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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 11 Jan 2016 10:19:59 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Jan/11/t1452507642mwc9mu18b9imqpy.htm/, Retrieved Sat, 04 May 2024 02:35:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=289417, Retrieved Sat, 04 May 2024 02:35:31 +0000

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Estimated Impact

130

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-     [International Conference on Virtual Learning 2008] [ICVL 2008 - Figure 2] [2008-06-30 15:48:43] [74be16979710d4c4e7c6647856088456]
- RMPD    [(Partial) Autocorrelation Function] [vraag 6] [2016-01-11 10:19:59] [5c12abf8e1d909674bdd524d224ad2b3] [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	2 seconds
R Server	'George Udny Yule' @ yule.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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289417&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]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289417&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289417&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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.755051	6.4068	0
2	0.396957	3.3683	0.000609
3	0.019396	0.1646	0.434869
4	-0.355898	-3.0199	0.001749
5	-0.608566	-5.1639	1e-06
6	-0.681383	-5.7817	0
7	-0.60791	-5.1583	1e-06
8	-0.378212	-3.2092	0.000994
9	-0.012976	-0.1101	0.456317
10	0.383253	3.252	0.000873
11	0.650207	5.5172	0
12	0.723167	6.1363	0
13	0.638001	5.4136	0
14	0.371578	3.1529	0.001179
15	0.009467	0.0803	0.468097
16	-0.2937	-2.4921	0.0075
17	-0.496742	-4.215	3.6e-05
18	-0.585559	-4.9686	2e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.755051 & 6.4068 & 0 \tabularnewline
2 & 0.396957 & 3.3683 & 0.000609 \tabularnewline
3 & 0.019396 & 0.1646 & 0.434869 \tabularnewline
4 & -0.355898 & -3.0199 & 0.001749 \tabularnewline
5 & -0.608566 & -5.1639 & 1e-06 \tabularnewline
6 & -0.681383 & -5.7817 & 0 \tabularnewline
7 & -0.60791 & -5.1583 & 1e-06 \tabularnewline
8 & -0.378212 & -3.2092 & 0.000994 \tabularnewline
9 & -0.012976 & -0.1101 & 0.456317 \tabularnewline
10 & 0.383253 & 3.252 & 0.000873 \tabularnewline
11 & 0.650207 & 5.5172 & 0 \tabularnewline
12 & 0.723167 & 6.1363 & 0 \tabularnewline
13 & 0.638001 & 5.4136 & 0 \tabularnewline
14 & 0.371578 & 3.1529 & 0.001179 \tabularnewline
15 & 0.009467 & 0.0803 & 0.468097 \tabularnewline
16 & -0.2937 & -2.4921 & 0.0075 \tabularnewline
17 & -0.496742 & -4.215 & 3.6e-05 \tabularnewline
18 & -0.585559 & -4.9686 & 2e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289417&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]0.755051[/C][C]6.4068[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.396957[/C][C]3.3683[/C][C]0.000609[/C][/ROW]
[ROW][C]3[/C][C]0.019396[/C][C]0.1646[/C][C]0.434869[/C][/ROW]
[ROW][C]4[/C][C]-0.355898[/C][C]-3.0199[/C][C]0.001749[/C][/ROW]
[ROW][C]5[/C][C]-0.608566[/C][C]-5.1639[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]-0.681383[/C][C]-5.7817[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.60791[/C][C]-5.1583[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]-0.378212[/C][C]-3.2092[/C][C]0.000994[/C][/ROW]
[ROW][C]9[/C][C]-0.012976[/C][C]-0.1101[/C][C]0.456317[/C][/ROW]
[ROW][C]10[/C][C]0.383253[/C][C]3.252[/C][C]0.000873[/C][/ROW]
[ROW][C]11[/C][C]0.650207[/C][C]5.5172[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.723167[/C][C]6.1363[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.638001[/C][C]5.4136[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.371578[/C][C]3.1529[/C][C]0.001179[/C][/ROW]
[ROW][C]15[/C][C]0.009467[/C][C]0.0803[/C][C]0.468097[/C][/ROW]
[ROW][C]16[/C][C]-0.2937[/C][C]-2.4921[/C][C]0.0075[/C][/ROW]
[ROW][C]17[/C][C]-0.496742[/C][C]-4.215[/C][C]3.6e-05[/C][/ROW]
[ROW][C]18[/C][C]-0.585559[/C][C]-4.9686[/C][C]2e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289417&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289417&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	0.755051	6.4068	0
2	0.396957	3.3683	0.000609
3	0.019396	0.1646	0.434869
4	-0.355898	-3.0199	0.001749
5	-0.608566	-5.1639	1e-06
6	-0.681383	-5.7817	0
7	-0.60791	-5.1583	1e-06
8	-0.378212	-3.2092	0.000994
9	-0.012976	-0.1101	0.456317
10	0.383253	3.252	0.000873
11	0.650207	5.5172	0
12	0.723167	6.1363	0
13	0.638001	5.4136	0
14	0.371578	3.1529	0.001179
15	0.009467	0.0803	0.468097
16	-0.2937	-2.4921	0.0075
17	-0.496742	-4.215	3.6e-05
18	-0.585559	-4.9686	2e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.755051	6.4068	0
2	-0.402759	-3.4175	0.000521
3	-0.269154	-2.2839	0.012666
4	-0.372371	-3.1597	0.001155
5	-0.192068	-1.6298	0.053761
6	-0.11561	-0.981	0.164943
7	-0.152737	-1.296	0.099555
8	0.005216	0.0443	0.48241
9	0.20164	1.711	0.045696
10	0.295303	2.5057	0.007241
11	0.120693	1.0241	0.154605
12	0.021604	0.1833	0.427534
13	0.138406	1.1744	0.12205
14	-0.026658	-0.2262	0.410844
15	-0.061025	-0.5178	0.303087
16	0.093598	0.7942	0.214843
17	0.133508	1.1329	0.130517
18	0.050714	0.4303	0.334124

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.755051 & 6.4068 & 0 \tabularnewline
2 & -0.402759 & -3.4175 & 0.000521 \tabularnewline
3 & -0.269154 & -2.2839 & 0.012666 \tabularnewline
4 & -0.372371 & -3.1597 & 0.001155 \tabularnewline
5 & -0.192068 & -1.6298 & 0.053761 \tabularnewline
6 & -0.11561 & -0.981 & 0.164943 \tabularnewline
7 & -0.152737 & -1.296 & 0.099555 \tabularnewline
8 & 0.005216 & 0.0443 & 0.48241 \tabularnewline
9 & 0.20164 & 1.711 & 0.045696 \tabularnewline
10 & 0.295303 & 2.5057 & 0.007241 \tabularnewline
11 & 0.120693 & 1.0241 & 0.154605 \tabularnewline
12 & 0.021604 & 0.1833 & 0.427534 \tabularnewline
13 & 0.138406 & 1.1744 & 0.12205 \tabularnewline
14 & -0.026658 & -0.2262 & 0.410844 \tabularnewline
15 & -0.061025 & -0.5178 & 0.303087 \tabularnewline
16 & 0.093598 & 0.7942 & 0.214843 \tabularnewline
17 & 0.133508 & 1.1329 & 0.130517 \tabularnewline
18 & 0.050714 & 0.4303 & 0.334124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289417&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]0.755051[/C][C]6.4068[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.402759[/C][C]-3.4175[/C][C]0.000521[/C][/ROW]
[ROW][C]3[/C][C]-0.269154[/C][C]-2.2839[/C][C]0.012666[/C][/ROW]
[ROW][C]4[/C][C]-0.372371[/C][C]-3.1597[/C][C]0.001155[/C][/ROW]
[ROW][C]5[/C][C]-0.192068[/C][C]-1.6298[/C][C]0.053761[/C][/ROW]
[ROW][C]6[/C][C]-0.11561[/C][C]-0.981[/C][C]0.164943[/C][/ROW]
[ROW][C]7[/C][C]-0.152737[/C][C]-1.296[/C][C]0.099555[/C][/ROW]
[ROW][C]8[/C][C]0.005216[/C][C]0.0443[/C][C]0.48241[/C][/ROW]
[ROW][C]9[/C][C]0.20164[/C][C]1.711[/C][C]0.045696[/C][/ROW]
[ROW][C]10[/C][C]0.295303[/C][C]2.5057[/C][C]0.007241[/C][/ROW]
[ROW][C]11[/C][C]0.120693[/C][C]1.0241[/C][C]0.154605[/C][/ROW]
[ROW][C]12[/C][C]0.021604[/C][C]0.1833[/C][C]0.427534[/C][/ROW]
[ROW][C]13[/C][C]0.138406[/C][C]1.1744[/C][C]0.12205[/C][/ROW]
[ROW][C]14[/C][C]-0.026658[/C][C]-0.2262[/C][C]0.410844[/C][/ROW]
[ROW][C]15[/C][C]-0.061025[/C][C]-0.5178[/C][C]0.303087[/C][/ROW]
[ROW][C]16[/C][C]0.093598[/C][C]0.7942[/C][C]0.214843[/C][/ROW]
[ROW][C]17[/C][C]0.133508[/C][C]1.1329[/C][C]0.130517[/C][/ROW]
[ROW][C]18[/C][C]0.050714[/C][C]0.4303[/C][C]0.334124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289417&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289417&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	0.755051	6.4068	0
2	-0.402759	-3.4175	0.000521
3	-0.269154	-2.2839	0.012666
4	-0.372371	-3.1597	0.001155
5	-0.192068	-1.6298	0.053761
6	-0.11561	-0.981	0.164943
7	-0.152737	-1.296	0.099555
8	0.005216	0.0443	0.48241
9	0.20164	1.711	0.045696
10	0.295303	2.5057	0.007241
11	0.120693	1.0241	0.154605
12	0.021604	0.1833	0.427534
13	0.138406	1.1744	0.12205
14	-0.026658	-0.2262	0.410844
15	-0.061025	-0.5178	0.303087
16	0.093598	0.7942	0.214843
17	0.133508	1.1329	0.130517
18	0.050714	0.4303	0.334124

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code