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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2016 16:14:02 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/20/t1482246875s1y3yi6v3x0p7y5.htm/, Retrieved Sun, 28 Apr 2024 00:19:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301704, Retrieved Sun, 28 Apr 2024 00:19:07 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-20 15:14:02] [361c8dad91b3f1ef2e651cd04783c23b] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301704&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301704&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301704&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.112694	-0.8281	0.205621
2	-0.139524	-1.0253	0.1549
3	0.19036	1.3989	0.083787
4	-0.116046	-0.8528	0.198779
5	-0.274259	-2.0154	0.024427
6	-0.128691	-0.9457	0.174261
7	0.14187	1.0425	0.150906
8	-0.287862	-2.1153	0.019515
9	-0.057048	-0.4192	0.33836
10	0.287156	2.1102	0.019747
11	0.001808	0.0133	0.494725
12	-0.060758	-0.4465	0.328518
13	0.151831	1.1157	0.134741
14	0.171457	1.2599	0.106554
15	-0.157881	-1.1602	0.125539
16	-0.052859	-0.3884	0.349613
17	0.100728	0.7402	0.231194

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.112694 & -0.8281 & 0.205621 \tabularnewline
2 & -0.139524 & -1.0253 & 0.1549 \tabularnewline
3 & 0.19036 & 1.3989 & 0.083787 \tabularnewline
4 & -0.116046 & -0.8528 & 0.198779 \tabularnewline
5 & -0.274259 & -2.0154 & 0.024427 \tabularnewline
6 & -0.128691 & -0.9457 & 0.174261 \tabularnewline
7 & 0.14187 & 1.0425 & 0.150906 \tabularnewline
8 & -0.287862 & -2.1153 & 0.019515 \tabularnewline
9 & -0.057048 & -0.4192 & 0.33836 \tabularnewline
10 & 0.287156 & 2.1102 & 0.019747 \tabularnewline
11 & 0.001808 & 0.0133 & 0.494725 \tabularnewline
12 & -0.060758 & -0.4465 & 0.328518 \tabularnewline
13 & 0.151831 & 1.1157 & 0.134741 \tabularnewline
14 & 0.171457 & 1.2599 & 0.106554 \tabularnewline
15 & -0.157881 & -1.1602 & 0.125539 \tabularnewline
16 & -0.052859 & -0.3884 & 0.349613 \tabularnewline
17 & 0.100728 & 0.7402 & 0.231194 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301704&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]-0.112694[/C][C]-0.8281[/C][C]0.205621[/C][/ROW]
[ROW][C]2[/C][C]-0.139524[/C][C]-1.0253[/C][C]0.1549[/C][/ROW]
[ROW][C]3[/C][C]0.19036[/C][C]1.3989[/C][C]0.083787[/C][/ROW]
[ROW][C]4[/C][C]-0.116046[/C][C]-0.8528[/C][C]0.198779[/C][/ROW]
[ROW][C]5[/C][C]-0.274259[/C][C]-2.0154[/C][C]0.024427[/C][/ROW]
[ROW][C]6[/C][C]-0.128691[/C][C]-0.9457[/C][C]0.174261[/C][/ROW]
[ROW][C]7[/C][C]0.14187[/C][C]1.0425[/C][C]0.150906[/C][/ROW]
[ROW][C]8[/C][C]-0.287862[/C][C]-2.1153[/C][C]0.019515[/C][/ROW]
[ROW][C]9[/C][C]-0.057048[/C][C]-0.4192[/C][C]0.33836[/C][/ROW]
[ROW][C]10[/C][C]0.287156[/C][C]2.1102[/C][C]0.019747[/C][/ROW]
[ROW][C]11[/C][C]0.001808[/C][C]0.0133[/C][C]0.494725[/C][/ROW]
[ROW][C]12[/C][C]-0.060758[/C][C]-0.4465[/C][C]0.328518[/C][/ROW]
[ROW][C]13[/C][C]0.151831[/C][C]1.1157[/C][C]0.134741[/C][/ROW]
[ROW][C]14[/C][C]0.171457[/C][C]1.2599[/C][C]0.106554[/C][/ROW]
[ROW][C]15[/C][C]-0.157881[/C][C]-1.1602[/C][C]0.125539[/C][/ROW]
[ROW][C]16[/C][C]-0.052859[/C][C]-0.3884[/C][C]0.349613[/C][/ROW]
[ROW][C]17[/C][C]0.100728[/C][C]0.7402[/C][C]0.231194[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301704&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301704&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	-0.112694	-0.8281	0.205621
2	-0.139524	-1.0253	0.1549
3	0.19036	1.3989	0.083787
4	-0.116046	-0.8528	0.198779
5	-0.274259	-2.0154	0.024427
6	-0.128691	-0.9457	0.174261
7	0.14187	1.0425	0.150906
8	-0.287862	-2.1153	0.019515
9	-0.057048	-0.4192	0.33836
10	0.287156	2.1102	0.019747
11	0.001808	0.0133	0.494725
12	-0.060758	-0.4465	0.328518
13	0.151831	1.1157	0.134741
14	0.171457	1.2599	0.106554
15	-0.157881	-1.1602	0.125539
16	-0.052859	-0.3884	0.349613
17	0.100728	0.7402	0.231194

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.112694	-0.8281	0.205621
2	-0.154182	-1.133	0.13111
3	0.160648	1.1805	0.121484
4	-0.102767	-0.7552	0.226711
5	-0.266146	-1.9558	0.027838
6	-0.279967	-2.0573	0.022248
7	0.064414	0.4733	0.318937
8	-0.292576	-2.15	0.018026
9	-0.171727	-1.2619	0.106199
10	0.01706	0.1254	0.450351
11	0.014231	0.1046	0.45855
12	-0.113625	-0.835	0.203707
13	-0.06361	-0.4674	0.321035
14	0.087042	0.6396	0.262559
15	0.009691	0.0712	0.471744
16	-0.087692	-0.6444	0.261022
17	-0.037142	-0.2729	0.392972

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.112694 & -0.8281 & 0.205621 \tabularnewline
2 & -0.154182 & -1.133 & 0.13111 \tabularnewline
3 & 0.160648 & 1.1805 & 0.121484 \tabularnewline
4 & -0.102767 & -0.7552 & 0.226711 \tabularnewline
5 & -0.266146 & -1.9558 & 0.027838 \tabularnewline
6 & -0.279967 & -2.0573 & 0.022248 \tabularnewline
7 & 0.064414 & 0.4733 & 0.318937 \tabularnewline
8 & -0.292576 & -2.15 & 0.018026 \tabularnewline
9 & -0.171727 & -1.2619 & 0.106199 \tabularnewline
10 & 0.01706 & 0.1254 & 0.450351 \tabularnewline
11 & 0.014231 & 0.1046 & 0.45855 \tabularnewline
12 & -0.113625 & -0.835 & 0.203707 \tabularnewline
13 & -0.06361 & -0.4674 & 0.321035 \tabularnewline
14 & 0.087042 & 0.6396 & 0.262559 \tabularnewline
15 & 0.009691 & 0.0712 & 0.471744 \tabularnewline
16 & -0.087692 & -0.6444 & 0.261022 \tabularnewline
17 & -0.037142 & -0.2729 & 0.392972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301704&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]-0.112694[/C][C]-0.8281[/C][C]0.205621[/C][/ROW]
[ROW][C]2[/C][C]-0.154182[/C][C]-1.133[/C][C]0.13111[/C][/ROW]
[ROW][C]3[/C][C]0.160648[/C][C]1.1805[/C][C]0.121484[/C][/ROW]
[ROW][C]4[/C][C]-0.102767[/C][C]-0.7552[/C][C]0.226711[/C][/ROW]
[ROW][C]5[/C][C]-0.266146[/C][C]-1.9558[/C][C]0.027838[/C][/ROW]
[ROW][C]6[/C][C]-0.279967[/C][C]-2.0573[/C][C]0.022248[/C][/ROW]
[ROW][C]7[/C][C]0.064414[/C][C]0.4733[/C][C]0.318937[/C][/ROW]
[ROW][C]8[/C][C]-0.292576[/C][C]-2.15[/C][C]0.018026[/C][/ROW]
[ROW][C]9[/C][C]-0.171727[/C][C]-1.2619[/C][C]0.106199[/C][/ROW]
[ROW][C]10[/C][C]0.01706[/C][C]0.1254[/C][C]0.450351[/C][/ROW]
[ROW][C]11[/C][C]0.014231[/C][C]0.1046[/C][C]0.45855[/C][/ROW]
[ROW][C]12[/C][C]-0.113625[/C][C]-0.835[/C][C]0.203707[/C][/ROW]
[ROW][C]13[/C][C]-0.06361[/C][C]-0.4674[/C][C]0.321035[/C][/ROW]
[ROW][C]14[/C][C]0.087042[/C][C]0.6396[/C][C]0.262559[/C][/ROW]
[ROW][C]15[/C][C]0.009691[/C][C]0.0712[/C][C]0.471744[/C][/ROW]
[ROW][C]16[/C][C]-0.087692[/C][C]-0.6444[/C][C]0.261022[/C][/ROW]
[ROW][C]17[/C][C]-0.037142[/C][C]-0.2729[/C][C]0.392972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301704&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301704&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	-0.112694	-0.8281	0.205621
2	-0.154182	-1.133	0.13111
3	0.160648	1.1805	0.121484
4	-0.102767	-0.7552	0.226711
5	-0.266146	-1.9558	0.027838
6	-0.279967	-2.0573	0.022248
7	0.064414	0.4733	0.318937
8	-0.292576	-2.15	0.018026
9	-0.171727	-1.2619	0.106199
10	0.01706	0.1254	0.450351
11	0.014231	0.1046	0.45855
12	-0.113625	-0.835	0.203707
13	-0.06361	-0.4674	0.321035
14	0.087042	0.6396	0.262559
15	0.009691	0.0712	0.471744
16	-0.087692	-0.6444	0.261022
17	-0.037142	-0.2729	0.392972

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

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PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; 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 <- '2'
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)
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,'ACF(k)',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,'PACF(k)',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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