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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 20 Oct 2016 21:50:50 +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/t1476996661m66ji6c5q090ta4.htm/, Retrieved Tue, 21 May 2024 04:04:57 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 21 May 2024 04:04:57 +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	-0.29952	-2.3007	0.012482
2	-0.26286	-2.0191	0.024016
3	0.161187	1.2381	0.110292
4	0.105714	0.812	0.210026
5	-0.103303	-0.7935	0.215336
6	-0.023399	-0.1797	0.428989
7	-0.096968	-0.7448	0.229666
8	0.021951	0.1686	0.433341
9	0.141165	1.0843	0.14132
10	-0.221009	-1.6976	0.047426
11	-0.038827	-0.2982	0.383286
12	0.330396	2.5378	0.006908
13	0.018954	0.1456	0.442372
14	-0.233246	-1.7916	0.039163
15	0.094397	0.7251	0.235636
16	0.026079	0.2003	0.420961
17	-0.03451	-0.2651	0.395938

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.29952 & -2.3007 & 0.012482 \tabularnewline
2 & -0.26286 & -2.0191 & 0.024016 \tabularnewline
3 & 0.161187 & 1.2381 & 0.110292 \tabularnewline
4 & 0.105714 & 0.812 & 0.210026 \tabularnewline
5 & -0.103303 & -0.7935 & 0.215336 \tabularnewline
6 & -0.023399 & -0.1797 & 0.428989 \tabularnewline
7 & -0.096968 & -0.7448 & 0.229666 \tabularnewline
8 & 0.021951 & 0.1686 & 0.433341 \tabularnewline
9 & 0.141165 & 1.0843 & 0.14132 \tabularnewline
10 & -0.221009 & -1.6976 & 0.047426 \tabularnewline
11 & -0.038827 & -0.2982 & 0.383286 \tabularnewline
12 & 0.330396 & 2.5378 & 0.006908 \tabularnewline
13 & 0.018954 & 0.1456 & 0.442372 \tabularnewline
14 & -0.233246 & -1.7916 & 0.039163 \tabularnewline
15 & 0.094397 & 0.7251 & 0.235636 \tabularnewline
16 & 0.026079 & 0.2003 & 0.420961 \tabularnewline
17 & -0.03451 & -0.2651 & 0.395938 \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]-0.29952[/C][C]-2.3007[/C][C]0.012482[/C][/ROW]
[ROW][C]2[/C][C]-0.26286[/C][C]-2.0191[/C][C]0.024016[/C][/ROW]
[ROW][C]3[/C][C]0.161187[/C][C]1.2381[/C][C]0.110292[/C][/ROW]
[ROW][C]4[/C][C]0.105714[/C][C]0.812[/C][C]0.210026[/C][/ROW]
[ROW][C]5[/C][C]-0.103303[/C][C]-0.7935[/C][C]0.215336[/C][/ROW]
[ROW][C]6[/C][C]-0.023399[/C][C]-0.1797[/C][C]0.428989[/C][/ROW]
[ROW][C]7[/C][C]-0.096968[/C][C]-0.7448[/C][C]0.229666[/C][/ROW]
[ROW][C]8[/C][C]0.021951[/C][C]0.1686[/C][C]0.433341[/C][/ROW]
[ROW][C]9[/C][C]0.141165[/C][C]1.0843[/C][C]0.14132[/C][/ROW]
[ROW][C]10[/C][C]-0.221009[/C][C]-1.6976[/C][C]0.047426[/C][/ROW]
[ROW][C]11[/C][C]-0.038827[/C][C]-0.2982[/C][C]0.383286[/C][/ROW]
[ROW][C]12[/C][C]0.330396[/C][C]2.5378[/C][C]0.006908[/C][/ROW]
[ROW][C]13[/C][C]0.018954[/C][C]0.1456[/C][C]0.442372[/C][/ROW]
[ROW][C]14[/C][C]-0.233246[/C][C]-1.7916[/C][C]0.039163[/C][/ROW]
[ROW][C]15[/C][C]0.094397[/C][C]0.7251[/C][C]0.235636[/C][/ROW]
[ROW][C]16[/C][C]0.026079[/C][C]0.2003[/C][C]0.420961[/C][/ROW]
[ROW][C]17[/C][C]-0.03451[/C][C]-0.2651[/C][C]0.395938[/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	-0.29952	-2.3007	0.012482
2	-0.26286	-2.0191	0.024016
3	0.161187	1.2381	0.110292
4	0.105714	0.812	0.210026
5	-0.103303	-0.7935	0.215336
6	-0.023399	-0.1797	0.428989
7	-0.096968	-0.7448	0.229666
8	0.021951	0.1686	0.433341
9	0.141165	1.0843	0.14132
10	-0.221009	-1.6976	0.047426
11	-0.038827	-0.2982	0.383286
12	0.330396	2.5378	0.006908
13	0.018954	0.1456	0.442372
14	-0.233246	-1.7916	0.039163
15	0.094397	0.7251	0.235636
16	0.026079	0.2003	0.420961
17	-0.03451	-0.2651	0.395938

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.29952	-2.3007	0.012482
2	-0.38732	-2.9751	0.00212
3	-0.08278	-0.6358	0.263667
4	0.054934	0.422	0.337295
5	0.011658	0.0895	0.464476
6	0.000976	0.0075	0.497022
7	-0.194624	-1.4949	0.070131
8	-0.149415	-1.1477	0.127868
9	0.047479	0.3647	0.358322
10	-0.170256	-1.3078	0.098014
11	-0.132997	-1.0216	0.155578
12	0.190673	1.4646	0.074171
13	0.254855	1.9576	0.027507
14	0.065987	0.5069	0.307074
15	0.025849	0.1985	0.421649
16	-0.125439	-0.9635	0.169611
17	-0.11533	-0.8859	0.189643

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.29952 & -2.3007 & 0.012482 \tabularnewline
2 & -0.38732 & -2.9751 & 0.00212 \tabularnewline
3 & -0.08278 & -0.6358 & 0.263667 \tabularnewline
4 & 0.054934 & 0.422 & 0.337295 \tabularnewline
5 & 0.011658 & 0.0895 & 0.464476 \tabularnewline
6 & 0.000976 & 0.0075 & 0.497022 \tabularnewline
7 & -0.194624 & -1.4949 & 0.070131 \tabularnewline
8 & -0.149415 & -1.1477 & 0.127868 \tabularnewline
9 & 0.047479 & 0.3647 & 0.358322 \tabularnewline
10 & -0.170256 & -1.3078 & 0.098014 \tabularnewline
11 & -0.132997 & -1.0216 & 0.155578 \tabularnewline
12 & 0.190673 & 1.4646 & 0.074171 \tabularnewline
13 & 0.254855 & 1.9576 & 0.027507 \tabularnewline
14 & 0.065987 & 0.5069 & 0.307074 \tabularnewline
15 & 0.025849 & 0.1985 & 0.421649 \tabularnewline
16 & -0.125439 & -0.9635 & 0.169611 \tabularnewline
17 & -0.11533 & -0.8859 & 0.189643 \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]-0.29952[/C][C]-2.3007[/C][C]0.012482[/C][/ROW]
[ROW][C]2[/C][C]-0.38732[/C][C]-2.9751[/C][C]0.00212[/C][/ROW]
[ROW][C]3[/C][C]-0.08278[/C][C]-0.6358[/C][C]0.263667[/C][/ROW]
[ROW][C]4[/C][C]0.054934[/C][C]0.422[/C][C]0.337295[/C][/ROW]
[ROW][C]5[/C][C]0.011658[/C][C]0.0895[/C][C]0.464476[/C][/ROW]
[ROW][C]6[/C][C]0.000976[/C][C]0.0075[/C][C]0.497022[/C][/ROW]
[ROW][C]7[/C][C]-0.194624[/C][C]-1.4949[/C][C]0.070131[/C][/ROW]
[ROW][C]8[/C][C]-0.149415[/C][C]-1.1477[/C][C]0.127868[/C][/ROW]
[ROW][C]9[/C][C]0.047479[/C][C]0.3647[/C][C]0.358322[/C][/ROW]
[ROW][C]10[/C][C]-0.170256[/C][C]-1.3078[/C][C]0.098014[/C][/ROW]
[ROW][C]11[/C][C]-0.132997[/C][C]-1.0216[/C][C]0.155578[/C][/ROW]
[ROW][C]12[/C][C]0.190673[/C][C]1.4646[/C][C]0.074171[/C][/ROW]
[ROW][C]13[/C][C]0.254855[/C][C]1.9576[/C][C]0.027507[/C][/ROW]
[ROW][C]14[/C][C]0.065987[/C][C]0.5069[/C][C]0.307074[/C][/ROW]
[ROW][C]15[/C][C]0.025849[/C][C]0.1985[/C][C]0.421649[/C][/ROW]
[ROW][C]16[/C][C]-0.125439[/C][C]-0.9635[/C][C]0.169611[/C][/ROW]
[ROW][C]17[/C][C]-0.11533[/C][C]-0.8859[/C][C]0.189643[/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	-0.29952	-2.3007	0.012482
2	-0.38732	-2.9751	0.00212
3	-0.08278	-0.6358	0.263667
4	0.054934	0.422	0.337295
5	0.011658	0.0895	0.464476
6	0.000976	0.0075	0.497022
7	-0.194624	-1.4949	0.070131
8	-0.149415	-1.1477	0.127868
9	0.047479	0.3647	0.358322
10	-0.170256	-1.3078	0.098014
11	-0.132997	-1.0216	0.155578
12	0.190673	1.4646	0.074171
13	0.254855	1.9576	0.027507
14	0.065987	0.5069	0.307074
15	0.025849	0.1985	0.421649
16	-0.125439	-0.9635	0.169611
17	-0.11533	-0.8859	0.189643

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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