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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2016 11:26:52 +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/t1482229700itul81peoyd3qjy.htm/, Retrieved Fri, 01 Nov 2024 03:34:04 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301580, Retrieved Fri, 01 Nov 2024 03:34:04 +0000

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No (this computation is public)

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Estimated Impact

138

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

-       [(Partial) Autocorrelation Function] [] [2016-12-20 10:26:52] [b2e25925e4919b0d6985405fcb461c0d] [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=301580&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=301580&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301580&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	0.778923	3.4834	0.001172
2	0.500141	2.2367	0.018429
3	0.296886	1.3277	0.099614
4	0.245367	1.0973	0.14277
5	0.173542	0.7761	0.223384
6	0.060785	0.2718	0.394266
7	-0.075513	-0.3377	0.369552
8	-0.092225	-0.4124	0.342202
9	-0.102682	-0.4592	0.325519
10	-0.111425	-0.4983	0.311851
11	-0.204348	-0.9139	0.185835
12	-0.331436	-1.4822	0.076933
13	-0.424616	-1.8989	0.036048

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.778923 & 3.4834 & 0.001172 \tabularnewline
2 & 0.500141 & 2.2367 & 0.018429 \tabularnewline
3 & 0.296886 & 1.3277 & 0.099614 \tabularnewline
4 & 0.245367 & 1.0973 & 0.14277 \tabularnewline
5 & 0.173542 & 0.7761 & 0.223384 \tabularnewline
6 & 0.060785 & 0.2718 & 0.394266 \tabularnewline
7 & -0.075513 & -0.3377 & 0.369552 \tabularnewline
8 & -0.092225 & -0.4124 & 0.342202 \tabularnewline
9 & -0.102682 & -0.4592 & 0.325519 \tabularnewline
10 & -0.111425 & -0.4983 & 0.311851 \tabularnewline
11 & -0.204348 & -0.9139 & 0.185835 \tabularnewline
12 & -0.331436 & -1.4822 & 0.076933 \tabularnewline
13 & -0.424616 & -1.8989 & 0.036048 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301580&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]0.778923[/C][C]3.4834[/C][C]0.001172[/C][/ROW]
[ROW][C]2[/C][C]0.500141[/C][C]2.2367[/C][C]0.018429[/C][/ROW]
[ROW][C]3[/C][C]0.296886[/C][C]1.3277[/C][C]0.099614[/C][/ROW]
[ROW][C]4[/C][C]0.245367[/C][C]1.0973[/C][C]0.14277[/C][/ROW]
[ROW][C]5[/C][C]0.173542[/C][C]0.7761[/C][C]0.223384[/C][/ROW]
[ROW][C]6[/C][C]0.060785[/C][C]0.2718[/C][C]0.394266[/C][/ROW]
[ROW][C]7[/C][C]-0.075513[/C][C]-0.3377[/C][C]0.369552[/C][/ROW]
[ROW][C]8[/C][C]-0.092225[/C][C]-0.4124[/C][C]0.342202[/C][/ROW]
[ROW][C]9[/C][C]-0.102682[/C][C]-0.4592[/C][C]0.325519[/C][/ROW]
[ROW][C]10[/C][C]-0.111425[/C][C]-0.4983[/C][C]0.311851[/C][/ROW]
[ROW][C]11[/C][C]-0.204348[/C][C]-0.9139[/C][C]0.185835[/C][/ROW]
[ROW][C]12[/C][C]-0.331436[/C][C]-1.4822[/C][C]0.076933[/C][/ROW]
[ROW][C]13[/C][C]-0.424616[/C][C]-1.8989[/C][C]0.036048[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301580&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301580&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	0.778923	3.4834	0.001172
2	0.500141	2.2367	0.018429
3	0.296886	1.3277	0.099614
4	0.245367	1.0973	0.14277
5	0.173542	0.7761	0.223384
6	0.060785	0.2718	0.394266
7	-0.075513	-0.3377	0.369552
8	-0.092225	-0.4124	0.342202
9	-0.102682	-0.4592	0.325519
10	-0.111425	-0.4983	0.311851
11	-0.204348	-0.9139	0.185835
12	-0.331436	-1.4822	0.076933
13	-0.424616	-1.8989	0.036048

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.778923	3.4834	0.001172
2	-0.271003	-1.212	0.119826
3	0.035207	0.1575	0.438234
4	0.203774	0.9113	0.186494
5	-0.206736	-0.9246	0.18311
6	-0.086767	-0.388	0.351045
7	-0.07529	-0.3367	0.369923
8	0.150173	0.6716	0.254763
9	-0.174397	-0.7799	0.222283
10	-0.001356	-0.0061	0.497611
11	-0.165277	-0.7391	0.234204
12	-0.237999	-1.0644	0.149924
13	-0.057567	-0.2574	0.399732

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.778923 & 3.4834 & 0.001172 \tabularnewline
2 & -0.271003 & -1.212 & 0.119826 \tabularnewline
3 & 0.035207 & 0.1575 & 0.438234 \tabularnewline
4 & 0.203774 & 0.9113 & 0.186494 \tabularnewline
5 & -0.206736 & -0.9246 & 0.18311 \tabularnewline
6 & -0.086767 & -0.388 & 0.351045 \tabularnewline
7 & -0.07529 & -0.3367 & 0.369923 \tabularnewline
8 & 0.150173 & 0.6716 & 0.254763 \tabularnewline
9 & -0.174397 & -0.7799 & 0.222283 \tabularnewline
10 & -0.001356 & -0.0061 & 0.497611 \tabularnewline
11 & -0.165277 & -0.7391 & 0.234204 \tabularnewline
12 & -0.237999 & -1.0644 & 0.149924 \tabularnewline
13 & -0.057567 & -0.2574 & 0.399732 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301580&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]0.778923[/C][C]3.4834[/C][C]0.001172[/C][/ROW]
[ROW][C]2[/C][C]-0.271003[/C][C]-1.212[/C][C]0.119826[/C][/ROW]
[ROW][C]3[/C][C]0.035207[/C][C]0.1575[/C][C]0.438234[/C][/ROW]
[ROW][C]4[/C][C]0.203774[/C][C]0.9113[/C][C]0.186494[/C][/ROW]
[ROW][C]5[/C][C]-0.206736[/C][C]-0.9246[/C][C]0.18311[/C][/ROW]
[ROW][C]6[/C][C]-0.086767[/C][C]-0.388[/C][C]0.351045[/C][/ROW]
[ROW][C]7[/C][C]-0.07529[/C][C]-0.3367[/C][C]0.369923[/C][/ROW]
[ROW][C]8[/C][C]0.150173[/C][C]0.6716[/C][C]0.254763[/C][/ROW]
[ROW][C]9[/C][C]-0.174397[/C][C]-0.7799[/C][C]0.222283[/C][/ROW]
[ROW][C]10[/C][C]-0.001356[/C][C]-0.0061[/C][C]0.497611[/C][/ROW]
[ROW][C]11[/C][C]-0.165277[/C][C]-0.7391[/C][C]0.234204[/C][/ROW]
[ROW][C]12[/C][C]-0.237999[/C][C]-1.0644[/C][C]0.149924[/C][/ROW]
[ROW][C]13[/C][C]-0.057567[/C][C]-0.2574[/C][C]0.399732[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301580&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301580&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	0.778923	3.4834	0.001172
2	-0.271003	-1.212	0.119826
3	0.035207	0.1575	0.438234
4	0.203774	0.9113	0.186494
5	-0.206736	-0.9246	0.18311
6	-0.086767	-0.388	0.351045
7	-0.07529	-0.3367	0.369923
8	0.150173	0.6716	0.254763
9	-0.174397	-0.7799	0.222283
10	-0.001356	-0.0061	0.497611
11	-0.165277	-0.7391	0.234204
12	-0.237999	-1.0644	0.149924
13	-0.057567	-0.2574	0.399732

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 = 60 ; 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):

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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Dataset

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Figures (Output of Computation)

Input Parameters & R Code