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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 18 Nov 2013 06:32:34 -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/18/t1384774365trdnpkmkwtq6hv8.htm/, Retrieved Sat, 27 Apr 2024 07:05:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=226041, Retrieved Sat, 27 Apr 2024 07:05:52 +0000

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-       [(Partial) Autocorrelation Function] [] [2013-11-18 11:32:34] [0867de6134d40384f45e4afedb3459b9] [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=226041&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=226041&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226041&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	0.902696	7.6596	0
2	0.796709	6.7603	0
3	0.685605	5.8176	0
4	0.574501	4.8748	3e-06
5	0.482318	4.0926	5.5e-05
6	0.399908	3.3933	0.000563
7	0.317497	2.694	0.004389
8	0.221471	1.8792	0.032129
9	0.150801	1.2796	0.102399
10	0.093371	0.7923	0.215401
11	0.027844	0.2363	0.406949
12	-0.017659	-0.1498	0.440654
13	-0.047783	-0.4054	0.343175
14	-0.077008	-0.6534	0.257779
15	-0.093019	-0.7893	0.216267
16	-0.10903	-0.9251	0.17899
17	-0.133924	-1.1364	0.129783
18	-0.168589	-1.4305	0.078446
19	-0.203255	-1.7247	0.044438

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.902696 & 7.6596 & 0 \tabularnewline
2 & 0.796709 & 6.7603 & 0 \tabularnewline
3 & 0.685605 & 5.8176 & 0 \tabularnewline
4 & 0.574501 & 4.8748 & 3e-06 \tabularnewline
5 & 0.482318 & 4.0926 & 5.5e-05 \tabularnewline
6 & 0.399908 & 3.3933 & 0.000563 \tabularnewline
7 & 0.317497 & 2.694 & 0.004389 \tabularnewline
8 & 0.221471 & 1.8792 & 0.032129 \tabularnewline
9 & 0.150801 & 1.2796 & 0.102399 \tabularnewline
10 & 0.093371 & 0.7923 & 0.215401 \tabularnewline
11 & 0.027844 & 0.2363 & 0.406949 \tabularnewline
12 & -0.017659 & -0.1498 & 0.440654 \tabularnewline
13 & -0.047783 & -0.4054 & 0.343175 \tabularnewline
14 & -0.077008 & -0.6534 & 0.257779 \tabularnewline
15 & -0.093019 & -0.7893 & 0.216267 \tabularnewline
16 & -0.10903 & -0.9251 & 0.17899 \tabularnewline
17 & -0.133924 & -1.1364 & 0.129783 \tabularnewline
18 & -0.168589 & -1.4305 & 0.078446 \tabularnewline
19 & -0.203255 & -1.7247 & 0.044438 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226041&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]0.902696[/C][C]7.6596[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.796709[/C][C]6.7603[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.685605[/C][C]5.8176[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.574501[/C][C]4.8748[/C][C]3e-06[/C][/ROW]
[ROW][C]5[/C][C]0.482318[/C][C]4.0926[/C][C]5.5e-05[/C][/ROW]
[ROW][C]6[/C][C]0.399908[/C][C]3.3933[/C][C]0.000563[/C][/ROW]
[ROW][C]7[/C][C]0.317497[/C][C]2.694[/C][C]0.004389[/C][/ROW]
[ROW][C]8[/C][C]0.221471[/C][C]1.8792[/C][C]0.032129[/C][/ROW]
[ROW][C]9[/C][C]0.150801[/C][C]1.2796[/C][C]0.102399[/C][/ROW]
[ROW][C]10[/C][C]0.093371[/C][C]0.7923[/C][C]0.215401[/C][/ROW]
[ROW][C]11[/C][C]0.027844[/C][C]0.2363[/C][C]0.406949[/C][/ROW]
[ROW][C]12[/C][C]-0.017659[/C][C]-0.1498[/C][C]0.440654[/C][/ROW]
[ROW][C]13[/C][C]-0.047783[/C][C]-0.4054[/C][C]0.343175[/C][/ROW]
[ROW][C]14[/C][C]-0.077008[/C][C]-0.6534[/C][C]0.257779[/C][/ROW]
[ROW][C]15[/C][C]-0.093019[/C][C]-0.7893[/C][C]0.216267[/C][/ROW]
[ROW][C]16[/C][C]-0.10903[/C][C]-0.9251[/C][C]0.17899[/C][/ROW]
[ROW][C]17[/C][C]-0.133924[/C][C]-1.1364[/C][C]0.129783[/C][/ROW]
[ROW][C]18[/C][C]-0.168589[/C][C]-1.4305[/C][C]0.078446[/C][/ROW]
[ROW][C]19[/C][C]-0.203255[/C][C]-1.7247[/C][C]0.044438[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226041&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226041&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	0.902696	7.6596	0
2	0.796709	6.7603	0
3	0.685605	5.8176	0
4	0.574501	4.8748	3e-06
5	0.482318	4.0926	5.5e-05
6	0.399908	3.3933	0.000563
7	0.317497	2.694	0.004389
8	0.221471	1.8792	0.032129
9	0.150801	1.2796	0.102399
10	0.093371	0.7923	0.215401
11	0.027844	0.2363	0.406949
12	-0.017659	-0.1498	0.440654
13	-0.047783	-0.4054	0.343175
14	-0.077008	-0.6534	0.257779
15	-0.093019	-0.7893	0.216267
16	-0.10903	-0.9251	0.17899
17	-0.133924	-1.1364	0.129783
18	-0.168589	-1.4305	0.078446
19	-0.203255	-1.7247	0.044438

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.902696	7.6596	0
2	-0.098034	-0.8318	0.204123
3	-0.085027	-0.7215	0.236477
4	-0.063923	-0.5424	0.294606
5	0.034275	0.2908	0.386007
6	-0.016847	-0.143	0.443363
7	-0.069724	-0.5916	0.277975
8	-0.14332	-1.2161	0.113957
9	0.078681	0.6676	0.253253
10	0.012129	0.1029	0.459156
11	-0.119457	-1.0136	0.157078
12	0.025222	0.214	0.415569
13	0.044778	0.38	0.352549
14	-0.033197	-0.2817	0.389495
15	0.013463	0.1142	0.454682
16	-0.060673	-0.5148	0.304126
17	-0.066672	-0.5657	0.286668
18	-0.068428	-0.5806	0.28165
19	-0.067152	-0.5698	0.285291

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.902696 & 7.6596 & 0 \tabularnewline
2 & -0.098034 & -0.8318 & 0.204123 \tabularnewline
3 & -0.085027 & -0.7215 & 0.236477 \tabularnewline
4 & -0.063923 & -0.5424 & 0.294606 \tabularnewline
5 & 0.034275 & 0.2908 & 0.386007 \tabularnewline
6 & -0.016847 & -0.143 & 0.443363 \tabularnewline
7 & -0.069724 & -0.5916 & 0.277975 \tabularnewline
8 & -0.14332 & -1.2161 & 0.113957 \tabularnewline
9 & 0.078681 & 0.6676 & 0.253253 \tabularnewline
10 & 0.012129 & 0.1029 & 0.459156 \tabularnewline
11 & -0.119457 & -1.0136 & 0.157078 \tabularnewline
12 & 0.025222 & 0.214 & 0.415569 \tabularnewline
13 & 0.044778 & 0.38 & 0.352549 \tabularnewline
14 & -0.033197 & -0.2817 & 0.389495 \tabularnewline
15 & 0.013463 & 0.1142 & 0.454682 \tabularnewline
16 & -0.060673 & -0.5148 & 0.304126 \tabularnewline
17 & -0.066672 & -0.5657 & 0.286668 \tabularnewline
18 & -0.068428 & -0.5806 & 0.28165 \tabularnewline
19 & -0.067152 & -0.5698 & 0.285291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=226041&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]0.902696[/C][C]7.6596[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.098034[/C][C]-0.8318[/C][C]0.204123[/C][/ROW]
[ROW][C]3[/C][C]-0.085027[/C][C]-0.7215[/C][C]0.236477[/C][/ROW]
[ROW][C]4[/C][C]-0.063923[/C][C]-0.5424[/C][C]0.294606[/C][/ROW]
[ROW][C]5[/C][C]0.034275[/C][C]0.2908[/C][C]0.386007[/C][/ROW]
[ROW][C]6[/C][C]-0.016847[/C][C]-0.143[/C][C]0.443363[/C][/ROW]
[ROW][C]7[/C][C]-0.069724[/C][C]-0.5916[/C][C]0.277975[/C][/ROW]
[ROW][C]8[/C][C]-0.14332[/C][C]-1.2161[/C][C]0.113957[/C][/ROW]
[ROW][C]9[/C][C]0.078681[/C][C]0.6676[/C][C]0.253253[/C][/ROW]
[ROW][C]10[/C][C]0.012129[/C][C]0.1029[/C][C]0.459156[/C][/ROW]
[ROW][C]11[/C][C]-0.119457[/C][C]-1.0136[/C][C]0.157078[/C][/ROW]
[ROW][C]12[/C][C]0.025222[/C][C]0.214[/C][C]0.415569[/C][/ROW]
[ROW][C]13[/C][C]0.044778[/C][C]0.38[/C][C]0.352549[/C][/ROW]
[ROW][C]14[/C][C]-0.033197[/C][C]-0.2817[/C][C]0.389495[/C][/ROW]
[ROW][C]15[/C][C]0.013463[/C][C]0.1142[/C][C]0.454682[/C][/ROW]
[ROW][C]16[/C][C]-0.060673[/C][C]-0.5148[/C][C]0.304126[/C][/ROW]
[ROW][C]17[/C][C]-0.066672[/C][C]-0.5657[/C][C]0.286668[/C][/ROW]
[ROW][C]18[/C][C]-0.068428[/C][C]-0.5806[/C][C]0.28165[/C][/ROW]
[ROW][C]19[/C][C]-0.067152[/C][C]-0.5698[/C][C]0.285291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=226041&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=226041&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	0.902696	7.6596	0
2	-0.098034	-0.8318	0.204123
3	-0.085027	-0.7215	0.236477
4	-0.063923	-0.5424	0.294606
5	0.034275	0.2908	0.386007
6	-0.016847	-0.143	0.443363
7	-0.069724	-0.5916	0.277975
8	-0.14332	-1.2161	0.113957
9	0.078681	0.6676	0.253253
10	0.012129	0.1029	0.459156
11	-0.119457	-1.0136	0.157078
12	0.025222	0.214	0.415569
13	0.044778	0.38	0.352549
14	-0.033197	-0.2817	0.389495
15	0.013463	0.1142	0.454682
16	-0.060673	-0.5148	0.304126
17	-0.066672	-0.5657	0.286668
18	-0.068428	-0.5806	0.28165
19	-0.067152	-0.5698	0.285291

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code