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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 16:45:06 +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/17/t1481989540eagopd1bwe19wlk.htm/, Retrieved Thu, 02 May 2024 11:27:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300860, Retrieved Thu, 02 May 2024 11:27:48 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2016-12-17 15:45:06] [153c3207812fd13fe5ceee3276565119] [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=300860&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=300860&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300860&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	0.344695	2.4616	0.008627
2	0.368547	2.6319	0.005602
3	0.37655	2.6891	0.004828
4	0.359658	2.5685	0.006593
5	0.231763	1.6551	0.052021
6	0.250325	1.7877	0.039885
7	0.168254	1.2016	0.117539
8	0.136814	0.977	0.166579
9	-0.0077	-0.055	0.478182
10	0.112727	0.805	0.212269
11	0.009978	0.0713	0.471736
12	-0.03838	-0.2741	0.392561
13	-0.218716	-1.5619	0.062243
14	-0.134466	-0.9603	0.170722
15	-0.106811	-0.7628	0.224554
16	-0.210388	-1.5025	0.069571
17	-0.242277	-1.7302	0.044821

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.344695 & 2.4616 & 0.008627 \tabularnewline
2 & 0.368547 & 2.6319 & 0.005602 \tabularnewline
3 & 0.37655 & 2.6891 & 0.004828 \tabularnewline
4 & 0.359658 & 2.5685 & 0.006593 \tabularnewline
5 & 0.231763 & 1.6551 & 0.052021 \tabularnewline
6 & 0.250325 & 1.7877 & 0.039885 \tabularnewline
7 & 0.168254 & 1.2016 & 0.117539 \tabularnewline
8 & 0.136814 & 0.977 & 0.166579 \tabularnewline
9 & -0.0077 & -0.055 & 0.478182 \tabularnewline
10 & 0.112727 & 0.805 & 0.212269 \tabularnewline
11 & 0.009978 & 0.0713 & 0.471736 \tabularnewline
12 & -0.03838 & -0.2741 & 0.392561 \tabularnewline
13 & -0.218716 & -1.5619 & 0.062243 \tabularnewline
14 & -0.134466 & -0.9603 & 0.170722 \tabularnewline
15 & -0.106811 & -0.7628 & 0.224554 \tabularnewline
16 & -0.210388 & -1.5025 & 0.069571 \tabularnewline
17 & -0.242277 & -1.7302 & 0.044821 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300860&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]0.344695[/C][C]2.4616[/C][C]0.008627[/C][/ROW]
[ROW][C]2[/C][C]0.368547[/C][C]2.6319[/C][C]0.005602[/C][/ROW]
[ROW][C]3[/C][C]0.37655[/C][C]2.6891[/C][C]0.004828[/C][/ROW]
[ROW][C]4[/C][C]0.359658[/C][C]2.5685[/C][C]0.006593[/C][/ROW]
[ROW][C]5[/C][C]0.231763[/C][C]1.6551[/C][C]0.052021[/C][/ROW]
[ROW][C]6[/C][C]0.250325[/C][C]1.7877[/C][C]0.039885[/C][/ROW]
[ROW][C]7[/C][C]0.168254[/C][C]1.2016[/C][C]0.117539[/C][/ROW]
[ROW][C]8[/C][C]0.136814[/C][C]0.977[/C][C]0.166579[/C][/ROW]
[ROW][C]9[/C][C]-0.0077[/C][C]-0.055[/C][C]0.478182[/C][/ROW]
[ROW][C]10[/C][C]0.112727[/C][C]0.805[/C][C]0.212269[/C][/ROW]
[ROW][C]11[/C][C]0.009978[/C][C]0.0713[/C][C]0.471736[/C][/ROW]
[ROW][C]12[/C][C]-0.03838[/C][C]-0.2741[/C][C]0.392561[/C][/ROW]
[ROW][C]13[/C][C]-0.218716[/C][C]-1.5619[/C][C]0.062243[/C][/ROW]
[ROW][C]14[/C][C]-0.134466[/C][C]-0.9603[/C][C]0.170722[/C][/ROW]
[ROW][C]15[/C][C]-0.106811[/C][C]-0.7628[/C][C]0.224554[/C][/ROW]
[ROW][C]16[/C][C]-0.210388[/C][C]-1.5025[/C][C]0.069571[/C][/ROW]
[ROW][C]17[/C][C]-0.242277[/C][C]-1.7302[/C][C]0.044821[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300860&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300860&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	0.344695	2.4616	0.008627
2	0.368547	2.6319	0.005602
3	0.37655	2.6891	0.004828
4	0.359658	2.5685	0.006593
5	0.231763	1.6551	0.052021
6	0.250325	1.7877	0.039885
7	0.168254	1.2016	0.117539
8	0.136814	0.977	0.166579
9	-0.0077	-0.055	0.478182
10	0.112727	0.805	0.212269
11	0.009978	0.0713	0.471736
12	-0.03838	-0.2741	0.392561
13	-0.218716	-1.5619	0.062243
14	-0.134466	-0.9603	0.170722
15	-0.106811	-0.7628	0.224554
16	-0.210388	-1.5025	0.069571
17	-0.242277	-1.7302	0.044821

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.344695	2.4616	0.008627
2	0.283404	2.0239	0.024117
3	0.231769	1.6552	0.052017
4	0.167096	1.1933	0.119136
5	-0.029914	-0.2136	0.415843
6	0.020642	0.1474	0.441692
7	-0.059119	-0.4222	0.33733
8	-0.042751	-0.3053	0.38069
9	-0.177674	-1.2688	0.105129
10	0.068005	0.4857	0.314647
11	-0.023402	-0.1671	0.433966
12	-0.050424	-0.3601	0.360129
13	-0.260696	-1.8617	0.034203
14	-0.084049	-0.6002	0.275505
15	0.084155	0.601	0.275256
16	-0.053129	-0.3794	0.352976
17	-0.064682	-0.4619	0.32305

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.344695 & 2.4616 & 0.008627 \tabularnewline
2 & 0.283404 & 2.0239 & 0.024117 \tabularnewline
3 & 0.231769 & 1.6552 & 0.052017 \tabularnewline
4 & 0.167096 & 1.1933 & 0.119136 \tabularnewline
5 & -0.029914 & -0.2136 & 0.415843 \tabularnewline
6 & 0.020642 & 0.1474 & 0.441692 \tabularnewline
7 & -0.059119 & -0.4222 & 0.33733 \tabularnewline
8 & -0.042751 & -0.3053 & 0.38069 \tabularnewline
9 & -0.177674 & -1.2688 & 0.105129 \tabularnewline
10 & 0.068005 & 0.4857 & 0.314647 \tabularnewline
11 & -0.023402 & -0.1671 & 0.433966 \tabularnewline
12 & -0.050424 & -0.3601 & 0.360129 \tabularnewline
13 & -0.260696 & -1.8617 & 0.034203 \tabularnewline
14 & -0.084049 & -0.6002 & 0.275505 \tabularnewline
15 & 0.084155 & 0.601 & 0.275256 \tabularnewline
16 & -0.053129 & -0.3794 & 0.352976 \tabularnewline
17 & -0.064682 & -0.4619 & 0.32305 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300860&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]0.344695[/C][C]2.4616[/C][C]0.008627[/C][/ROW]
[ROW][C]2[/C][C]0.283404[/C][C]2.0239[/C][C]0.024117[/C][/ROW]
[ROW][C]3[/C][C]0.231769[/C][C]1.6552[/C][C]0.052017[/C][/ROW]
[ROW][C]4[/C][C]0.167096[/C][C]1.1933[/C][C]0.119136[/C][/ROW]
[ROW][C]5[/C][C]-0.029914[/C][C]-0.2136[/C][C]0.415843[/C][/ROW]
[ROW][C]6[/C][C]0.020642[/C][C]0.1474[/C][C]0.441692[/C][/ROW]
[ROW][C]7[/C][C]-0.059119[/C][C]-0.4222[/C][C]0.33733[/C][/ROW]
[ROW][C]8[/C][C]-0.042751[/C][C]-0.3053[/C][C]0.38069[/C][/ROW]
[ROW][C]9[/C][C]-0.177674[/C][C]-1.2688[/C][C]0.105129[/C][/ROW]
[ROW][C]10[/C][C]0.068005[/C][C]0.4857[/C][C]0.314647[/C][/ROW]
[ROW][C]11[/C][C]-0.023402[/C][C]-0.1671[/C][C]0.433966[/C][/ROW]
[ROW][C]12[/C][C]-0.050424[/C][C]-0.3601[/C][C]0.360129[/C][/ROW]
[ROW][C]13[/C][C]-0.260696[/C][C]-1.8617[/C][C]0.034203[/C][/ROW]
[ROW][C]14[/C][C]-0.084049[/C][C]-0.6002[/C][C]0.275505[/C][/ROW]
[ROW][C]15[/C][C]0.084155[/C][C]0.601[/C][C]0.275256[/C][/ROW]
[ROW][C]16[/C][C]-0.053129[/C][C]-0.3794[/C][C]0.352976[/C][/ROW]
[ROW][C]17[/C][C]-0.064682[/C][C]-0.4619[/C][C]0.32305[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300860&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300860&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	0.344695	2.4616	0.008627
2	0.283404	2.0239	0.024117
3	0.231769	1.6552	0.052017
4	0.167096	1.1933	0.119136
5	-0.029914	-0.2136	0.415843
6	0.020642	0.1474	0.441692
7	-0.059119	-0.4222	0.33733
8	-0.042751	-0.3053	0.38069
9	-0.177674	-1.2688	0.105129
10	0.068005	0.4857	0.314647
11	-0.023402	-0.1671	0.433966
12	-0.050424	-0.3601	0.360129
13	-0.260696	-1.8617	0.034203
14	-0.084049	-0.6002	0.275505
15	0.084155	0.601	0.275256
16	-0.053129	-0.3794	0.352976
17	-0.064682	-0.4619	0.32305

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 = 1 ; 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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '1'
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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Input Parameters & R Code