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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2016 14:51:07 +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/t1482501151k62dlh32o6bkz9z.htm/, Retrieved Tue, 07 May 2024 06:36:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302950, Retrieved Tue, 07 May 2024 06:36:06 +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] [Autocorrelatie] [2016-12-23 13:51:07] [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=302950&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=302950&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302950&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	0.898773	5.3926	2e-06
2	0.797542	4.7853	1.4e-05
3	0.724481	4.3469	5.4e-05
4	0.68069	4.0841	0.000118
5	0.591645	3.5499	0.000547
6	0.503881	3.0233	0.002294
7	0.432663	2.596	0.006784
8	0.388162	2.329	0.012795
9	0.292998	1.758	0.043625
10	0.201241	1.2074	0.117567
11	0.130375	0.7822	0.219592
12	0.076892	0.4614	0.323661
13	-0.013905	-0.0834	0.466987
14	-0.084045	-0.5043	0.308572
15	-0.139134	-0.8348	0.204667

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.898773 & 5.3926 & 2e-06 \tabularnewline
2 & 0.797542 & 4.7853 & 1.4e-05 \tabularnewline
3 & 0.724481 & 4.3469 & 5.4e-05 \tabularnewline
4 & 0.68069 & 4.0841 & 0.000118 \tabularnewline
5 & 0.591645 & 3.5499 & 0.000547 \tabularnewline
6 & 0.503881 & 3.0233 & 0.002294 \tabularnewline
7 & 0.432663 & 2.596 & 0.006784 \tabularnewline
8 & 0.388162 & 2.329 & 0.012795 \tabularnewline
9 & 0.292998 & 1.758 & 0.043625 \tabularnewline
10 & 0.201241 & 1.2074 & 0.117567 \tabularnewline
11 & 0.130375 & 0.7822 & 0.219592 \tabularnewline
12 & 0.076892 & 0.4614 & 0.323661 \tabularnewline
13 & -0.013905 & -0.0834 & 0.466987 \tabularnewline
14 & -0.084045 & -0.5043 & 0.308572 \tabularnewline
15 & -0.139134 & -0.8348 & 0.204667 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302950&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]0.898773[/C][C]5.3926[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]0.797542[/C][C]4.7853[/C][C]1.4e-05[/C][/ROW]
[ROW][C]3[/C][C]0.724481[/C][C]4.3469[/C][C]5.4e-05[/C][/ROW]
[ROW][C]4[/C][C]0.68069[/C][C]4.0841[/C][C]0.000118[/C][/ROW]
[ROW][C]5[/C][C]0.591645[/C][C]3.5499[/C][C]0.000547[/C][/ROW]
[ROW][C]6[/C][C]0.503881[/C][C]3.0233[/C][C]0.002294[/C][/ROW]
[ROW][C]7[/C][C]0.432663[/C][C]2.596[/C][C]0.006784[/C][/ROW]
[ROW][C]8[/C][C]0.388162[/C][C]2.329[/C][C]0.012795[/C][/ROW]
[ROW][C]9[/C][C]0.292998[/C][C]1.758[/C][C]0.043625[/C][/ROW]
[ROW][C]10[/C][C]0.201241[/C][C]1.2074[/C][C]0.117567[/C][/ROW]
[ROW][C]11[/C][C]0.130375[/C][C]0.7822[/C][C]0.219592[/C][/ROW]
[ROW][C]12[/C][C]0.076892[/C][C]0.4614[/C][C]0.323661[/C][/ROW]
[ROW][C]13[/C][C]-0.013905[/C][C]-0.0834[/C][C]0.466987[/C][/ROW]
[ROW][C]14[/C][C]-0.084045[/C][C]-0.5043[/C][C]0.308572[/C][/ROW]
[ROW][C]15[/C][C]-0.139134[/C][C]-0.8348[/C][C]0.204667[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302950&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302950&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	0.898773	5.3926	2e-06
2	0.797542	4.7853	1.4e-05
3	0.724481	4.3469	5.4e-05
4	0.68069	4.0841	0.000118
5	0.591645	3.5499	0.000547
6	0.503881	3.0233	0.002294
7	0.432663	2.596	0.006784
8	0.388162	2.329	0.012795
9	0.292998	1.758	0.043625
10	0.201241	1.2074	0.117567
11	0.130375	0.7822	0.219592
12	0.076892	0.4614	0.323661
13	-0.013905	-0.0834	0.466987
14	-0.084045	-0.5043	0.308572
15	-0.139134	-0.8348	0.204667

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.898773	5.3926	2e-06
2	-0.05333	-0.32	0.375417
3	0.090659	0.544	0.294914
4	0.109532	0.6572	0.257619
5	-0.251064	-1.5064	0.070347
6	-0.003996	-0.024	0.490503
7	0.002141	0.0128	0.494911
8	0.034513	0.2071	0.418559
9	-0.256564	-1.5394	0.066227
10	-0.001985	-0.0119	0.495281
11	0.003581	0.0215	0.491489
12	-0.075579	-0.4535	0.326465
13	-0.155982	-0.9359	0.177783
14	0.079769	0.4786	0.317555
15	-0.053735	-0.3224	0.374503

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.898773 & 5.3926 & 2e-06 \tabularnewline
2 & -0.05333 & -0.32 & 0.375417 \tabularnewline
3 & 0.090659 & 0.544 & 0.294914 \tabularnewline
4 & 0.109532 & 0.6572 & 0.257619 \tabularnewline
5 & -0.251064 & -1.5064 & 0.070347 \tabularnewline
6 & -0.003996 & -0.024 & 0.490503 \tabularnewline
7 & 0.002141 & 0.0128 & 0.494911 \tabularnewline
8 & 0.034513 & 0.2071 & 0.418559 \tabularnewline
9 & -0.256564 & -1.5394 & 0.066227 \tabularnewline
10 & -0.001985 & -0.0119 & 0.495281 \tabularnewline
11 & 0.003581 & 0.0215 & 0.491489 \tabularnewline
12 & -0.075579 & -0.4535 & 0.326465 \tabularnewline
13 & -0.155982 & -0.9359 & 0.177783 \tabularnewline
14 & 0.079769 & 0.4786 & 0.317555 \tabularnewline
15 & -0.053735 & -0.3224 & 0.374503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302950&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]0.898773[/C][C]5.3926[/C][C]2e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.05333[/C][C]-0.32[/C][C]0.375417[/C][/ROW]
[ROW][C]3[/C][C]0.090659[/C][C]0.544[/C][C]0.294914[/C][/ROW]
[ROW][C]4[/C][C]0.109532[/C][C]0.6572[/C][C]0.257619[/C][/ROW]
[ROW][C]5[/C][C]-0.251064[/C][C]-1.5064[/C][C]0.070347[/C][/ROW]
[ROW][C]6[/C][C]-0.003996[/C][C]-0.024[/C][C]0.490503[/C][/ROW]
[ROW][C]7[/C][C]0.002141[/C][C]0.0128[/C][C]0.494911[/C][/ROW]
[ROW][C]8[/C][C]0.034513[/C][C]0.2071[/C][C]0.418559[/C][/ROW]
[ROW][C]9[/C][C]-0.256564[/C][C]-1.5394[/C][C]0.066227[/C][/ROW]
[ROW][C]10[/C][C]-0.001985[/C][C]-0.0119[/C][C]0.495281[/C][/ROW]
[ROW][C]11[/C][C]0.003581[/C][C]0.0215[/C][C]0.491489[/C][/ROW]
[ROW][C]12[/C][C]-0.075579[/C][C]-0.4535[/C][C]0.326465[/C][/ROW]
[ROW][C]13[/C][C]-0.155982[/C][C]-0.9359[/C][C]0.177783[/C][/ROW]
[ROW][C]14[/C][C]0.079769[/C][C]0.4786[/C][C]0.317555[/C][/ROW]
[ROW][C]15[/C][C]-0.053735[/C][C]-0.3224[/C][C]0.374503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302950&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302950&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	0.898773	5.3926	2e-06
2	-0.05333	-0.32	0.375417
3	0.090659	0.544	0.294914
4	0.109532	0.6572	0.257619
5	-0.251064	-1.5064	0.070347
6	-0.003996	-0.024	0.490503
7	0.002141	0.0128	0.494911
8	0.034513	0.2071	0.418559
9	-0.256564	-1.5394	0.066227
10	-0.001985	-0.0119	0.495281
11	0.003581	0.0215	0.491489
12	-0.075579	-0.4535	0.326465
13	-0.155982	-0.9359	0.177783
14	0.079769	0.4786	0.317555
15	-0.053735	-0.3224	0.374503

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):

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