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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2016 19:59:40 +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/t1482260416mfnqw84kl916ygg.htm/, Retrieved Sun, 28 Apr 2024 18:49:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301776, Retrieved Sun, 28 Apr 2024 18:49:08 +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] [] [2016-12-20 18:59:40] [672675941468e072e71d9fb024f2b817] [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=301776&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=301776&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301776&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	-0.442826	-2.7298	0.004776
2	0.013468	0.083	0.467134
3	-0.184614	-1.138	0.131114
4	0.42073	2.5936	0.006708
5	-0.139478	-0.8598	0.197645
6	-0.064165	-0.3955	0.347328
7	-0.170868	-1.0533	0.149428
8	0.416797	2.5693	0.007119
9	-0.133961	-0.8258	0.207038
10	-0.148271	-0.914	0.18324
11	0.019614	0.1209	0.452199
12	0.15241	0.9395	0.1767
13	-0.06519	-0.4019	0.345021
14	-0.159008	-0.9802	0.166595
15	0.03254	0.2006	0.421045
16	0.276943	1.7072	0.047973
17	-0.247613	-1.5264	0.067597

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.442826 & -2.7298 & 0.004776 \tabularnewline
2 & 0.013468 & 0.083 & 0.467134 \tabularnewline
3 & -0.184614 & -1.138 & 0.131114 \tabularnewline
4 & 0.42073 & 2.5936 & 0.006708 \tabularnewline
5 & -0.139478 & -0.8598 & 0.197645 \tabularnewline
6 & -0.064165 & -0.3955 & 0.347328 \tabularnewline
7 & -0.170868 & -1.0533 & 0.149428 \tabularnewline
8 & 0.416797 & 2.5693 & 0.007119 \tabularnewline
9 & -0.133961 & -0.8258 & 0.207038 \tabularnewline
10 & -0.148271 & -0.914 & 0.18324 \tabularnewline
11 & 0.019614 & 0.1209 & 0.452199 \tabularnewline
12 & 0.15241 & 0.9395 & 0.1767 \tabularnewline
13 & -0.06519 & -0.4019 & 0.345021 \tabularnewline
14 & -0.159008 & -0.9802 & 0.166595 \tabularnewline
15 & 0.03254 & 0.2006 & 0.421045 \tabularnewline
16 & 0.276943 & 1.7072 & 0.047973 \tabularnewline
17 & -0.247613 & -1.5264 & 0.067597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301776&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]-0.442826[/C][C]-2.7298[/C][C]0.004776[/C][/ROW]
[ROW][C]2[/C][C]0.013468[/C][C]0.083[/C][C]0.467134[/C][/ROW]
[ROW][C]3[/C][C]-0.184614[/C][C]-1.138[/C][C]0.131114[/C][/ROW]
[ROW][C]4[/C][C]0.42073[/C][C]2.5936[/C][C]0.006708[/C][/ROW]
[ROW][C]5[/C][C]-0.139478[/C][C]-0.8598[/C][C]0.197645[/C][/ROW]
[ROW][C]6[/C][C]-0.064165[/C][C]-0.3955[/C][C]0.347328[/C][/ROW]
[ROW][C]7[/C][C]-0.170868[/C][C]-1.0533[/C][C]0.149428[/C][/ROW]
[ROW][C]8[/C][C]0.416797[/C][C]2.5693[/C][C]0.007119[/C][/ROW]
[ROW][C]9[/C][C]-0.133961[/C][C]-0.8258[/C][C]0.207038[/C][/ROW]
[ROW][C]10[/C][C]-0.148271[/C][C]-0.914[/C][C]0.18324[/C][/ROW]
[ROW][C]11[/C][C]0.019614[/C][C]0.1209[/C][C]0.452199[/C][/ROW]
[ROW][C]12[/C][C]0.15241[/C][C]0.9395[/C][C]0.1767[/C][/ROW]
[ROW][C]13[/C][C]-0.06519[/C][C]-0.4019[/C][C]0.345021[/C][/ROW]
[ROW][C]14[/C][C]-0.159008[/C][C]-0.9802[/C][C]0.166595[/C][/ROW]
[ROW][C]15[/C][C]0.03254[/C][C]0.2006[/C][C]0.421045[/C][/ROW]
[ROW][C]16[/C][C]0.276943[/C][C]1.7072[/C][C]0.047973[/C][/ROW]
[ROW][C]17[/C][C]-0.247613[/C][C]-1.5264[/C][C]0.067597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301776&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301776&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	-0.442826	-2.7298	0.004776
2	0.013468	0.083	0.467134
3	-0.184614	-1.138	0.131114
4	0.42073	2.5936	0.006708
5	-0.139478	-0.8598	0.197645
6	-0.064165	-0.3955	0.347328
7	-0.170868	-1.0533	0.149428
8	0.416797	2.5693	0.007119
9	-0.133961	-0.8258	0.207038
10	-0.148271	-0.914	0.18324
11	0.019614	0.1209	0.452199
12	0.15241	0.9395	0.1767
13	-0.06519	-0.4019	0.345021
14	-0.159008	-0.9802	0.166595
15	0.03254	0.2006	0.421045
16	0.276943	1.7072	0.047973
17	-0.247613	-1.5264	0.067597

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.442826	-2.7298	0.004776
2	-0.227174	-1.4004	0.084754
3	-0.364491	-2.2469	0.015268
4	0.226038	1.3934	0.085799
5	0.20988	1.2938	0.101774
6	0.053533	0.33	0.371606
7	-0.174138	-1.0735	0.144917
8	0.184296	1.1361	0.131519
9	0.148132	0.9131	0.183462
10	-0.106141	-0.6543	0.258431
11	0.052866	0.3259	0.373149
12	-0.045039	-0.2776	0.391396
13	-0.129697	-0.7995	0.214484
14	-0.165991	-1.0232	0.156333
15	-0.065994	-0.4068	0.343214
16	0.228311	1.4074	0.083718
17	-0.100844	-0.6216	0.268943

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.442826 & -2.7298 & 0.004776 \tabularnewline
2 & -0.227174 & -1.4004 & 0.084754 \tabularnewline
3 & -0.364491 & -2.2469 & 0.015268 \tabularnewline
4 & 0.226038 & 1.3934 & 0.085799 \tabularnewline
5 & 0.20988 & 1.2938 & 0.101774 \tabularnewline
6 & 0.053533 & 0.33 & 0.371606 \tabularnewline
7 & -0.174138 & -1.0735 & 0.144917 \tabularnewline
8 & 0.184296 & 1.1361 & 0.131519 \tabularnewline
9 & 0.148132 & 0.9131 & 0.183462 \tabularnewline
10 & -0.106141 & -0.6543 & 0.258431 \tabularnewline
11 & 0.052866 & 0.3259 & 0.373149 \tabularnewline
12 & -0.045039 & -0.2776 & 0.391396 \tabularnewline
13 & -0.129697 & -0.7995 & 0.214484 \tabularnewline
14 & -0.165991 & -1.0232 & 0.156333 \tabularnewline
15 & -0.065994 & -0.4068 & 0.343214 \tabularnewline
16 & 0.228311 & 1.4074 & 0.083718 \tabularnewline
17 & -0.100844 & -0.6216 & 0.268943 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301776&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]-0.442826[/C][C]-2.7298[/C][C]0.004776[/C][/ROW]
[ROW][C]2[/C][C]-0.227174[/C][C]-1.4004[/C][C]0.084754[/C][/ROW]
[ROW][C]3[/C][C]-0.364491[/C][C]-2.2469[/C][C]0.015268[/C][/ROW]
[ROW][C]4[/C][C]0.226038[/C][C]1.3934[/C][C]0.085799[/C][/ROW]
[ROW][C]5[/C][C]0.20988[/C][C]1.2938[/C][C]0.101774[/C][/ROW]
[ROW][C]6[/C][C]0.053533[/C][C]0.33[/C][C]0.371606[/C][/ROW]
[ROW][C]7[/C][C]-0.174138[/C][C]-1.0735[/C][C]0.144917[/C][/ROW]
[ROW][C]8[/C][C]0.184296[/C][C]1.1361[/C][C]0.131519[/C][/ROW]
[ROW][C]9[/C][C]0.148132[/C][C]0.9131[/C][C]0.183462[/C][/ROW]
[ROW][C]10[/C][C]-0.106141[/C][C]-0.6543[/C][C]0.258431[/C][/ROW]
[ROW][C]11[/C][C]0.052866[/C][C]0.3259[/C][C]0.373149[/C][/ROW]
[ROW][C]12[/C][C]-0.045039[/C][C]-0.2776[/C][C]0.391396[/C][/ROW]
[ROW][C]13[/C][C]-0.129697[/C][C]-0.7995[/C][C]0.214484[/C][/ROW]
[ROW][C]14[/C][C]-0.165991[/C][C]-1.0232[/C][C]0.156333[/C][/ROW]
[ROW][C]15[/C][C]-0.065994[/C][C]-0.4068[/C][C]0.343214[/C][/ROW]
[ROW][C]16[/C][C]0.228311[/C][C]1.4074[/C][C]0.083718[/C][/ROW]
[ROW][C]17[/C][C]-0.100844[/C][C]-0.6216[/C][C]0.268943[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301776&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301776&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	-0.442826	-2.7298	0.004776
2	-0.227174	-1.4004	0.084754
3	-0.364491	-2.2469	0.015268
4	0.226038	1.3934	0.085799
5	0.20988	1.2938	0.101774
6	0.053533	0.33	0.371606
7	-0.174138	-1.0735	0.144917
8	0.184296	1.1361	0.131519
9	0.148132	0.9131	0.183462
10	-0.106141	-0.6543	0.258431
11	0.052866	0.3259	0.373149
12	-0.045039	-0.2776	0.391396
13	-0.129697	-0.7995	0.214484
14	-0.165991	-1.0232	0.156333
15	-0.065994	-0.4068	0.343214
16	0.228311	1.4074	0.083718
17	-0.100844	-0.6216	0.268943

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = multiplicative ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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 <- '0'
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