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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 02 Dec 2011 06:02:59 -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/2011/Dec/02/t1322823949kq75rnamicmx0k4.htm/, Retrieved Mon, 29 Apr 2024 05:25:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150098, Retrieved Mon, 29 Apr 2024 05:25:19 +0000

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-       [(Partial) Autocorrelation Function] [] [2011-12-02 11:02:59] [13d85cac30d4a10947636c080219d4f4] [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	'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=150098&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=150098&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150098&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	-0.085406	-0.5124	0.305738
2	-0.042509	-0.2551	0.400067
3	-0.077064	-0.4624	0.323293
4	0.049278	0.2957	0.38459
5	0.180265	1.0816	0.143313
6	-0.089462	-0.5368	0.297363
7	-0.300777	-1.8047	0.039749
8	-0.178839	-1.073	0.145198
9	0.06765	0.4059	0.343609
10	-0.028205	-0.1692	0.433283
11	-0.080073	-0.4804	0.316911
12	-0.249955	-1.4997	0.071202
13	0.092692	0.5562	0.290774
14	0.122822	0.7369	0.23297
15	0.018938	0.1136	0.455083
16	-0.139971	-0.8398	0.203275
17	0.171959	1.0318	0.154535

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.085406 & -0.5124 & 0.305738 \tabularnewline
2 & -0.042509 & -0.2551 & 0.400067 \tabularnewline
3 & -0.077064 & -0.4624 & 0.323293 \tabularnewline
4 & 0.049278 & 0.2957 & 0.38459 \tabularnewline
5 & 0.180265 & 1.0816 & 0.143313 \tabularnewline
6 & -0.089462 & -0.5368 & 0.297363 \tabularnewline
7 & -0.300777 & -1.8047 & 0.039749 \tabularnewline
8 & -0.178839 & -1.073 & 0.145198 \tabularnewline
9 & 0.06765 & 0.4059 & 0.343609 \tabularnewline
10 & -0.028205 & -0.1692 & 0.433283 \tabularnewline
11 & -0.080073 & -0.4804 & 0.316911 \tabularnewline
12 & -0.249955 & -1.4997 & 0.071202 \tabularnewline
13 & 0.092692 & 0.5562 & 0.290774 \tabularnewline
14 & 0.122822 & 0.7369 & 0.23297 \tabularnewline
15 & 0.018938 & 0.1136 & 0.455083 \tabularnewline
16 & -0.139971 & -0.8398 & 0.203275 \tabularnewline
17 & 0.171959 & 1.0318 & 0.154535 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150098&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]-0.085406[/C][C]-0.5124[/C][C]0.305738[/C][/ROW]
[ROW][C]2[/C][C]-0.042509[/C][C]-0.2551[/C][C]0.400067[/C][/ROW]
[ROW][C]3[/C][C]-0.077064[/C][C]-0.4624[/C][C]0.323293[/C][/ROW]
[ROW][C]4[/C][C]0.049278[/C][C]0.2957[/C][C]0.38459[/C][/ROW]
[ROW][C]5[/C][C]0.180265[/C][C]1.0816[/C][C]0.143313[/C][/ROW]
[ROW][C]6[/C][C]-0.089462[/C][C]-0.5368[/C][C]0.297363[/C][/ROW]
[ROW][C]7[/C][C]-0.300777[/C][C]-1.8047[/C][C]0.039749[/C][/ROW]
[ROW][C]8[/C][C]-0.178839[/C][C]-1.073[/C][C]0.145198[/C][/ROW]
[ROW][C]9[/C][C]0.06765[/C][C]0.4059[/C][C]0.343609[/C][/ROW]
[ROW][C]10[/C][C]-0.028205[/C][C]-0.1692[/C][C]0.433283[/C][/ROW]
[ROW][C]11[/C][C]-0.080073[/C][C]-0.4804[/C][C]0.316911[/C][/ROW]
[ROW][C]12[/C][C]-0.249955[/C][C]-1.4997[/C][C]0.071202[/C][/ROW]
[ROW][C]13[/C][C]0.092692[/C][C]0.5562[/C][C]0.290774[/C][/ROW]
[ROW][C]14[/C][C]0.122822[/C][C]0.7369[/C][C]0.23297[/C][/ROW]
[ROW][C]15[/C][C]0.018938[/C][C]0.1136[/C][C]0.455083[/C][/ROW]
[ROW][C]16[/C][C]-0.139971[/C][C]-0.8398[/C][C]0.203275[/C][/ROW]
[ROW][C]17[/C][C]0.171959[/C][C]1.0318[/C][C]0.154535[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150098&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150098&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	-0.085406	-0.5124	0.305738
2	-0.042509	-0.2551	0.400067
3	-0.077064	-0.4624	0.323293
4	0.049278	0.2957	0.38459
5	0.180265	1.0816	0.143313
6	-0.089462	-0.5368	0.297363
7	-0.300777	-1.8047	0.039749
8	-0.178839	-1.073	0.145198
9	0.06765	0.4059	0.343609
10	-0.028205	-0.1692	0.433283
11	-0.080073	-0.4804	0.316911
12	-0.249955	-1.4997	0.071202
13	0.092692	0.5562	0.290774
14	0.122822	0.7369	0.23297
15	0.018938	0.1136	0.455083
16	-0.139971	-0.8398	0.203275
17	0.171959	1.0318	0.154535

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.085406	-0.5124	0.305738
2	-0.050169	-0.301	0.382568
3	-0.086004	-0.516	0.304496
4	0.032789	0.1967	0.42257
5	0.183046	1.0983	0.139687
6	-0.060906	-0.3654	0.358461
7	-0.308769	-1.8526	0.036075
8	-0.25262	-1.5157	0.069161
9	-0.029128	-0.1748	0.431121
10	-0.105381	-0.6323	0.265598
11	-0.089544	-0.5373	0.297196
12	-0.209418	-1.2565	0.108513
13	0.021083	0.1265	0.45002
14	-0.020308	-0.1218	0.451849
15	-0.128566	-0.7714	0.222753
16	-0.236741	-1.4204	0.082041
17	0.160705	0.9642	0.170681

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.085406 & -0.5124 & 0.305738 \tabularnewline
2 & -0.050169 & -0.301 & 0.382568 \tabularnewline
3 & -0.086004 & -0.516 & 0.304496 \tabularnewline
4 & 0.032789 & 0.1967 & 0.42257 \tabularnewline
5 & 0.183046 & 1.0983 & 0.139687 \tabularnewline
6 & -0.060906 & -0.3654 & 0.358461 \tabularnewline
7 & -0.308769 & -1.8526 & 0.036075 \tabularnewline
8 & -0.25262 & -1.5157 & 0.069161 \tabularnewline
9 & -0.029128 & -0.1748 & 0.431121 \tabularnewline
10 & -0.105381 & -0.6323 & 0.265598 \tabularnewline
11 & -0.089544 & -0.5373 & 0.297196 \tabularnewline
12 & -0.209418 & -1.2565 & 0.108513 \tabularnewline
13 & 0.021083 & 0.1265 & 0.45002 \tabularnewline
14 & -0.020308 & -0.1218 & 0.451849 \tabularnewline
15 & -0.128566 & -0.7714 & 0.222753 \tabularnewline
16 & -0.236741 & -1.4204 & 0.082041 \tabularnewline
17 & 0.160705 & 0.9642 & 0.170681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150098&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]-0.085406[/C][C]-0.5124[/C][C]0.305738[/C][/ROW]
[ROW][C]2[/C][C]-0.050169[/C][C]-0.301[/C][C]0.382568[/C][/ROW]
[ROW][C]3[/C][C]-0.086004[/C][C]-0.516[/C][C]0.304496[/C][/ROW]
[ROW][C]4[/C][C]0.032789[/C][C]0.1967[/C][C]0.42257[/C][/ROW]
[ROW][C]5[/C][C]0.183046[/C][C]1.0983[/C][C]0.139687[/C][/ROW]
[ROW][C]6[/C][C]-0.060906[/C][C]-0.3654[/C][C]0.358461[/C][/ROW]
[ROW][C]7[/C][C]-0.308769[/C][C]-1.8526[/C][C]0.036075[/C][/ROW]
[ROW][C]8[/C][C]-0.25262[/C][C]-1.5157[/C][C]0.069161[/C][/ROW]
[ROW][C]9[/C][C]-0.029128[/C][C]-0.1748[/C][C]0.431121[/C][/ROW]
[ROW][C]10[/C][C]-0.105381[/C][C]-0.6323[/C][C]0.265598[/C][/ROW]
[ROW][C]11[/C][C]-0.089544[/C][C]-0.5373[/C][C]0.297196[/C][/ROW]
[ROW][C]12[/C][C]-0.209418[/C][C]-1.2565[/C][C]0.108513[/C][/ROW]
[ROW][C]13[/C][C]0.021083[/C][C]0.1265[/C][C]0.45002[/C][/ROW]
[ROW][C]14[/C][C]-0.020308[/C][C]-0.1218[/C][C]0.451849[/C][/ROW]
[ROW][C]15[/C][C]-0.128566[/C][C]-0.7714[/C][C]0.222753[/C][/ROW]
[ROW][C]16[/C][C]-0.236741[/C][C]-1.4204[/C][C]0.082041[/C][/ROW]
[ROW][C]17[/C][C]0.160705[/C][C]0.9642[/C][C]0.170681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150098&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150098&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	-0.085406	-0.5124	0.305738
2	-0.050169	-0.301	0.382568
3	-0.086004	-0.516	0.304496
4	0.032789	0.1967	0.42257
5	0.183046	1.0983	0.139687
6	-0.060906	-0.3654	0.358461
7	-0.308769	-1.8526	0.036075
8	-0.25262	-1.5157	0.069161
9	-0.029128	-0.1748	0.431121
10	-0.105381	-0.6323	0.265598
11	-0.089544	-0.5373	0.297196
12	-0.209418	-1.2565	0.108513
13	0.021083	0.1265	0.45002
14	-0.020308	-0.1218	0.451849
15	-0.128566	-0.7714	0.222753
16	-0.236741	-1.4204	0.082041
17	0.160705	0.9642	0.170681

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 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 2 ; 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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