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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 26 May 2012 07:47:28 -0400

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/2012/May/26/t1338032891ky5g3njmz7gzld5.htm/, Retrieved Thu, 02 May 2024 20:11:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167585, Retrieved Thu, 02 May 2024 20:11:20 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W11

Estimated Impact

106

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-       [(Partial) Autocorrelation Function] [Autocorrelation f...] [2012-05-26 11:47:28] [a2709f7ab86902c8a6d752383a828f6c] [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	'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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167585&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167585&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167585&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.581191	4.5019	1.6e-05
2	0.366467	2.8386	0.003087
3	0.143157	1.1089	0.135952
4	0.022204	0.172	0.432011
5	0.032109	0.2487	0.402214
6	0.016271	0.126	0.450064
7	-0.03923	-0.3039	0.381138
8	-0.043867	-0.3398	0.367601
9	-0.060991	-0.4724	0.319166
10	-0.278502	-2.1573	0.0175
11	-0.435643	-3.3745	0.000651
12	-0.550778	-4.2663	3.6e-05
13	-0.417675	-3.2353	0.000989
14	-0.213554	-1.6542	0.051656
15	-0.01961	-0.1519	0.439889
16	-0.098895	-0.766	0.223328
17	-0.011575	-0.0897	0.464429
18	-0.009765	-0.0756	0.469979

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.581191 & 4.5019 & 1.6e-05 \tabularnewline
2 & 0.366467 & 2.8386 & 0.003087 \tabularnewline
3 & 0.143157 & 1.1089 & 0.135952 \tabularnewline
4 & 0.022204 & 0.172 & 0.432011 \tabularnewline
5 & 0.032109 & 0.2487 & 0.402214 \tabularnewline
6 & 0.016271 & 0.126 & 0.450064 \tabularnewline
7 & -0.03923 & -0.3039 & 0.381138 \tabularnewline
8 & -0.043867 & -0.3398 & 0.367601 \tabularnewline
9 & -0.060991 & -0.4724 & 0.319166 \tabularnewline
10 & -0.278502 & -2.1573 & 0.0175 \tabularnewline
11 & -0.435643 & -3.3745 & 0.000651 \tabularnewline
12 & -0.550778 & -4.2663 & 3.6e-05 \tabularnewline
13 & -0.417675 & -3.2353 & 0.000989 \tabularnewline
14 & -0.213554 & -1.6542 & 0.051656 \tabularnewline
15 & -0.01961 & -0.1519 & 0.439889 \tabularnewline
16 & -0.098895 & -0.766 & 0.223328 \tabularnewline
17 & -0.011575 & -0.0897 & 0.464429 \tabularnewline
18 & -0.009765 & -0.0756 & 0.469979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167585&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]0.581191[/C][C]4.5019[/C][C]1.6e-05[/C][/ROW]
[ROW][C]2[/C][C]0.366467[/C][C]2.8386[/C][C]0.003087[/C][/ROW]
[ROW][C]3[/C][C]0.143157[/C][C]1.1089[/C][C]0.135952[/C][/ROW]
[ROW][C]4[/C][C]0.022204[/C][C]0.172[/C][C]0.432011[/C][/ROW]
[ROW][C]5[/C][C]0.032109[/C][C]0.2487[/C][C]0.402214[/C][/ROW]
[ROW][C]6[/C][C]0.016271[/C][C]0.126[/C][C]0.450064[/C][/ROW]
[ROW][C]7[/C][C]-0.03923[/C][C]-0.3039[/C][C]0.381138[/C][/ROW]
[ROW][C]8[/C][C]-0.043867[/C][C]-0.3398[/C][C]0.367601[/C][/ROW]
[ROW][C]9[/C][C]-0.060991[/C][C]-0.4724[/C][C]0.319166[/C][/ROW]
[ROW][C]10[/C][C]-0.278502[/C][C]-2.1573[/C][C]0.0175[/C][/ROW]
[ROW][C]11[/C][C]-0.435643[/C][C]-3.3745[/C][C]0.000651[/C][/ROW]
[ROW][C]12[/C][C]-0.550778[/C][C]-4.2663[/C][C]3.6e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.417675[/C][C]-3.2353[/C][C]0.000989[/C][/ROW]
[ROW][C]14[/C][C]-0.213554[/C][C]-1.6542[/C][C]0.051656[/C][/ROW]
[ROW][C]15[/C][C]-0.01961[/C][C]-0.1519[/C][C]0.439889[/C][/ROW]
[ROW][C]16[/C][C]-0.098895[/C][C]-0.766[/C][C]0.223328[/C][/ROW]
[ROW][C]17[/C][C]-0.011575[/C][C]-0.0897[/C][C]0.464429[/C][/ROW]
[ROW][C]18[/C][C]-0.009765[/C][C]-0.0756[/C][C]0.469979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167585&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167585&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	0.581191	4.5019	1.6e-05
2	0.366467	2.8386	0.003087
3	0.143157	1.1089	0.135952
4	0.022204	0.172	0.432011
5	0.032109	0.2487	0.402214
6	0.016271	0.126	0.450064
7	-0.03923	-0.3039	0.381138
8	-0.043867	-0.3398	0.367601
9	-0.060991	-0.4724	0.319166
10	-0.278502	-2.1573	0.0175
11	-0.435643	-3.3745	0.000651
12	-0.550778	-4.2663	3.6e-05
13	-0.417675	-3.2353	0.000989
14	-0.213554	-1.6542	0.051656
15	-0.01961	-0.1519	0.439889
16	-0.098895	-0.766	0.223328
17	-0.011575	-0.0897	0.464429
18	-0.009765	-0.0756	0.469979

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.581191	4.5019	1.6e-05
2	0.043314	0.3355	0.369206
3	-0.129777	-1.0052	0.159407
4	-0.038609	-0.2991	0.382963
5	0.099607	0.7716	0.221703
6	-0.016915	-0.131	0.448097
7	-0.104024	-0.8058	0.211779
8	0.015847	0.1227	0.451358
9	-0.00253	-0.0196	0.492214
10	-0.370425	-2.8693	0.002836
11	-0.275131	-2.1312	0.018591
12	-0.186274	-1.4429	0.077129
13	0.098999	0.7668	0.223091
14	0.080144	0.6208	0.268543
15	0.106702	0.8265	0.205895
16	-0.274173	-2.1237	0.018912
17	0.122904	0.952	0.172455
18	0.036793	0.285	0.388313

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.581191 & 4.5019 & 1.6e-05 \tabularnewline
2 & 0.043314 & 0.3355 & 0.369206 \tabularnewline
3 & -0.129777 & -1.0052 & 0.159407 \tabularnewline
4 & -0.038609 & -0.2991 & 0.382963 \tabularnewline
5 & 0.099607 & 0.7716 & 0.221703 \tabularnewline
6 & -0.016915 & -0.131 & 0.448097 \tabularnewline
7 & -0.104024 & -0.8058 & 0.211779 \tabularnewline
8 & 0.015847 & 0.1227 & 0.451358 \tabularnewline
9 & -0.00253 & -0.0196 & 0.492214 \tabularnewline
10 & -0.370425 & -2.8693 & 0.002836 \tabularnewline
11 & -0.275131 & -2.1312 & 0.018591 \tabularnewline
12 & -0.186274 & -1.4429 & 0.077129 \tabularnewline
13 & 0.098999 & 0.7668 & 0.223091 \tabularnewline
14 & 0.080144 & 0.6208 & 0.268543 \tabularnewline
15 & 0.106702 & 0.8265 & 0.205895 \tabularnewline
16 & -0.274173 & -2.1237 & 0.018912 \tabularnewline
17 & 0.122904 & 0.952 & 0.172455 \tabularnewline
18 & 0.036793 & 0.285 & 0.388313 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167585&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]0.581191[/C][C]4.5019[/C][C]1.6e-05[/C][/ROW]
[ROW][C]2[/C][C]0.043314[/C][C]0.3355[/C][C]0.369206[/C][/ROW]
[ROW][C]3[/C][C]-0.129777[/C][C]-1.0052[/C][C]0.159407[/C][/ROW]
[ROW][C]4[/C][C]-0.038609[/C][C]-0.2991[/C][C]0.382963[/C][/ROW]
[ROW][C]5[/C][C]0.099607[/C][C]0.7716[/C][C]0.221703[/C][/ROW]
[ROW][C]6[/C][C]-0.016915[/C][C]-0.131[/C][C]0.448097[/C][/ROW]
[ROW][C]7[/C][C]-0.104024[/C][C]-0.8058[/C][C]0.211779[/C][/ROW]
[ROW][C]8[/C][C]0.015847[/C][C]0.1227[/C][C]0.451358[/C][/ROW]
[ROW][C]9[/C][C]-0.00253[/C][C]-0.0196[/C][C]0.492214[/C][/ROW]
[ROW][C]10[/C][C]-0.370425[/C][C]-2.8693[/C][C]0.002836[/C][/ROW]
[ROW][C]11[/C][C]-0.275131[/C][C]-2.1312[/C][C]0.018591[/C][/ROW]
[ROW][C]12[/C][C]-0.186274[/C][C]-1.4429[/C][C]0.077129[/C][/ROW]
[ROW][C]13[/C][C]0.098999[/C][C]0.7668[/C][C]0.223091[/C][/ROW]
[ROW][C]14[/C][C]0.080144[/C][C]0.6208[/C][C]0.268543[/C][/ROW]
[ROW][C]15[/C][C]0.106702[/C][C]0.8265[/C][C]0.205895[/C][/ROW]
[ROW][C]16[/C][C]-0.274173[/C][C]-2.1237[/C][C]0.018912[/C][/ROW]
[ROW][C]17[/C][C]0.122904[/C][C]0.952[/C][C]0.172455[/C][/ROW]
[ROW][C]18[/C][C]0.036793[/C][C]0.285[/C][C]0.388313[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167585&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167585&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	0.581191	4.5019	1.6e-05
2	0.043314	0.3355	0.369206
3	-0.129777	-1.0052	0.159407
4	-0.038609	-0.2991	0.382963
5	0.099607	0.7716	0.221703
6	-0.016915	-0.131	0.448097
7	-0.104024	-0.8058	0.211779
8	0.015847	0.1227	0.451358
9	-0.00253	-0.0196	0.492214
10	-0.370425	-2.8693	0.002836
11	-0.275131	-2.1312	0.018591
12	-0.186274	-1.4429	0.077129
13	0.098999	0.7668	0.223091
14	0.080144	0.6208	0.268543
15	0.106702	0.8265	0.205895
16	-0.274173	-2.1237	0.018912
17	0.122904	0.952	0.172455
18	0.036793	0.285	0.388313

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 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code