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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2016 13:53:10 +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/23/t1482497684dlo686d277u4n57.htm/, Retrieved Wed, 08 May 2024 00:06:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302914, Retrieved Wed, 08 May 2024 00:06:16 +0000

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-       [(Partial) Autocorrelation Function] [Autocorrelatie] [2016-12-23 12:53:10] [c6c2c19ee5e10dd65276916b11a37d00] [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=302914&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=302914&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302914&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	-0.136006	-0.8046	0.213234
2	-0.560681	-3.317	0.001065
3	-0.102909	-0.6088	0.273287
4	0.733984	4.3423	5.7e-05
5	-0.124709	-0.7378	0.23278
6	-0.463352	-2.7412	0.004788
7	-0.085588	-0.5063	0.307894
8	0.597115	3.5326	0.000589
9	-0.070141	-0.415	0.340351
10	-0.393963	-2.3307	0.012828
11	-0.09451	-0.5591	0.289818
12	0.502676	2.9739	0.002648
13	-0.031495	-0.1863	0.426632
14	-0.401104	-2.373	0.011635
15	-0.074854	-0.4428	0.330303

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.136006 & -0.8046 & 0.213234 \tabularnewline
2 & -0.560681 & -3.317 & 0.001065 \tabularnewline
3 & -0.102909 & -0.6088 & 0.273287 \tabularnewline
4 & 0.733984 & 4.3423 & 5.7e-05 \tabularnewline
5 & -0.124709 & -0.7378 & 0.23278 \tabularnewline
6 & -0.463352 & -2.7412 & 0.004788 \tabularnewline
7 & -0.085588 & -0.5063 & 0.307894 \tabularnewline
8 & 0.597115 & 3.5326 & 0.000589 \tabularnewline
9 & -0.070141 & -0.415 & 0.340351 \tabularnewline
10 & -0.393963 & -2.3307 & 0.012828 \tabularnewline
11 & -0.09451 & -0.5591 & 0.289818 \tabularnewline
12 & 0.502676 & 2.9739 & 0.002648 \tabularnewline
13 & -0.031495 & -0.1863 & 0.426632 \tabularnewline
14 & -0.401104 & -2.373 & 0.011635 \tabularnewline
15 & -0.074854 & -0.4428 & 0.330303 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302914&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]-0.136006[/C][C]-0.8046[/C][C]0.213234[/C][/ROW]
[ROW][C]2[/C][C]-0.560681[/C][C]-3.317[/C][C]0.001065[/C][/ROW]
[ROW][C]3[/C][C]-0.102909[/C][C]-0.6088[/C][C]0.273287[/C][/ROW]
[ROW][C]4[/C][C]0.733984[/C][C]4.3423[/C][C]5.7e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.124709[/C][C]-0.7378[/C][C]0.23278[/C][/ROW]
[ROW][C]6[/C][C]-0.463352[/C][C]-2.7412[/C][C]0.004788[/C][/ROW]
[ROW][C]7[/C][C]-0.085588[/C][C]-0.5063[/C][C]0.307894[/C][/ROW]
[ROW][C]8[/C][C]0.597115[/C][C]3.5326[/C][C]0.000589[/C][/ROW]
[ROW][C]9[/C][C]-0.070141[/C][C]-0.415[/C][C]0.340351[/C][/ROW]
[ROW][C]10[/C][C]-0.393963[/C][C]-2.3307[/C][C]0.012828[/C][/ROW]
[ROW][C]11[/C][C]-0.09451[/C][C]-0.5591[/C][C]0.289818[/C][/ROW]
[ROW][C]12[/C][C]0.502676[/C][C]2.9739[/C][C]0.002648[/C][/ROW]
[ROW][C]13[/C][C]-0.031495[/C][C]-0.1863[/C][C]0.426632[/C][/ROW]
[ROW][C]14[/C][C]-0.401104[/C][C]-2.373[/C][C]0.011635[/C][/ROW]
[ROW][C]15[/C][C]-0.074854[/C][C]-0.4428[/C][C]0.330303[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302914&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302914&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	-0.136006	-0.8046	0.213234
2	-0.560681	-3.317	0.001065
3	-0.102909	-0.6088	0.273287
4	0.733984	4.3423	5.7e-05
5	-0.124709	-0.7378	0.23278
6	-0.463352	-2.7412	0.004788
7	-0.085588	-0.5063	0.307894
8	0.597115	3.5326	0.000589
9	-0.070141	-0.415	0.340351
10	-0.393963	-2.3307	0.012828
11	-0.09451	-0.5591	0.289818
12	0.502676	2.9739	0.002648
13	-0.031495	-0.1863	0.426632
14	-0.401104	-2.373	0.011635
15	-0.074854	-0.4428	0.330303

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.136006	-0.8046	0.213234
2	-0.590094	-3.491	0.000661
3	-0.475856	-2.8152	0.003976
4	0.463873	2.7443	0.004751
5	-0.088985	-0.5264	0.300951
6	0.004179	0.0247	0.490208
7	-0.113061	-0.6689	0.25398
8	0.049413	0.2923	0.38588
9	0.044194	0.2615	0.397637
10	0.001247	0.0074	0.497078
11	-0.049746	-0.2943	0.385133
12	0.026738	0.1582	0.43761
13	0.00803	0.0475	0.481189
14	-0.153927	-0.9106	0.184356
15	-0.029511	-0.1746	0.431203

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.136006 & -0.8046 & 0.213234 \tabularnewline
2 & -0.590094 & -3.491 & 0.000661 \tabularnewline
3 & -0.475856 & -2.8152 & 0.003976 \tabularnewline
4 & 0.463873 & 2.7443 & 0.004751 \tabularnewline
5 & -0.088985 & -0.5264 & 0.300951 \tabularnewline
6 & 0.004179 & 0.0247 & 0.490208 \tabularnewline
7 & -0.113061 & -0.6689 & 0.25398 \tabularnewline
8 & 0.049413 & 0.2923 & 0.38588 \tabularnewline
9 & 0.044194 & 0.2615 & 0.397637 \tabularnewline
10 & 0.001247 & 0.0074 & 0.497078 \tabularnewline
11 & -0.049746 & -0.2943 & 0.385133 \tabularnewline
12 & 0.026738 & 0.1582 & 0.43761 \tabularnewline
13 & 0.00803 & 0.0475 & 0.481189 \tabularnewline
14 & -0.153927 & -0.9106 & 0.184356 \tabularnewline
15 & -0.029511 & -0.1746 & 0.431203 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302914&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]-0.136006[/C][C]-0.8046[/C][C]0.213234[/C][/ROW]
[ROW][C]2[/C][C]-0.590094[/C][C]-3.491[/C][C]0.000661[/C][/ROW]
[ROW][C]3[/C][C]-0.475856[/C][C]-2.8152[/C][C]0.003976[/C][/ROW]
[ROW][C]4[/C][C]0.463873[/C][C]2.7443[/C][C]0.004751[/C][/ROW]
[ROW][C]5[/C][C]-0.088985[/C][C]-0.5264[/C][C]0.300951[/C][/ROW]
[ROW][C]6[/C][C]0.004179[/C][C]0.0247[/C][C]0.490208[/C][/ROW]
[ROW][C]7[/C][C]-0.113061[/C][C]-0.6689[/C][C]0.25398[/C][/ROW]
[ROW][C]8[/C][C]0.049413[/C][C]0.2923[/C][C]0.38588[/C][/ROW]
[ROW][C]9[/C][C]0.044194[/C][C]0.2615[/C][C]0.397637[/C][/ROW]
[ROW][C]10[/C][C]0.001247[/C][C]0.0074[/C][C]0.497078[/C][/ROW]
[ROW][C]11[/C][C]-0.049746[/C][C]-0.2943[/C][C]0.385133[/C][/ROW]
[ROW][C]12[/C][C]0.026738[/C][C]0.1582[/C][C]0.43761[/C][/ROW]
[ROW][C]13[/C][C]0.00803[/C][C]0.0475[/C][C]0.481189[/C][/ROW]
[ROW][C]14[/C][C]-0.153927[/C][C]-0.9106[/C][C]0.184356[/C][/ROW]
[ROW][C]15[/C][C]-0.029511[/C][C]-0.1746[/C][C]0.431203[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302914&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302914&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	-0.136006	-0.8046	0.213234
2	-0.590094	-3.491	0.000661
3	-0.475856	-2.8152	0.003976
4	0.463873	2.7443	0.004751
5	-0.088985	-0.5264	0.300951
6	0.004179	0.0247	0.490208
7	-0.113061	-0.6689	0.25398
8	0.049413	0.2923	0.38588
9	0.044194	0.2615	0.397637
10	0.001247	0.0074	0.497078
11	-0.049746	-0.2943	0.385133
12	0.026738	0.1582	0.43761
13	0.00803	0.0475	0.481189
14	-0.153927	-0.9106	0.184356
15	-0.029511	-0.1746	0.431203

Figure 1

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Figure 2

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Figure 3

PNG link

Postscript link

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Parameters (Session):

par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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Input Parameters & R Code