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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2016 12:47:57 +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/23/t1482493692wmh2wqh3zpgaus4.htm/, Retrieved Tue, 07 May 2024 17:22:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302877, Retrieved Tue, 07 May 2024 17:22:10 +0000

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-       [(Partial) Autocorrelation Function] [N2797] [2016-12-23 11:47:57] [8e56909c70ba580a071e942d9a393c42] [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=302877&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=302877&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302877&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	0.162785	1.3225	0.095287
2	0.184529	1.4991	0.069305
3	0.084005	0.6825	0.248668
4	0.191927	1.5592	0.061863
5	-0.028374	-0.2305	0.409204
6	0.052196	0.424	0.336456
7	0.133588	1.0853	0.140874
8	0.01908	0.155	0.438645
9	-0.017969	-0.146	0.44219
10	0.036468	0.2963	0.383977
11	0.144383	1.173	0.122512
12	-0.46136	-3.7481	0.000189
13	-0.16613	-1.3496	0.09087
14	-0.125441	-1.0191	0.155941
15	-0.106346	-0.864	0.19537
16	-0.163332	-1.3269	0.094555
17	-0.098063	-0.7967	0.214251
18	-0.047544	-0.3862	0.350278

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.162785 & 1.3225 & 0.095287 \tabularnewline
2 & 0.184529 & 1.4991 & 0.069305 \tabularnewline
3 & 0.084005 & 0.6825 & 0.248668 \tabularnewline
4 & 0.191927 & 1.5592 & 0.061863 \tabularnewline
5 & -0.028374 & -0.2305 & 0.409204 \tabularnewline
6 & 0.052196 & 0.424 & 0.336456 \tabularnewline
7 & 0.133588 & 1.0853 & 0.140874 \tabularnewline
8 & 0.01908 & 0.155 & 0.438645 \tabularnewline
9 & -0.017969 & -0.146 & 0.44219 \tabularnewline
10 & 0.036468 & 0.2963 & 0.383977 \tabularnewline
11 & 0.144383 & 1.173 & 0.122512 \tabularnewline
12 & -0.46136 & -3.7481 & 0.000189 \tabularnewline
13 & -0.16613 & -1.3496 & 0.09087 \tabularnewline
14 & -0.125441 & -1.0191 & 0.155941 \tabularnewline
15 & -0.106346 & -0.864 & 0.19537 \tabularnewline
16 & -0.163332 & -1.3269 & 0.094555 \tabularnewline
17 & -0.098063 & -0.7967 & 0.214251 \tabularnewline
18 & -0.047544 & -0.3862 & 0.350278 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302877&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]0.162785[/C][C]1.3225[/C][C]0.095287[/C][/ROW]
[ROW][C]2[/C][C]0.184529[/C][C]1.4991[/C][C]0.069305[/C][/ROW]
[ROW][C]3[/C][C]0.084005[/C][C]0.6825[/C][C]0.248668[/C][/ROW]
[ROW][C]4[/C][C]0.191927[/C][C]1.5592[/C][C]0.061863[/C][/ROW]
[ROW][C]5[/C][C]-0.028374[/C][C]-0.2305[/C][C]0.409204[/C][/ROW]
[ROW][C]6[/C][C]0.052196[/C][C]0.424[/C][C]0.336456[/C][/ROW]
[ROW][C]7[/C][C]0.133588[/C][C]1.0853[/C][C]0.140874[/C][/ROW]
[ROW][C]8[/C][C]0.01908[/C][C]0.155[/C][C]0.438645[/C][/ROW]
[ROW][C]9[/C][C]-0.017969[/C][C]-0.146[/C][C]0.44219[/C][/ROW]
[ROW][C]10[/C][C]0.036468[/C][C]0.2963[/C][C]0.383977[/C][/ROW]
[ROW][C]11[/C][C]0.144383[/C][C]1.173[/C][C]0.122512[/C][/ROW]
[ROW][C]12[/C][C]-0.46136[/C][C]-3.7481[/C][C]0.000189[/C][/ROW]
[ROW][C]13[/C][C]-0.16613[/C][C]-1.3496[/C][C]0.09087[/C][/ROW]
[ROW][C]14[/C][C]-0.125441[/C][C]-1.0191[/C][C]0.155941[/C][/ROW]
[ROW][C]15[/C][C]-0.106346[/C][C]-0.864[/C][C]0.19537[/C][/ROW]
[ROW][C]16[/C][C]-0.163332[/C][C]-1.3269[/C][C]0.094555[/C][/ROW]
[ROW][C]17[/C][C]-0.098063[/C][C]-0.7967[/C][C]0.214251[/C][/ROW]
[ROW][C]18[/C][C]-0.047544[/C][C]-0.3862[/C][C]0.350278[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302877&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302877&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	0.162785	1.3225	0.095287
2	0.184529	1.4991	0.069305
3	0.084005	0.6825	0.248668
4	0.191927	1.5592	0.061863
5	-0.028374	-0.2305	0.409204
6	0.052196	0.424	0.336456
7	0.133588	1.0853	0.140874
8	0.01908	0.155	0.438645
9	-0.017969	-0.146	0.44219
10	0.036468	0.2963	0.383977
11	0.144383	1.173	0.122512
12	-0.46136	-3.7481	0.000189
13	-0.16613	-1.3496	0.09087
14	-0.125441	-1.0191	0.155941
15	-0.106346	-0.864	0.19537
16	-0.163332	-1.3269	0.094555
17	-0.098063	-0.7967	0.214251
18	-0.047544	-0.3862	0.350278

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.162785	1.3225	0.095287
2	0.162332	1.3188	0.095899
3	0.034201	0.2779	0.390998
4	0.154506	1.2552	0.106914
5	-0.098899	-0.8035	0.212296
6	0.014595	0.1186	0.452989
7	0.139001	1.1293	0.13144
8	-0.055471	-0.4506	0.32686
9	-0.03439	-0.2794	0.39041
10	0.029418	0.239	0.405925
11	0.115623	0.9393	0.175495
12	-0.543685	-4.4169	1.9e-05
13	-0.064994	-0.528	0.299629
14	0.06968	0.5661	0.28663
15	-0.116697	-0.948	0.173281
16	0.080664	0.6553	0.25727
17	-0.123282	-1.0016	0.160109
18	-0.011414	-0.0927	0.463201

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.162785 & 1.3225 & 0.095287 \tabularnewline
2 & 0.162332 & 1.3188 & 0.095899 \tabularnewline
3 & 0.034201 & 0.2779 & 0.390998 \tabularnewline
4 & 0.154506 & 1.2552 & 0.106914 \tabularnewline
5 & -0.098899 & -0.8035 & 0.212296 \tabularnewline
6 & 0.014595 & 0.1186 & 0.452989 \tabularnewline
7 & 0.139001 & 1.1293 & 0.13144 \tabularnewline
8 & -0.055471 & -0.4506 & 0.32686 \tabularnewline
9 & -0.03439 & -0.2794 & 0.39041 \tabularnewline
10 & 0.029418 & 0.239 & 0.405925 \tabularnewline
11 & 0.115623 & 0.9393 & 0.175495 \tabularnewline
12 & -0.543685 & -4.4169 & 1.9e-05 \tabularnewline
13 & -0.064994 & -0.528 & 0.299629 \tabularnewline
14 & 0.06968 & 0.5661 & 0.28663 \tabularnewline
15 & -0.116697 & -0.948 & 0.173281 \tabularnewline
16 & 0.080664 & 0.6553 & 0.25727 \tabularnewline
17 & -0.123282 & -1.0016 & 0.160109 \tabularnewline
18 & -0.011414 & -0.0927 & 0.463201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302877&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]0.162785[/C][C]1.3225[/C][C]0.095287[/C][/ROW]
[ROW][C]2[/C][C]0.162332[/C][C]1.3188[/C][C]0.095899[/C][/ROW]
[ROW][C]3[/C][C]0.034201[/C][C]0.2779[/C][C]0.390998[/C][/ROW]
[ROW][C]4[/C][C]0.154506[/C][C]1.2552[/C][C]0.106914[/C][/ROW]
[ROW][C]5[/C][C]-0.098899[/C][C]-0.8035[/C][C]0.212296[/C][/ROW]
[ROW][C]6[/C][C]0.014595[/C][C]0.1186[/C][C]0.452989[/C][/ROW]
[ROW][C]7[/C][C]0.139001[/C][C]1.1293[/C][C]0.13144[/C][/ROW]
[ROW][C]8[/C][C]-0.055471[/C][C]-0.4506[/C][C]0.32686[/C][/ROW]
[ROW][C]9[/C][C]-0.03439[/C][C]-0.2794[/C][C]0.39041[/C][/ROW]
[ROW][C]10[/C][C]0.029418[/C][C]0.239[/C][C]0.405925[/C][/ROW]
[ROW][C]11[/C][C]0.115623[/C][C]0.9393[/C][C]0.175495[/C][/ROW]
[ROW][C]12[/C][C]-0.543685[/C][C]-4.4169[/C][C]1.9e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.064994[/C][C]-0.528[/C][C]0.299629[/C][/ROW]
[ROW][C]14[/C][C]0.06968[/C][C]0.5661[/C][C]0.28663[/C][/ROW]
[ROW][C]15[/C][C]-0.116697[/C][C]-0.948[/C][C]0.173281[/C][/ROW]
[ROW][C]16[/C][C]0.080664[/C][C]0.6553[/C][C]0.25727[/C][/ROW]
[ROW][C]17[/C][C]-0.123282[/C][C]-1.0016[/C][C]0.160109[/C][/ROW]
[ROW][C]18[/C][C]-0.011414[/C][C]-0.0927[/C][C]0.463201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302877&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302877&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	0.162785	1.3225	0.095287
2	0.162332	1.3188	0.095899
3	0.034201	0.2779	0.390998
4	0.154506	1.2552	0.106914
5	-0.098899	-0.8035	0.212296
6	0.014595	0.1186	0.452989
7	0.139001	1.1293	0.13144
8	-0.055471	-0.4506	0.32686
9	-0.03439	-0.2794	0.39041
10	0.029418	0.239	0.405925
11	0.115623	0.9393	0.175495
12	-0.543685	-4.4169	1.9e-05
13	-0.064994	-0.528	0.299629
14	0.06968	0.5661	0.28663
15	-0.116697	-0.948	0.173281
16	0.080664	0.6553	0.25727
17	-0.123282	-1.0016	0.160109
18	-0.011414	-0.0927	0.463201

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 = additive ; par2 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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Input Parameters & R Code