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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 12 Aug 2016 20:39:13 +0100

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/Aug/12/t1471030767a0xrf05790kibhn.htm/, Retrieved Sun, 05 May 2024 10:51:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296467, Retrieved Sun, 05 May 2024 10:51:06 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-08-12 19:39:13] [517bf63cbd197750110a40d4d2cd39d6] [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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296467&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296467&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296467&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.869406	9.5239	0
2	0.765557	8.3863	0
3	0.723465	7.9252	0
4	0.686961	7.5253	0
5	0.704161	7.7137	0
6	0.723819	7.929	0
7	0.677797	7.4249	0
8	0.627214	6.8708	0
9	0.627479	6.8737	0
10	0.613802	6.7239	0
11	0.664022	7.274	0
12	0.722977	7.9198	0
13	0.600405	6.5771	0
14	0.494973	5.4222	0
15	0.447252	4.8994	2e-06
16	0.409729	4.4884	8e-06
17	0.423491	4.6391	4e-06
18	0.448355	4.9115	1e-06
19	0.407343	4.4622	9e-06
20	0.34875	3.8204	0.000106

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.869406 & 9.5239 & 0 \tabularnewline
2 & 0.765557 & 8.3863 & 0 \tabularnewline
3 & 0.723465 & 7.9252 & 0 \tabularnewline
4 & 0.686961 & 7.5253 & 0 \tabularnewline
5 & 0.704161 & 7.7137 & 0 \tabularnewline
6 & 0.723819 & 7.929 & 0 \tabularnewline
7 & 0.677797 & 7.4249 & 0 \tabularnewline
8 & 0.627214 & 6.8708 & 0 \tabularnewline
9 & 0.627479 & 6.8737 & 0 \tabularnewline
10 & 0.613802 & 6.7239 & 0 \tabularnewline
11 & 0.664022 & 7.274 & 0 \tabularnewline
12 & 0.722977 & 7.9198 & 0 \tabularnewline
13 & 0.600405 & 6.5771 & 0 \tabularnewline
14 & 0.494973 & 5.4222 & 0 \tabularnewline
15 & 0.447252 & 4.8994 & 2e-06 \tabularnewline
16 & 0.409729 & 4.4884 & 8e-06 \tabularnewline
17 & 0.423491 & 4.6391 & 4e-06 \tabularnewline
18 & 0.448355 & 4.9115 & 1e-06 \tabularnewline
19 & 0.407343 & 4.4622 & 9e-06 \tabularnewline
20 & 0.34875 & 3.8204 & 0.000106 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296467&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]0.869406[/C][C]9.5239[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.765557[/C][C]8.3863[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.723465[/C][C]7.9252[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.686961[/C][C]7.5253[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.704161[/C][C]7.7137[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.723819[/C][C]7.929[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.677797[/C][C]7.4249[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.627214[/C][C]6.8708[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.627479[/C][C]6.8737[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.613802[/C][C]6.7239[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.664022[/C][C]7.274[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.722977[/C][C]7.9198[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.600405[/C][C]6.5771[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.494973[/C][C]5.4222[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.447252[/C][C]4.8994[/C][C]2e-06[/C][/ROW]
[ROW][C]16[/C][C]0.409729[/C][C]4.4884[/C][C]8e-06[/C][/ROW]
[ROW][C]17[/C][C]0.423491[/C][C]4.6391[/C][C]4e-06[/C][/ROW]
[ROW][C]18[/C][C]0.448355[/C][C]4.9115[/C][C]1e-06[/C][/ROW]
[ROW][C]19[/C][C]0.407343[/C][C]4.4622[/C][C]9e-06[/C][/ROW]
[ROW][C]20[/C][C]0.34875[/C][C]3.8204[/C][C]0.000106[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296467&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296467&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	0.869406	9.5239	0
2	0.765557	8.3863	0
3	0.723465	7.9252	0
4	0.686961	7.5253	0
5	0.704161	7.7137	0
6	0.723819	7.929	0
7	0.677797	7.4249	0
8	0.627214	6.8708	0
9	0.627479	6.8737	0
10	0.613802	6.7239	0
11	0.664022	7.274	0
12	0.722977	7.9198	0
13	0.600405	6.5771	0
14	0.494973	5.4222	0
15	0.447252	4.8994	2e-06
16	0.409729	4.4884	8e-06
17	0.423491	4.6391	4e-06
18	0.448355	4.9115	1e-06
19	0.407343	4.4622	9e-06
20	0.34875	3.8204	0.000106

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.869406	9.5239	0
2	0.03969	0.4348	0.332249
3	0.204292	2.2379	0.013536
4	0.048742	0.5339	0.297187
5	0.27969	3.0638	0.001349
6	0.120368	1.3186	0.094912
7	-0.114245	-1.2515	0.106595
8	-0.029209	-0.32	0.374775
9	0.167381	1.8336	0.034598
10	-0.022765	-0.2494	0.401748
11	0.294518	3.2263	0.000808
12	0.151056	1.6547	0.050296
13	-0.593748	-6.5042	0
14	-0.119012	-1.3037	0.097413
15	-0.003789	-0.0415	0.483482
16	-0.027319	-0.2993	0.382626
17	0.010588	0.116	0.453931
18	0.04866	0.533	0.297493
19	0.022947	0.2514	0.40098
20	-0.089467	-0.9801	0.164513

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.869406 & 9.5239 & 0 \tabularnewline
2 & 0.03969 & 0.4348 & 0.332249 \tabularnewline
3 & 0.204292 & 2.2379 & 0.013536 \tabularnewline
4 & 0.048742 & 0.5339 & 0.297187 \tabularnewline
5 & 0.27969 & 3.0638 & 0.001349 \tabularnewline
6 & 0.120368 & 1.3186 & 0.094912 \tabularnewline
7 & -0.114245 & -1.2515 & 0.106595 \tabularnewline
8 & -0.029209 & -0.32 & 0.374775 \tabularnewline
9 & 0.167381 & 1.8336 & 0.034598 \tabularnewline
10 & -0.022765 & -0.2494 & 0.401748 \tabularnewline
11 & 0.294518 & 3.2263 & 0.000808 \tabularnewline
12 & 0.151056 & 1.6547 & 0.050296 \tabularnewline
13 & -0.593748 & -6.5042 & 0 \tabularnewline
14 & -0.119012 & -1.3037 & 0.097413 \tabularnewline
15 & -0.003789 & -0.0415 & 0.483482 \tabularnewline
16 & -0.027319 & -0.2993 & 0.382626 \tabularnewline
17 & 0.010588 & 0.116 & 0.453931 \tabularnewline
18 & 0.04866 & 0.533 & 0.297493 \tabularnewline
19 & 0.022947 & 0.2514 & 0.40098 \tabularnewline
20 & -0.089467 & -0.9801 & 0.164513 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296467&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]0.869406[/C][C]9.5239[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.03969[/C][C]0.4348[/C][C]0.332249[/C][/ROW]
[ROW][C]3[/C][C]0.204292[/C][C]2.2379[/C][C]0.013536[/C][/ROW]
[ROW][C]4[/C][C]0.048742[/C][C]0.5339[/C][C]0.297187[/C][/ROW]
[ROW][C]5[/C][C]0.27969[/C][C]3.0638[/C][C]0.001349[/C][/ROW]
[ROW][C]6[/C][C]0.120368[/C][C]1.3186[/C][C]0.094912[/C][/ROW]
[ROW][C]7[/C][C]-0.114245[/C][C]-1.2515[/C][C]0.106595[/C][/ROW]
[ROW][C]8[/C][C]-0.029209[/C][C]-0.32[/C][C]0.374775[/C][/ROW]
[ROW][C]9[/C][C]0.167381[/C][C]1.8336[/C][C]0.034598[/C][/ROW]
[ROW][C]10[/C][C]-0.022765[/C][C]-0.2494[/C][C]0.401748[/C][/ROW]
[ROW][C]11[/C][C]0.294518[/C][C]3.2263[/C][C]0.000808[/C][/ROW]
[ROW][C]12[/C][C]0.151056[/C][C]1.6547[/C][C]0.050296[/C][/ROW]
[ROW][C]13[/C][C]-0.593748[/C][C]-6.5042[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]-0.119012[/C][C]-1.3037[/C][C]0.097413[/C][/ROW]
[ROW][C]15[/C][C]-0.003789[/C][C]-0.0415[/C][C]0.483482[/C][/ROW]
[ROW][C]16[/C][C]-0.027319[/C][C]-0.2993[/C][C]0.382626[/C][/ROW]
[ROW][C]17[/C][C]0.010588[/C][C]0.116[/C][C]0.453931[/C][/ROW]
[ROW][C]18[/C][C]0.04866[/C][C]0.533[/C][C]0.297493[/C][/ROW]
[ROW][C]19[/C][C]0.022947[/C][C]0.2514[/C][C]0.40098[/C][/ROW]
[ROW][C]20[/C][C]-0.089467[/C][C]-0.9801[/C][C]0.164513[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296467&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296467&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	0.869406	9.5239	0
2	0.03969	0.4348	0.332249
3	0.204292	2.2379	0.013536
4	0.048742	0.5339	0.297187
5	0.27969	3.0638	0.001349
6	0.120368	1.3186	0.094912
7	-0.114245	-1.2515	0.106595
8	-0.029209	-0.32	0.374775
9	0.167381	1.8336	0.034598
10	-0.022765	-0.2494	0.401748
11	0.294518	3.2263	0.000808
12	0.151056	1.6547	0.050296
13	-0.593748	-6.5042	0
14	-0.119012	-1.3037	0.097413
15	-0.003789	-0.0415	0.483482
16	-0.027319	-0.2993	0.382626
17	0.010588	0.116	0.453931
18	0.04866	0.533	0.297493
19	0.022947	0.2514	0.40098
20	-0.089467	-0.9801	0.164513

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):

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