.1988	0.11769
7	-0.116121	-0.8919	0.188024
8	0.074822	0.5747	0.283834
9	0.127281	0.9777	0.166117
10	0.012013	0.0923	0.463397
11	0.056968	0.4376	0.331645
12	0.261347	2.0074	0.024645
13	-0.025926	-0.1991	0.421419
14	0.019054	0.1464	0.442071
15	-0.15862	-1.2184	0.113964
16	-0.029154	-0.2239	0.411791
17	0.210558	1.6173	0.055571

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.555782 & -4.269 & 3.6e-05 \tabularnewline
2 & -0.315461 & -2.4231 & 0.009238 \tabularnewline
3 & -0.126131 & -0.9688 & 0.168292 \tabularnewline
4 & 0.101826 & 0.7821 & 0.218629 \tabularnewline
5 & -0.232862 & -1.7886 & 0.039403 \tabularnewline
6 & 0.156077 & 1.1988 & 0.11769 \tabularnewline
7 & -0.116121 & -0.8919 & 0.188024 \tabularnewline
8 & 0.074822 & 0.5747 & 0.283834 \tabularnewline
9 & 0.127281 & 0.9777 & 0.166117 \tabularnewline
10 & 0.012013 & 0.0923 & 0.463397 \tabularnewline
11 & 0.056968 & 0.4376 & 0.331645 \tabularnewline
12 & 0.261347 & 2.0074 & 0.024645 \tabularnewline
13 & -0.025926 & -0.1991 & 0.421419 \tabularnewline
14 & 0.019054 & 0.1464 & 0.442071 \tabularnewline
15 & -0.15862 & -1.2184 & 0.113964 \tabularnewline
16 & -0.029154 & -0.2239 & 0.411791 \tabularnewline
17 & 0.210558 & 1.6173 & 0.055571 \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]-0.555782[/C][C]-4.269[/C][C]3.6e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.315461[/C][C]-2.4231[/C][C]0.009238[/C][/ROW]
[ROW][C]3[/C][C]-0.126131[/C][C]-0.9688[/C][C]0.168292[/C][/ROW]
[ROW][C]4[/C][C]0.101826[/C][C]0.7821[/C][C]0.218629[/C][/ROW]
[ROW][C]5[/C][C]-0.232862[/C][C]-1.7886[/C][C]0.039403[/C][/ROW]
[ROW][C]6[/C][C]0.156077[/C][C]1.1988[/C][C]0.11769[/C][/ROW]
[ROW][C]7[/C][C]-0.116121[/C][C]-0.8919[/C][C]0.188024[/C][/ROW]
[ROW][C]8[/C][C]0.074822[/C][C]0.5747[/C][C]0.283834[/C][/ROW]
[ROW][C]9[/C][C]0.127281[/C][C]0.9777[/C][C]0.166117[/C][/ROW]
[ROW][C]10[/C][C]0.012013[/C][C]0.0923[/C][C]0.463397[/C][/ROW]
[ROW][C]11[/C][C]0.056968[/C][C]0.4376[/C][C]0.331645[/C][/ROW]
[ROW][C]12[/C][C]0.261347[/C][C]2.0074[/C][C]0.024645[/C][/ROW]
[ROW][C]13[/C][C]-0.025926[/C][C]-0.1991[/C][C]0.421419[/C][/ROW]
[ROW][C]14[/C][C]0.019054[/C][C]0.1464[/C][C]0.442071[/C][/ROW]
[ROW][C]15[/C][C]-0.15862[/C][C]-1.2184[/C][C]0.113964[/C][/ROW]
[ROW][C]16[/C][C]-0.029154[/C][C]-0.2239[/C][C]0.411791[/C][/ROW]
[ROW][C]17[/C][C]0.210558[/C][C]1.6173[/C][C]0.055571[/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	-0.555782	-4.269	3.6e-05
2	-0.315461	-2.4231	0.009238
3	-0.126131	-0.9688	0.168292
4	0.101826	0.7821	0.218629
5	-0.232862	-1.7886	0.039403
6	0.156077	1.1988	0.11769
7	-0.116121	-0.8919	0.188024
8	0.074822	0.5747	0.283834
9	0.127281	0.9777	0.166117
10	0.012013	0.0923	0.463397
11	0.056968	0.4376	0.331645
12	0.261347	2.0074	0.024645
13	-0.025926	-0.1991	0.421419
14	0.019054	0.1464	0.442071
15	-0.15862	-1.2184	0.113964
16	-0.029154	-0.2239	0.411791
17	0.210558	1.6173	0.055571

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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