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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Nov 2012 17:25:16 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/18/t1353277535l1m66zb2efoccbl.htm/, Retrieved Mon, 29 Apr 2024 22:11:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=190383, Retrieved Mon, 29 Apr 2024 22:11:17 +0000

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-       [(Partial) Autocorrelation Function] [] [2012-11-18 22:25:16] [4d2251dc83b8e36495234b85db35e813] [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	3 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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190383&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]3 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=190383&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190383&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.018385	0.1549	0.438664
2	-0.191106	-1.6103	0.055886
3	0.087585	0.738	0.231472
4	-0.039911	-0.3363	0.36882
5	-0.135398	-1.1409	0.128875
6	0.043248	0.3644	0.358317
7	-0.034203	-0.2882	0.387016
8	-0.018482	-0.1557	0.438343
9	0.080062	0.6746	0.251056
10	-0.14874	-1.2533	0.107103
11	0.065395	0.551	0.291673
12	0.101716	0.8571	0.197145
13	-0.114268	-0.9628	0.169448
14	0.010853	0.0915	0.463696
15	0.3061	2.5792	0.005987
16	0.086029	0.7249	0.23545
17	-0.090761	-0.7648	0.223474
18	-0.03044	-0.2565	0.399157

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.018385 & 0.1549 & 0.438664 \tabularnewline
2 & -0.191106 & -1.6103 & 0.055886 \tabularnewline
3 & 0.087585 & 0.738 & 0.231472 \tabularnewline
4 & -0.039911 & -0.3363 & 0.36882 \tabularnewline
5 & -0.135398 & -1.1409 & 0.128875 \tabularnewline
6 & 0.043248 & 0.3644 & 0.358317 \tabularnewline
7 & -0.034203 & -0.2882 & 0.387016 \tabularnewline
8 & -0.018482 & -0.1557 & 0.438343 \tabularnewline
9 & 0.080062 & 0.6746 & 0.251056 \tabularnewline
10 & -0.14874 & -1.2533 & 0.107103 \tabularnewline
11 & 0.065395 & 0.551 & 0.291673 \tabularnewline
12 & 0.101716 & 0.8571 & 0.197145 \tabularnewline
13 & -0.114268 & -0.9628 & 0.169448 \tabularnewline
14 & 0.010853 & 0.0915 & 0.463696 \tabularnewline
15 & 0.3061 & 2.5792 & 0.005987 \tabularnewline
16 & 0.086029 & 0.7249 & 0.23545 \tabularnewline
17 & -0.090761 & -0.7648 & 0.223474 \tabularnewline
18 & -0.03044 & -0.2565 & 0.399157 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190383&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]0.018385[/C][C]0.1549[/C][C]0.438664[/C][/ROW]
[ROW][C]2[/C][C]-0.191106[/C][C]-1.6103[/C][C]0.055886[/C][/ROW]
[ROW][C]3[/C][C]0.087585[/C][C]0.738[/C][C]0.231472[/C][/ROW]
[ROW][C]4[/C][C]-0.039911[/C][C]-0.3363[/C][C]0.36882[/C][/ROW]
[ROW][C]5[/C][C]-0.135398[/C][C]-1.1409[/C][C]0.128875[/C][/ROW]
[ROW][C]6[/C][C]0.043248[/C][C]0.3644[/C][C]0.358317[/C][/ROW]
[ROW][C]7[/C][C]-0.034203[/C][C]-0.2882[/C][C]0.387016[/C][/ROW]
[ROW][C]8[/C][C]-0.018482[/C][C]-0.1557[/C][C]0.438343[/C][/ROW]
[ROW][C]9[/C][C]0.080062[/C][C]0.6746[/C][C]0.251056[/C][/ROW]
[ROW][C]10[/C][C]-0.14874[/C][C]-1.2533[/C][C]0.107103[/C][/ROW]
[ROW][C]11[/C][C]0.065395[/C][C]0.551[/C][C]0.291673[/C][/ROW]
[ROW][C]12[/C][C]0.101716[/C][C]0.8571[/C][C]0.197145[/C][/ROW]
[ROW][C]13[/C][C]-0.114268[/C][C]-0.9628[/C][C]0.169448[/C][/ROW]
[ROW][C]14[/C][C]0.010853[/C][C]0.0915[/C][C]0.463696[/C][/ROW]
[ROW][C]15[/C][C]0.3061[/C][C]2.5792[/C][C]0.005987[/C][/ROW]
[ROW][C]16[/C][C]0.086029[/C][C]0.7249[/C][C]0.23545[/C][/ROW]
[ROW][C]17[/C][C]-0.090761[/C][C]-0.7648[/C][C]0.223474[/C][/ROW]
[ROW][C]18[/C][C]-0.03044[/C][C]-0.2565[/C][C]0.399157[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190383&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190383&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	0.018385	0.1549	0.438664
2	-0.191106	-1.6103	0.055886
3	0.087585	0.738	0.231472
4	-0.039911	-0.3363	0.36882
5	-0.135398	-1.1409	0.128875
6	0.043248	0.3644	0.358317
7	-0.034203	-0.2882	0.387016
8	-0.018482	-0.1557	0.438343
9	0.080062	0.6746	0.251056
10	-0.14874	-1.2533	0.107103
11	0.065395	0.551	0.291673
12	0.101716	0.8571	0.197145
13	-0.114268	-0.9628	0.169448
14	0.010853	0.0915	0.463696
15	0.3061	2.5792	0.005987
16	0.086029	0.7249	0.23545
17	-0.090761	-0.7648	0.223474
18	-0.03044	-0.2565	0.399157

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.018385	0.1549	0.438664
2	-0.191509	-1.6137	0.055516
3	0.098954	0.8338	0.203596
4	-0.08633	-0.7274	0.234678
5	-0.099135	-0.8353	0.203169
6	0.021231	0.1789	0.429264
7	-0.077387	-0.6521	0.25823
8	0.016493	0.139	0.444934
9	0.041653	0.351	0.363324
10	-0.169	-1.424	0.07941
11	0.119571	1.0075	0.158552
12	0.004705	0.0396	0.484245
13	-0.063247	-0.5329	0.297874
14	0.040625	0.3423	0.366563
15	0.247001	2.0813	0.020508
16	0.139019	1.1714	0.122679
17	-0.011404	-0.0961	0.461859
18	-0.050932	-0.4292	0.334552

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.018385 & 0.1549 & 0.438664 \tabularnewline
2 & -0.191509 & -1.6137 & 0.055516 \tabularnewline
3 & 0.098954 & 0.8338 & 0.203596 \tabularnewline
4 & -0.08633 & -0.7274 & 0.234678 \tabularnewline
5 & -0.099135 & -0.8353 & 0.203169 \tabularnewline
6 & 0.021231 & 0.1789 & 0.429264 \tabularnewline
7 & -0.077387 & -0.6521 & 0.25823 \tabularnewline
8 & 0.016493 & 0.139 & 0.444934 \tabularnewline
9 & 0.041653 & 0.351 & 0.363324 \tabularnewline
10 & -0.169 & -1.424 & 0.07941 \tabularnewline
11 & 0.119571 & 1.0075 & 0.158552 \tabularnewline
12 & 0.004705 & 0.0396 & 0.484245 \tabularnewline
13 & -0.063247 & -0.5329 & 0.297874 \tabularnewline
14 & 0.040625 & 0.3423 & 0.366563 \tabularnewline
15 & 0.247001 & 2.0813 & 0.020508 \tabularnewline
16 & 0.139019 & 1.1714 & 0.122679 \tabularnewline
17 & -0.011404 & -0.0961 & 0.461859 \tabularnewline
18 & -0.050932 & -0.4292 & 0.334552 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190383&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]0.018385[/C][C]0.1549[/C][C]0.438664[/C][/ROW]
[ROW][C]2[/C][C]-0.191509[/C][C]-1.6137[/C][C]0.055516[/C][/ROW]
[ROW][C]3[/C][C]0.098954[/C][C]0.8338[/C][C]0.203596[/C][/ROW]
[ROW][C]4[/C][C]-0.08633[/C][C]-0.7274[/C][C]0.234678[/C][/ROW]
[ROW][C]5[/C][C]-0.099135[/C][C]-0.8353[/C][C]0.203169[/C][/ROW]
[ROW][C]6[/C][C]0.021231[/C][C]0.1789[/C][C]0.429264[/C][/ROW]
[ROW][C]7[/C][C]-0.077387[/C][C]-0.6521[/C][C]0.25823[/C][/ROW]
[ROW][C]8[/C][C]0.016493[/C][C]0.139[/C][C]0.444934[/C][/ROW]
[ROW][C]9[/C][C]0.041653[/C][C]0.351[/C][C]0.363324[/C][/ROW]
[ROW][C]10[/C][C]-0.169[/C][C]-1.424[/C][C]0.07941[/C][/ROW]
[ROW][C]11[/C][C]0.119571[/C][C]1.0075[/C][C]0.158552[/C][/ROW]
[ROW][C]12[/C][C]0.004705[/C][C]0.0396[/C][C]0.484245[/C][/ROW]
[ROW][C]13[/C][C]-0.063247[/C][C]-0.5329[/C][C]0.297874[/C][/ROW]
[ROW][C]14[/C][C]0.040625[/C][C]0.3423[/C][C]0.366563[/C][/ROW]
[ROW][C]15[/C][C]0.247001[/C][C]2.0813[/C][C]0.020508[/C][/ROW]
[ROW][C]16[/C][C]0.139019[/C][C]1.1714[/C][C]0.122679[/C][/ROW]
[ROW][C]17[/C][C]-0.011404[/C][C]-0.0961[/C][C]0.461859[/C][/ROW]
[ROW][C]18[/C][C]-0.050932[/C][C]-0.4292[/C][C]0.334552[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190383&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190383&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	0.018385	0.1549	0.438664
2	-0.191509	-1.6137	0.055516
3	0.098954	0.8338	0.203596
4	-0.08633	-0.7274	0.234678
5	-0.099135	-0.8353	0.203169
6	0.021231	0.1789	0.429264
7	-0.077387	-0.6521	0.25823
8	0.016493	0.139	0.444934
9	0.041653	0.351	0.363324
10	-0.169	-1.424	0.07941
11	0.119571	1.0075	0.158552
12	0.004705	0.0396	0.484245
13	-0.063247	-0.5329	0.297874
14	0.040625	0.3423	0.366563
15	0.247001	2.0813	0.020508
16	0.139019	1.1714	0.122679
17	-0.011404	-0.0961	0.461859
18	-0.050932	-0.4292	0.334552

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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