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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 14 Dec 2016 14:37:32 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/14/t1481722663gbo89o4o2hei6gu.htm/, Retrieved Fri, 17 May 2024 00:15:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299423, Retrieved Fri, 17 May 2024 00:15:12 +0000

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No (this computation is public)

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Estimated Impact

100

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [] [2016-12-14 13:37:32] [2802fcbee976b89d2ab84425d3d65dcf] [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	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299423&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299423&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299423&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.885494	5.9401	0
2	0.769214	5.16	3e-06
3	0.673994	4.5213	2.2e-05
4	0.597862	4.0106	0.000113
5	0.52771	3.54	0.000472
6	0.452592	3.0361	0.001988
7	0.37506	2.516	0.007753
8	0.308158	2.0672	0.022249
9	0.248491	1.6669	0.051237
10	0.197902	1.3276	0.095508
11	0.134253	0.9006	0.186299
12	0.073412	0.4925	0.312393
13	0.032783	0.2199	0.413467
14	-0.003088	-0.0207	0.491782
15	-0.02488	-0.1669	0.434097
16	-0.039813	-0.2671	0.395318

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.885494 & 5.9401 & 0 \tabularnewline
2 & 0.769214 & 5.16 & 3e-06 \tabularnewline
3 & 0.673994 & 4.5213 & 2.2e-05 \tabularnewline
4 & 0.597862 & 4.0106 & 0.000113 \tabularnewline
5 & 0.52771 & 3.54 & 0.000472 \tabularnewline
6 & 0.452592 & 3.0361 & 0.001988 \tabularnewline
7 & 0.37506 & 2.516 & 0.007753 \tabularnewline
8 & 0.308158 & 2.0672 & 0.022249 \tabularnewline
9 & 0.248491 & 1.6669 & 0.051237 \tabularnewline
10 & 0.197902 & 1.3276 & 0.095508 \tabularnewline
11 & 0.134253 & 0.9006 & 0.186299 \tabularnewline
12 & 0.073412 & 0.4925 & 0.312393 \tabularnewline
13 & 0.032783 & 0.2199 & 0.413467 \tabularnewline
14 & -0.003088 & -0.0207 & 0.491782 \tabularnewline
15 & -0.02488 & -0.1669 & 0.434097 \tabularnewline
16 & -0.039813 & -0.2671 & 0.395318 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299423&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]0.885494[/C][C]5.9401[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.769214[/C][C]5.16[/C][C]3e-06[/C][/ROW]
[ROW][C]3[/C][C]0.673994[/C][C]4.5213[/C][C]2.2e-05[/C][/ROW]
[ROW][C]4[/C][C]0.597862[/C][C]4.0106[/C][C]0.000113[/C][/ROW]
[ROW][C]5[/C][C]0.52771[/C][C]3.54[/C][C]0.000472[/C][/ROW]
[ROW][C]6[/C][C]0.452592[/C][C]3.0361[/C][C]0.001988[/C][/ROW]
[ROW][C]7[/C][C]0.37506[/C][C]2.516[/C][C]0.007753[/C][/ROW]
[ROW][C]8[/C][C]0.308158[/C][C]2.0672[/C][C]0.022249[/C][/ROW]
[ROW][C]9[/C][C]0.248491[/C][C]1.6669[/C][C]0.051237[/C][/ROW]
[ROW][C]10[/C][C]0.197902[/C][C]1.3276[/C][C]0.095508[/C][/ROW]
[ROW][C]11[/C][C]0.134253[/C][C]0.9006[/C][C]0.186299[/C][/ROW]
[ROW][C]12[/C][C]0.073412[/C][C]0.4925[/C][C]0.312393[/C][/ROW]
[ROW][C]13[/C][C]0.032783[/C][C]0.2199[/C][C]0.413467[/C][/ROW]
[ROW][C]14[/C][C]-0.003088[/C][C]-0.0207[/C][C]0.491782[/C][/ROW]
[ROW][C]15[/C][C]-0.02488[/C][C]-0.1669[/C][C]0.434097[/C][/ROW]
[ROW][C]16[/C][C]-0.039813[/C][C]-0.2671[/C][C]0.395318[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299423&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299423&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	0.885494	5.9401	0
2	0.769214	5.16	3e-06
3	0.673994	4.5213	2.2e-05
4	0.597862	4.0106	0.000113
5	0.52771	3.54	0.000472
6	0.452592	3.0361	0.001988
7	0.37506	2.516	0.007753
8	0.308158	2.0672	0.022249
9	0.248491	1.6669	0.051237
10	0.197902	1.3276	0.095508
11	0.134253	0.9006	0.186299
12	0.073412	0.4925	0.312393
13	0.032783	0.2199	0.413467
14	-0.003088	-0.0207	0.491782
15	-0.02488	-0.1669	0.434097
16	-0.039813	-0.2671	0.395318

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.885494	5.9401	0
2	-0.06895	-0.4625	0.322965
3	0.032343	0.217	0.414608
4	0.029525	0.1981	0.421945
5	-0.01543	-0.1035	0.45901
6	-0.057403	-0.3851	0.350999
7	-0.051915	-0.3483	0.364637
8	-0.004407	-0.0296	0.488273
9	-0.022497	-0.1509	0.440359
10	-0.003166	-0.0212	0.491576
11	-0.097856	-0.6564	0.257444
12	-0.02873	-0.1927	0.424021
13	0.035001	0.2348	0.407716
14	-0.031749	-0.213	0.416154
15	0.033515	0.2248	0.411567
16	0.011979	0.0804	0.468154

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.885494 & 5.9401 & 0 \tabularnewline
2 & -0.06895 & -0.4625 & 0.322965 \tabularnewline
3 & 0.032343 & 0.217 & 0.414608 \tabularnewline
4 & 0.029525 & 0.1981 & 0.421945 \tabularnewline
5 & -0.01543 & -0.1035 & 0.45901 \tabularnewline
6 & -0.057403 & -0.3851 & 0.350999 \tabularnewline
7 & -0.051915 & -0.3483 & 0.364637 \tabularnewline
8 & -0.004407 & -0.0296 & 0.488273 \tabularnewline
9 & -0.022497 & -0.1509 & 0.440359 \tabularnewline
10 & -0.003166 & -0.0212 & 0.491576 \tabularnewline
11 & -0.097856 & -0.6564 & 0.257444 \tabularnewline
12 & -0.02873 & -0.1927 & 0.424021 \tabularnewline
13 & 0.035001 & 0.2348 & 0.407716 \tabularnewline
14 & -0.031749 & -0.213 & 0.416154 \tabularnewline
15 & 0.033515 & 0.2248 & 0.411567 \tabularnewline
16 & 0.011979 & 0.0804 & 0.468154 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299423&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]0.885494[/C][C]5.9401[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.06895[/C][C]-0.4625[/C][C]0.322965[/C][/ROW]
[ROW][C]3[/C][C]0.032343[/C][C]0.217[/C][C]0.414608[/C][/ROW]
[ROW][C]4[/C][C]0.029525[/C][C]0.1981[/C][C]0.421945[/C][/ROW]
[ROW][C]5[/C][C]-0.01543[/C][C]-0.1035[/C][C]0.45901[/C][/ROW]
[ROW][C]6[/C][C]-0.057403[/C][C]-0.3851[/C][C]0.350999[/C][/ROW]
[ROW][C]7[/C][C]-0.051915[/C][C]-0.3483[/C][C]0.364637[/C][/ROW]
[ROW][C]8[/C][C]-0.004407[/C][C]-0.0296[/C][C]0.488273[/C][/ROW]
[ROW][C]9[/C][C]-0.022497[/C][C]-0.1509[/C][C]0.440359[/C][/ROW]
[ROW][C]10[/C][C]-0.003166[/C][C]-0.0212[/C][C]0.491576[/C][/ROW]
[ROW][C]11[/C][C]-0.097856[/C][C]-0.6564[/C][C]0.257444[/C][/ROW]
[ROW][C]12[/C][C]-0.02873[/C][C]-0.1927[/C][C]0.424021[/C][/ROW]
[ROW][C]13[/C][C]0.035001[/C][C]0.2348[/C][C]0.407716[/C][/ROW]
[ROW][C]14[/C][C]-0.031749[/C][C]-0.213[/C][C]0.416154[/C][/ROW]
[ROW][C]15[/C][C]0.033515[/C][C]0.2248[/C][C]0.411567[/C][/ROW]
[ROW][C]16[/C][C]0.011979[/C][C]0.0804[/C][C]0.468154[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299423&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299423&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	0.885494	5.9401	0
2	-0.06895	-0.4625	0.322965
3	0.032343	0.217	0.414608
4	0.029525	0.1981	0.421945
5	-0.01543	-0.1035	0.45901
6	-0.057403	-0.3851	0.350999
7	-0.051915	-0.3483	0.364637
8	-0.004407	-0.0296	0.488273
9	-0.022497	-0.1509	0.440359
10	-0.003166	-0.0212	0.491576
11	-0.097856	-0.6564	0.257444
12	-0.02873	-0.1927	0.424021
13	0.035001	0.2348	0.407716
14	-0.031749	-0.213	0.416154
15	0.033515	0.2248	0.411567
16	0.011979	0.0804	0.468154

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