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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 13 Nov 2013 04:05:25 -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/2013/Nov/13/t13843335848qnsu1fcmtuwk5e.htm/, Retrieved Mon, 29 Apr 2024 07:13:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=224647, Retrieved Mon, 29 Apr 2024 07:13:41 +0000

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-       [(Partial) Autocorrelation Function] [] [2013-11-13 09:05:25] [3050d341fa02a6066b7b273abfa2c28b] [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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224647&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224647&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224647&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.185916	-1.5666	0.060833
2	-0.188498	-1.5883	0.058329
3	-0.191081	-1.6101	0.05591
4	-0.176996	-1.4914	0.070144
5	-0.179578	-1.5132	0.06734
6	0.695113	5.8571	0
7	0.047076	0.3967	0.3464
8	-0.170658	-1.438	0.077415
9	-0.17324	-1.4597	0.074385
10	-0.159155	-1.3411	0.092087
11	-0.161737	-1.3628	0.088622
12	0.390226	3.2881	0.000785
13	0.280068	2.3599	0.010516
14	-0.152817	-1.2877	0.101023
15	-0.1554	-1.3094	0.097307
16	-0.141315	-1.1907	0.118861
17	-0.143897	-1.2125	0.114671
18	0.08534	0.7191	0.237224

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.185916 & -1.5666 & 0.060833 \tabularnewline
2 & -0.188498 & -1.5883 & 0.058329 \tabularnewline
3 & -0.191081 & -1.6101 & 0.05591 \tabularnewline
4 & -0.176996 & -1.4914 & 0.070144 \tabularnewline
5 & -0.179578 & -1.5132 & 0.06734 \tabularnewline
6 & 0.695113 & 5.8571 & 0 \tabularnewline
7 & 0.047076 & 0.3967 & 0.3464 \tabularnewline
8 & -0.170658 & -1.438 & 0.077415 \tabularnewline
9 & -0.17324 & -1.4597 & 0.074385 \tabularnewline
10 & -0.159155 & -1.3411 & 0.092087 \tabularnewline
11 & -0.161737 & -1.3628 & 0.088622 \tabularnewline
12 & 0.390226 & 3.2881 & 0.000785 \tabularnewline
13 & 0.280068 & 2.3599 & 0.010516 \tabularnewline
14 & -0.152817 & -1.2877 & 0.101023 \tabularnewline
15 & -0.1554 & -1.3094 & 0.097307 \tabularnewline
16 & -0.141315 & -1.1907 & 0.118861 \tabularnewline
17 & -0.143897 & -1.2125 & 0.114671 \tabularnewline
18 & 0.08534 & 0.7191 & 0.237224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224647&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]-0.185916[/C][C]-1.5666[/C][C]0.060833[/C][/ROW]
[ROW][C]2[/C][C]-0.188498[/C][C]-1.5883[/C][C]0.058329[/C][/ROW]
[ROW][C]3[/C][C]-0.191081[/C][C]-1.6101[/C][C]0.05591[/C][/ROW]
[ROW][C]4[/C][C]-0.176996[/C][C]-1.4914[/C][C]0.070144[/C][/ROW]
[ROW][C]5[/C][C]-0.179578[/C][C]-1.5132[/C][C]0.06734[/C][/ROW]
[ROW][C]6[/C][C]0.695113[/C][C]5.8571[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.047076[/C][C]0.3967[/C][C]0.3464[/C][/ROW]
[ROW][C]8[/C][C]-0.170658[/C][C]-1.438[/C][C]0.077415[/C][/ROW]
[ROW][C]9[/C][C]-0.17324[/C][C]-1.4597[/C][C]0.074385[/C][/ROW]
[ROW][C]10[/C][C]-0.159155[/C][C]-1.3411[/C][C]0.092087[/C][/ROW]
[ROW][C]11[/C][C]-0.161737[/C][C]-1.3628[/C][C]0.088622[/C][/ROW]
[ROW][C]12[/C][C]0.390226[/C][C]3.2881[/C][C]0.000785[/C][/ROW]
[ROW][C]13[/C][C]0.280068[/C][C]2.3599[/C][C]0.010516[/C][/ROW]
[ROW][C]14[/C][C]-0.152817[/C][C]-1.2877[/C][C]0.101023[/C][/ROW]
[ROW][C]15[/C][C]-0.1554[/C][C]-1.3094[/C][C]0.097307[/C][/ROW]
[ROW][C]16[/C][C]-0.141315[/C][C]-1.1907[/C][C]0.118861[/C][/ROW]
[ROW][C]17[/C][C]-0.143897[/C][C]-1.2125[/C][C]0.114671[/C][/ROW]
[ROW][C]18[/C][C]0.08534[/C][C]0.7191[/C][C]0.237224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224647&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224647&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	-0.185916	-1.5666	0.060833
2	-0.188498	-1.5883	0.058329
3	-0.191081	-1.6101	0.05591
4	-0.176996	-1.4914	0.070144
5	-0.179578	-1.5132	0.06734
6	0.695113	5.8571	0
7	0.047076	0.3967	0.3464
8	-0.170658	-1.438	0.077415
9	-0.17324	-1.4597	0.074385
10	-0.159155	-1.3411	0.092087
11	-0.161737	-1.3628	0.088622
12	0.390226	3.2881	0.000785
13	0.280068	2.3599	0.010516
14	-0.152817	-1.2877	0.101023
15	-0.1554	-1.3094	0.097307
16	-0.141315	-1.1907	0.118861
17	-0.143897	-1.2125	0.114671
18	0.08534	0.7191	0.237224

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.185915	-1.5666	0.060833
2	-0.231048	-1.9468	0.027755
3	-0.303291	-2.5556	0.006372
4	-0.418327	-3.5249	0.000373
5	-0.722877	-6.0911	0
6	0.067692	0.5704	0.285109
7	0.094712	0.7981	0.213748
8	0.002482	0.0209	0.491686
9	-0.006474	-0.0545	0.478325
10	0.0027	0.0227	0.490957
11	0.023593	0.1988	0.421493
12	-0.22621	-1.9061	0.030344
13	0.057445	0.484	0.314925
14	-0.008434	-0.0711	0.471771
15	-0.009	-0.0758	0.46988
16	0.013746	0.1158	0.454057
17	0.032463	0.2735	0.392617
18	-0.304347	-2.5645	0.006225

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.185915 & -1.5666 & 0.060833 \tabularnewline
2 & -0.231048 & -1.9468 & 0.027755 \tabularnewline
3 & -0.303291 & -2.5556 & 0.006372 \tabularnewline
4 & -0.418327 & -3.5249 & 0.000373 \tabularnewline
5 & -0.722877 & -6.0911 & 0 \tabularnewline
6 & 0.067692 & 0.5704 & 0.285109 \tabularnewline
7 & 0.094712 & 0.7981 & 0.213748 \tabularnewline
8 & 0.002482 & 0.0209 & 0.491686 \tabularnewline
9 & -0.006474 & -0.0545 & 0.478325 \tabularnewline
10 & 0.0027 & 0.0227 & 0.490957 \tabularnewline
11 & 0.023593 & 0.1988 & 0.421493 \tabularnewline
12 & -0.22621 & -1.9061 & 0.030344 \tabularnewline
13 & 0.057445 & 0.484 & 0.314925 \tabularnewline
14 & -0.008434 & -0.0711 & 0.471771 \tabularnewline
15 & -0.009 & -0.0758 & 0.46988 \tabularnewline
16 & 0.013746 & 0.1158 & 0.454057 \tabularnewline
17 & 0.032463 & 0.2735 & 0.392617 \tabularnewline
18 & -0.304347 & -2.5645 & 0.006225 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224647&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]-0.185915[/C][C]-1.5666[/C][C]0.060833[/C][/ROW]
[ROW][C]2[/C][C]-0.231048[/C][C]-1.9468[/C][C]0.027755[/C][/ROW]
[ROW][C]3[/C][C]-0.303291[/C][C]-2.5556[/C][C]0.006372[/C][/ROW]
[ROW][C]4[/C][C]-0.418327[/C][C]-3.5249[/C][C]0.000373[/C][/ROW]
[ROW][C]5[/C][C]-0.722877[/C][C]-6.0911[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.067692[/C][C]0.5704[/C][C]0.285109[/C][/ROW]
[ROW][C]7[/C][C]0.094712[/C][C]0.7981[/C][C]0.213748[/C][/ROW]
[ROW][C]8[/C][C]0.002482[/C][C]0.0209[/C][C]0.491686[/C][/ROW]
[ROW][C]9[/C][C]-0.006474[/C][C]-0.0545[/C][C]0.478325[/C][/ROW]
[ROW][C]10[/C][C]0.0027[/C][C]0.0227[/C][C]0.490957[/C][/ROW]
[ROW][C]11[/C][C]0.023593[/C][C]0.1988[/C][C]0.421493[/C][/ROW]
[ROW][C]12[/C][C]-0.22621[/C][C]-1.9061[/C][C]0.030344[/C][/ROW]
[ROW][C]13[/C][C]0.057445[/C][C]0.484[/C][C]0.314925[/C][/ROW]
[ROW][C]14[/C][C]-0.008434[/C][C]-0.0711[/C][C]0.471771[/C][/ROW]
[ROW][C]15[/C][C]-0.009[/C][C]-0.0758[/C][C]0.46988[/C][/ROW]
[ROW][C]16[/C][C]0.013746[/C][C]0.1158[/C][C]0.454057[/C][/ROW]
[ROW][C]17[/C][C]0.032463[/C][C]0.2735[/C][C]0.392617[/C][/ROW]
[ROW][C]18[/C][C]-0.304347[/C][C]-2.5645[/C][C]0.006225[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224647&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224647&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	-0.185915	-1.5666	0.060833
2	-0.231048	-1.9468	0.027755
3	-0.303291	-2.5556	0.006372
4	-0.418327	-3.5249	0.000373
5	-0.722877	-6.0911	0
6	0.067692	0.5704	0.285109
7	0.094712	0.7981	0.213748
8	0.002482	0.0209	0.491686
9	-0.006474	-0.0545	0.478325
10	0.0027	0.0227	0.490957
11	0.023593	0.1988	0.421493
12	-0.22621	-1.9061	0.030344
13	0.057445	0.484	0.314925
14	-0.008434	-0.0711	0.471771
15	-0.009	-0.0758	0.46988
16	0.013746	0.1158	0.454057
17	0.032463	0.2735	0.392617
18	-0.304347	-2.5645	0.006225

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '1'
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)
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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code