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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2016 14:07:07 +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/20/t1482239239jo0vu3ie6lhdhbb.htm/, Retrieved Sat, 27 Apr 2024 13:39:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301644, Retrieved Sat, 27 Apr 2024 13:39:26 +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] [] [2016-12-20 13:07:07] [672675941468e072e71d9fb024f2b817] [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=301644&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=301644&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301644&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	0.922985	6.907	0
2	0.840923	6.2929	0
3	0.755379	5.6527	0
4	0.673743	5.0418	3e-06
5	0.59656	4.4642	2e-05
6	0.51855	3.8805	0.000138
7	0.448316	3.3549	0.000715
8	0.379958	2.8433	0.00311
9	0.312645	2.3396	0.011447
10	0.25098	1.8782	0.032784
11	0.191591	1.4337	0.078604
12	0.134694	1.008	0.158906
13	0.081679	0.6112	0.271761
14	0.034999	0.2619	0.397177
15	-0.008257	-0.0618	0.475475
16	-0.043861	-0.3282	0.371981
17	-0.063065	-0.4719	0.319403

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.922985 & 6.907 & 0 \tabularnewline
2 & 0.840923 & 6.2929 & 0 \tabularnewline
3 & 0.755379 & 5.6527 & 0 \tabularnewline
4 & 0.673743 & 5.0418 & 3e-06 \tabularnewline
5 & 0.59656 & 4.4642 & 2e-05 \tabularnewline
6 & 0.51855 & 3.8805 & 0.000138 \tabularnewline
7 & 0.448316 & 3.3549 & 0.000715 \tabularnewline
8 & 0.379958 & 2.8433 & 0.00311 \tabularnewline
9 & 0.312645 & 2.3396 & 0.011447 \tabularnewline
10 & 0.25098 & 1.8782 & 0.032784 \tabularnewline
11 & 0.191591 & 1.4337 & 0.078604 \tabularnewline
12 & 0.134694 & 1.008 & 0.158906 \tabularnewline
13 & 0.081679 & 0.6112 & 0.271761 \tabularnewline
14 & 0.034999 & 0.2619 & 0.397177 \tabularnewline
15 & -0.008257 & -0.0618 & 0.475475 \tabularnewline
16 & -0.043861 & -0.3282 & 0.371981 \tabularnewline
17 & -0.063065 & -0.4719 & 0.319403 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301644&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]0.922985[/C][C]6.907[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.840923[/C][C]6.2929[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.755379[/C][C]5.6527[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.673743[/C][C]5.0418[/C][C]3e-06[/C][/ROW]
[ROW][C]5[/C][C]0.59656[/C][C]4.4642[/C][C]2e-05[/C][/ROW]
[ROW][C]6[/C][C]0.51855[/C][C]3.8805[/C][C]0.000138[/C][/ROW]
[ROW][C]7[/C][C]0.448316[/C][C]3.3549[/C][C]0.000715[/C][/ROW]
[ROW][C]8[/C][C]0.379958[/C][C]2.8433[/C][C]0.00311[/C][/ROW]
[ROW][C]9[/C][C]0.312645[/C][C]2.3396[/C][C]0.011447[/C][/ROW]
[ROW][C]10[/C][C]0.25098[/C][C]1.8782[/C][C]0.032784[/C][/ROW]
[ROW][C]11[/C][C]0.191591[/C][C]1.4337[/C][C]0.078604[/C][/ROW]
[ROW][C]12[/C][C]0.134694[/C][C]1.008[/C][C]0.158906[/C][/ROW]
[ROW][C]13[/C][C]0.081679[/C][C]0.6112[/C][C]0.271761[/C][/ROW]
[ROW][C]14[/C][C]0.034999[/C][C]0.2619[/C][C]0.397177[/C][/ROW]
[ROW][C]15[/C][C]-0.008257[/C][C]-0.0618[/C][C]0.475475[/C][/ROW]
[ROW][C]16[/C][C]-0.043861[/C][C]-0.3282[/C][C]0.371981[/C][/ROW]
[ROW][C]17[/C][C]-0.063065[/C][C]-0.4719[/C][C]0.319403[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301644&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301644&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	0.922985	6.907	0
2	0.840923	6.2929	0
3	0.755379	5.6527	0
4	0.673743	5.0418	3e-06
5	0.59656	4.4642	2e-05
6	0.51855	3.8805	0.000138
7	0.448316	3.3549	0.000715
8	0.379958	2.8433	0.00311
9	0.312645	2.3396	0.011447
10	0.25098	1.8782	0.032784
11	0.191591	1.4337	0.078604
12	0.134694	1.008	0.158906
13	0.081679	0.6112	0.271761
14	0.034999	0.2619	0.397177
15	-0.008257	-0.0618	0.475475
16	-0.043861	-0.3282	0.371981
17	-0.063065	-0.4719	0.319403

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.922985	6.907	0
2	-0.074126	-0.5547	0.290651
3	-0.067193	-0.5028	0.30853
4	-0.020766	-0.1554	0.438533
5	-0.019505	-0.146	0.442238
6	-0.057004	-0.4266	0.335661
7	0.00149	0.0112	0.495571
8	-0.037597	-0.2813	0.38974
9	-0.04583	-0.343	0.366455
10	-0.012163	-0.091	0.4639
11	-0.034503	-0.2582	0.3986
12	-0.037496	-0.2806	0.390027
13	-0.023223	-0.1738	0.431329
14	-0.007519	-0.0563	0.477663
15	-0.029465	-0.2205	0.413143
16	0.004581	0.0343	0.486388
17	0.067333	0.5039	0.308162

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.922985 & 6.907 & 0 \tabularnewline
2 & -0.074126 & -0.5547 & 0.290651 \tabularnewline
3 & -0.067193 & -0.5028 & 0.30853 \tabularnewline
4 & -0.020766 & -0.1554 & 0.438533 \tabularnewline
5 & -0.019505 & -0.146 & 0.442238 \tabularnewline
6 & -0.057004 & -0.4266 & 0.335661 \tabularnewline
7 & 0.00149 & 0.0112 & 0.495571 \tabularnewline
8 & -0.037597 & -0.2813 & 0.38974 \tabularnewline
9 & -0.04583 & -0.343 & 0.366455 \tabularnewline
10 & -0.012163 & -0.091 & 0.4639 \tabularnewline
11 & -0.034503 & -0.2582 & 0.3986 \tabularnewline
12 & -0.037496 & -0.2806 & 0.390027 \tabularnewline
13 & -0.023223 & -0.1738 & 0.431329 \tabularnewline
14 & -0.007519 & -0.0563 & 0.477663 \tabularnewline
15 & -0.029465 & -0.2205 & 0.413143 \tabularnewline
16 & 0.004581 & 0.0343 & 0.486388 \tabularnewline
17 & 0.067333 & 0.5039 & 0.308162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301644&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]0.922985[/C][C]6.907[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.074126[/C][C]-0.5547[/C][C]0.290651[/C][/ROW]
[ROW][C]3[/C][C]-0.067193[/C][C]-0.5028[/C][C]0.30853[/C][/ROW]
[ROW][C]4[/C][C]-0.020766[/C][C]-0.1554[/C][C]0.438533[/C][/ROW]
[ROW][C]5[/C][C]-0.019505[/C][C]-0.146[/C][C]0.442238[/C][/ROW]
[ROW][C]6[/C][C]-0.057004[/C][C]-0.4266[/C][C]0.335661[/C][/ROW]
[ROW][C]7[/C][C]0.00149[/C][C]0.0112[/C][C]0.495571[/C][/ROW]
[ROW][C]8[/C][C]-0.037597[/C][C]-0.2813[/C][C]0.38974[/C][/ROW]
[ROW][C]9[/C][C]-0.04583[/C][C]-0.343[/C][C]0.366455[/C][/ROW]
[ROW][C]10[/C][C]-0.012163[/C][C]-0.091[/C][C]0.4639[/C][/ROW]
[ROW][C]11[/C][C]-0.034503[/C][C]-0.2582[/C][C]0.3986[/C][/ROW]
[ROW][C]12[/C][C]-0.037496[/C][C]-0.2806[/C][C]0.390027[/C][/ROW]
[ROW][C]13[/C][C]-0.023223[/C][C]-0.1738[/C][C]0.431329[/C][/ROW]
[ROW][C]14[/C][C]-0.007519[/C][C]-0.0563[/C][C]0.477663[/C][/ROW]
[ROW][C]15[/C][C]-0.029465[/C][C]-0.2205[/C][C]0.413143[/C][/ROW]
[ROW][C]16[/C][C]0.004581[/C][C]0.0343[/C][C]0.486388[/C][/ROW]
[ROW][C]17[/C][C]0.067333[/C][C]0.5039[/C][C]0.308162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301644&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301644&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	0.922985	6.907	0
2	-0.074126	-0.5547	0.290651
3	-0.067193	-0.5028	0.30853
4	-0.020766	-0.1554	0.438533
5	-0.019505	-0.146	0.442238
6	-0.057004	-0.4266	0.335661
7	0.00149	0.0112	0.495571
8	-0.037597	-0.2813	0.38974
9	-0.04583	-0.343	0.366455
10	-0.012163	-0.091	0.4639
11	-0.034503	-0.2582	0.3986
12	-0.037496	-0.2806	0.390027
13	-0.023223	-0.1738	0.431329
14	-0.007519	-0.0563	0.477663
15	-0.029465	-0.2205	0.413143
16	0.004581	0.0343	0.486388
17	0.067333	0.5039	0.308162

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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