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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 04 Apr 2012 11:39:45 -0400

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Apr/04/t1333554034zduf5y9nnbeikbj.htm/, Retrieved Mon, 29 Apr 2024 07:42:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164306, Retrieved Mon, 29 Apr 2024 07:42:39 +0000

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-       [(Partial) Autocorrelation Function] [] [2012-04-04 15:39:45] [606e5654d317e57bd58e5a48c9e4e9a9] [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	'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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164306&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164306&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164306&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.947524	7.3395	0
2	0.894223	6.9266	0
3	0.839482	6.5026	0
4	0.800152	6.198	0
5	0.762206	5.904	0
6	0.718431	5.5649	0
7	0.672231	5.2071	1e-06
8	0.628447	4.8679	4e-06
9	0.577813	4.4757	1.7e-05
10	0.532102	4.1216	5.9e-05
11	0.479157	3.7115	0.000227
12	0.428738	3.321	0.000765
13	0.374616	2.9018	0.002591
14	0.318334	2.4658	0.008273
15	0.265103	2.0535	0.022196
16	0.221511	1.7158	0.045678
17	0.18457	1.4297	0.078998

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.947524 & 7.3395 & 0 \tabularnewline
2 & 0.894223 & 6.9266 & 0 \tabularnewline
3 & 0.839482 & 6.5026 & 0 \tabularnewline
4 & 0.800152 & 6.198 & 0 \tabularnewline
5 & 0.762206 & 5.904 & 0 \tabularnewline
6 & 0.718431 & 5.5649 & 0 \tabularnewline
7 & 0.672231 & 5.2071 & 1e-06 \tabularnewline
8 & 0.628447 & 4.8679 & 4e-06 \tabularnewline
9 & 0.577813 & 4.4757 & 1.7e-05 \tabularnewline
10 & 0.532102 & 4.1216 & 5.9e-05 \tabularnewline
11 & 0.479157 & 3.7115 & 0.000227 \tabularnewline
12 & 0.428738 & 3.321 & 0.000765 \tabularnewline
13 & 0.374616 & 2.9018 & 0.002591 \tabularnewline
14 & 0.318334 & 2.4658 & 0.008273 \tabularnewline
15 & 0.265103 & 2.0535 & 0.022196 \tabularnewline
16 & 0.221511 & 1.7158 & 0.045678 \tabularnewline
17 & 0.18457 & 1.4297 & 0.078998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164306&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]0.947524[/C][C]7.3395[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.894223[/C][C]6.9266[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.839482[/C][C]6.5026[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.800152[/C][C]6.198[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.762206[/C][C]5.904[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.718431[/C][C]5.5649[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.672231[/C][C]5.2071[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.628447[/C][C]4.8679[/C][C]4e-06[/C][/ROW]
[ROW][C]9[/C][C]0.577813[/C][C]4.4757[/C][C]1.7e-05[/C][/ROW]
[ROW][C]10[/C][C]0.532102[/C][C]4.1216[/C][C]5.9e-05[/C][/ROW]
[ROW][C]11[/C][C]0.479157[/C][C]3.7115[/C][C]0.000227[/C][/ROW]
[ROW][C]12[/C][C]0.428738[/C][C]3.321[/C][C]0.000765[/C][/ROW]
[ROW][C]13[/C][C]0.374616[/C][C]2.9018[/C][C]0.002591[/C][/ROW]
[ROW][C]14[/C][C]0.318334[/C][C]2.4658[/C][C]0.008273[/C][/ROW]
[ROW][C]15[/C][C]0.265103[/C][C]2.0535[/C][C]0.022196[/C][/ROW]
[ROW][C]16[/C][C]0.221511[/C][C]1.7158[/C][C]0.045678[/C][/ROW]
[ROW][C]17[/C][C]0.18457[/C][C]1.4297[/C][C]0.078998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164306&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164306&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	0.947524	7.3395	0
2	0.894223	6.9266	0
3	0.839482	6.5026	0
4	0.800152	6.198	0
5	0.762206	5.904	0
6	0.718431	5.5649	0
7	0.672231	5.2071	1e-06
8	0.628447	4.8679	4e-06
9	0.577813	4.4757	1.7e-05
10	0.532102	4.1216	5.9e-05
11	0.479157	3.7115	0.000227
12	0.428738	3.321	0.000765
13	0.374616	2.9018	0.002591
14	0.318334	2.4658	0.008273
15	0.265103	2.0535	0.022196
16	0.221511	1.7158	0.045678
17	0.18457	1.4297	0.078998

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.947524	7.3395	0
2	-0.035023	-0.2713	0.393551
3	-0.042184	-0.3268	0.372495
4	0.121692	0.9426	0.174828
5	-0.011358	-0.088	0.465093
6	-0.085344	-0.6611	0.25555
7	-0.027223	-0.2109	0.416853
8	0.003579	0.0277	0.488989
9	-0.112814	-0.8739	0.192841
10	0.01301	0.1008	0.460034
11	-0.089366	-0.6922	0.245732
12	-0.030972	-0.2399	0.40561
13	-0.062664	-0.4854	0.314581
14	-0.070759	-0.5481	0.292828
15	-0.011098	-0.086	0.465891
16	0.051791	0.4012	0.344859
17	0.025564	0.198	0.421849

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.947524 & 7.3395 & 0 \tabularnewline
2 & -0.035023 & -0.2713 & 0.393551 \tabularnewline
3 & -0.042184 & -0.3268 & 0.372495 \tabularnewline
4 & 0.121692 & 0.9426 & 0.174828 \tabularnewline
5 & -0.011358 & -0.088 & 0.465093 \tabularnewline
6 & -0.085344 & -0.6611 & 0.25555 \tabularnewline
7 & -0.027223 & -0.2109 & 0.416853 \tabularnewline
8 & 0.003579 & 0.0277 & 0.488989 \tabularnewline
9 & -0.112814 & -0.8739 & 0.192841 \tabularnewline
10 & 0.01301 & 0.1008 & 0.460034 \tabularnewline
11 & -0.089366 & -0.6922 & 0.245732 \tabularnewline
12 & -0.030972 & -0.2399 & 0.40561 \tabularnewline
13 & -0.062664 & -0.4854 & 0.314581 \tabularnewline
14 & -0.070759 & -0.5481 & 0.292828 \tabularnewline
15 & -0.011098 & -0.086 & 0.465891 \tabularnewline
16 & 0.051791 & 0.4012 & 0.344859 \tabularnewline
17 & 0.025564 & 0.198 & 0.421849 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164306&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]0.947524[/C][C]7.3395[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.035023[/C][C]-0.2713[/C][C]0.393551[/C][/ROW]
[ROW][C]3[/C][C]-0.042184[/C][C]-0.3268[/C][C]0.372495[/C][/ROW]
[ROW][C]4[/C][C]0.121692[/C][C]0.9426[/C][C]0.174828[/C][/ROW]
[ROW][C]5[/C][C]-0.011358[/C][C]-0.088[/C][C]0.465093[/C][/ROW]
[ROW][C]6[/C][C]-0.085344[/C][C]-0.6611[/C][C]0.25555[/C][/ROW]
[ROW][C]7[/C][C]-0.027223[/C][C]-0.2109[/C][C]0.416853[/C][/ROW]
[ROW][C]8[/C][C]0.003579[/C][C]0.0277[/C][C]0.488989[/C][/ROW]
[ROW][C]9[/C][C]-0.112814[/C][C]-0.8739[/C][C]0.192841[/C][/ROW]
[ROW][C]10[/C][C]0.01301[/C][C]0.1008[/C][C]0.460034[/C][/ROW]
[ROW][C]11[/C][C]-0.089366[/C][C]-0.6922[/C][C]0.245732[/C][/ROW]
[ROW][C]12[/C][C]-0.030972[/C][C]-0.2399[/C][C]0.40561[/C][/ROW]
[ROW][C]13[/C][C]-0.062664[/C][C]-0.4854[/C][C]0.314581[/C][/ROW]
[ROW][C]14[/C][C]-0.070759[/C][C]-0.5481[/C][C]0.292828[/C][/ROW]
[ROW][C]15[/C][C]-0.011098[/C][C]-0.086[/C][C]0.465891[/C][/ROW]
[ROW][C]16[/C][C]0.051791[/C][C]0.4012[/C][C]0.344859[/C][/ROW]
[ROW][C]17[/C][C]0.025564[/C][C]0.198[/C][C]0.421849[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164306&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164306&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	0.947524	7.3395	0
2	-0.035023	-0.2713	0.393551
3	-0.042184	-0.3268	0.372495
4	0.121692	0.9426	0.174828
5	-0.011358	-0.088	0.465093
6	-0.085344	-0.6611	0.25555
7	-0.027223	-0.2109	0.416853
8	0.003579	0.0277	0.488989
9	-0.112814	-0.8739	0.192841
10	0.01301	0.1008	0.460034
11	-0.089366	-0.6922	0.245732
12	-0.030972	-0.2399	0.40561
13	-0.062664	-0.4854	0.314581
14	-0.070759	-0.5481	0.292828
15	-0.011098	-0.086	0.465891
16	0.051791	0.4012	0.344859
17	0.025564	0.198	0.421849

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)
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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