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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 14:39:57 +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/t1481982015cak7o9xqnpybmx6.htm/, Retrieved Thu, 02 May 2024 07:44:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300785, Retrieved Thu, 02 May 2024 07:44:59 +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] [N1179 ACF I] [2016-12-17 13:39:57] [2e11ca31a00cf8de75c33c1af2d59434] [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=300785&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=300785&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300785&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	-0.256766	-1.0271	0.159834
2	0.262391	1.0496	0.154757
3	-0.430193	-1.7208	0.052284
4	0.545888	2.1836	0.022117
5	-0.295113	-1.1805	0.127537
6	0.191358	0.7654	0.227578
7	-0.285697	-1.1428	0.13497
8	0.315903	1.2636	0.112236
9	-0.293641	-1.1746	0.128677
10	-0.007301	-0.0292	0.488532
11	-0.242444	-0.9698	0.173295
12	0.221774	0.8871	0.194084

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.256766 & -1.0271 & 0.159834 \tabularnewline
2 & 0.262391 & 1.0496 & 0.154757 \tabularnewline
3 & -0.430193 & -1.7208 & 0.052284 \tabularnewline
4 & 0.545888 & 2.1836 & 0.022117 \tabularnewline
5 & -0.295113 & -1.1805 & 0.127537 \tabularnewline
6 & 0.191358 & 0.7654 & 0.227578 \tabularnewline
7 & -0.285697 & -1.1428 & 0.13497 \tabularnewline
8 & 0.315903 & 1.2636 & 0.112236 \tabularnewline
9 & -0.293641 & -1.1746 & 0.128677 \tabularnewline
10 & -0.007301 & -0.0292 & 0.488532 \tabularnewline
11 & -0.242444 & -0.9698 & 0.173295 \tabularnewline
12 & 0.221774 & 0.8871 & 0.194084 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300785&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]-0.256766[/C][C]-1.0271[/C][C]0.159834[/C][/ROW]
[ROW][C]2[/C][C]0.262391[/C][C]1.0496[/C][C]0.154757[/C][/ROW]
[ROW][C]3[/C][C]-0.430193[/C][C]-1.7208[/C][C]0.052284[/C][/ROW]
[ROW][C]4[/C][C]0.545888[/C][C]2.1836[/C][C]0.022117[/C][/ROW]
[ROW][C]5[/C][C]-0.295113[/C][C]-1.1805[/C][C]0.127537[/C][/ROW]
[ROW][C]6[/C][C]0.191358[/C][C]0.7654[/C][C]0.227578[/C][/ROW]
[ROW][C]7[/C][C]-0.285697[/C][C]-1.1428[/C][C]0.13497[/C][/ROW]
[ROW][C]8[/C][C]0.315903[/C][C]1.2636[/C][C]0.112236[/C][/ROW]
[ROW][C]9[/C][C]-0.293641[/C][C]-1.1746[/C][C]0.128677[/C][/ROW]
[ROW][C]10[/C][C]-0.007301[/C][C]-0.0292[/C][C]0.488532[/C][/ROW]
[ROW][C]11[/C][C]-0.242444[/C][C]-0.9698[/C][C]0.173295[/C][/ROW]
[ROW][C]12[/C][C]0.221774[/C][C]0.8871[/C][C]0.194084[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300785&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300785&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	-0.256766	-1.0271	0.159834
2	0.262391	1.0496	0.154757
3	-0.430193	-1.7208	0.052284
4	0.545888	2.1836	0.022117
5	-0.295113	-1.1805	0.127537
6	0.191358	0.7654	0.227578
7	-0.285697	-1.1428	0.13497
8	0.315903	1.2636	0.112236
9	-0.293641	-1.1746	0.128677
10	-0.007301	-0.0292	0.488532
11	-0.242444	-0.9698	0.173295
12	0.221774	0.8871	0.194084

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.256766	-1.0271	0.159834
2	0.210329	0.8413	0.206284
3	-0.361787	-1.4471	0.083582
4	0.467281	1.8691	0.040011
5	-0.144246	-0.577	0.28599
6	-0.133273	-0.5331	0.300649
7	0.18867	0.7547	0.230703
8	-0.120282	-0.4811	0.318469
9	-0.147004	-0.588	0.282365
10	-0.173852	-0.6954	0.248388
11	-0.08903	-0.3561	0.363202
12	0.023048	0.0922	0.463845

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.256766 & -1.0271 & 0.159834 \tabularnewline
2 & 0.210329 & 0.8413 & 0.206284 \tabularnewline
3 & -0.361787 & -1.4471 & 0.083582 \tabularnewline
4 & 0.467281 & 1.8691 & 0.040011 \tabularnewline
5 & -0.144246 & -0.577 & 0.28599 \tabularnewline
6 & -0.133273 & -0.5331 & 0.300649 \tabularnewline
7 & 0.18867 & 0.7547 & 0.230703 \tabularnewline
8 & -0.120282 & -0.4811 & 0.318469 \tabularnewline
9 & -0.147004 & -0.588 & 0.282365 \tabularnewline
10 & -0.173852 & -0.6954 & 0.248388 \tabularnewline
11 & -0.08903 & -0.3561 & 0.363202 \tabularnewline
12 & 0.023048 & 0.0922 & 0.463845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300785&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]-0.256766[/C][C]-1.0271[/C][C]0.159834[/C][/ROW]
[ROW][C]2[/C][C]0.210329[/C][C]0.8413[/C][C]0.206284[/C][/ROW]
[ROW][C]3[/C][C]-0.361787[/C][C]-1.4471[/C][C]0.083582[/C][/ROW]
[ROW][C]4[/C][C]0.467281[/C][C]1.8691[/C][C]0.040011[/C][/ROW]
[ROW][C]5[/C][C]-0.144246[/C][C]-0.577[/C][C]0.28599[/C][/ROW]
[ROW][C]6[/C][C]-0.133273[/C][C]-0.5331[/C][C]0.300649[/C][/ROW]
[ROW][C]7[/C][C]0.18867[/C][C]0.7547[/C][C]0.230703[/C][/ROW]
[ROW][C]8[/C][C]-0.120282[/C][C]-0.4811[/C][C]0.318469[/C][/ROW]
[ROW][C]9[/C][C]-0.147004[/C][C]-0.588[/C][C]0.282365[/C][/ROW]
[ROW][C]10[/C][C]-0.173852[/C][C]-0.6954[/C][C]0.248388[/C][/ROW]
[ROW][C]11[/C][C]-0.08903[/C][C]-0.3561[/C][C]0.363202[/C][/ROW]
[ROW][C]12[/C][C]0.023048[/C][C]0.0922[/C][C]0.463845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300785&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300785&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	-0.256766	-1.0271	0.159834
2	0.210329	0.8413	0.206284
3	-0.361787	-1.4471	0.083582
4	0.467281	1.8691	0.040011
5	-0.144246	-0.577	0.28599
6	-0.133273	-0.5331	0.300649
7	0.18867	0.7547	0.230703
8	-0.120282	-0.4811	0.318469
9	-0.147004	-0.588	0.282365
10	-0.173852	-0.6954	0.248388
11	-0.08903	-0.3561	0.363202
12	0.023048	0.0922	0.463845

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 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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 <- '0'
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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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code