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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2016 10:36:09 +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/t1482485784q0w46dihlz3fnd2.htm/, Retrieved Tue, 07 May 2024 05:51:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302818, Retrieved Tue, 07 May 2024 05:51:23 +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] [ACF N2583] [2016-12-23 09:36:09] [11b61e09f442d73f657668491c17a736] [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=302818&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=302818&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302818&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	0.143191	1.4532	0.074601
2	-0.058745	-0.5962	0.276176
3	0.18803	1.9083	0.029569
4	0.055458	0.5628	0.287385
5	0.23064	2.3407	0.010586
6	0.096293	0.9773	0.165363
7	-0.115337	-1.1705	0.122242
8	0.066872	0.6787	0.249432
9	0.119038	1.2081	0.114887
10	0.102074	1.0359	0.151328
11	-0.033444	-0.3394	0.367492
12	-0.332672	-3.3762	0.000519
13	0.006006	0.061	0.475756
14	0.063297	0.6424	0.261021
15	-0.05551	-0.5634	0.287206
16	0.075371	0.7649	0.22303
17	-0.015842	-0.1608	0.436291
18	0.073473	0.7457	0.228782
19	0.057676	0.5853	0.279798
20	-0.005882	-0.0597	0.476255

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.143191 & 1.4532 & 0.074601 \tabularnewline
2 & -0.058745 & -0.5962 & 0.276176 \tabularnewline
3 & 0.18803 & 1.9083 & 0.029569 \tabularnewline
4 & 0.055458 & 0.5628 & 0.287385 \tabularnewline
5 & 0.23064 & 2.3407 & 0.010586 \tabularnewline
6 & 0.096293 & 0.9773 & 0.165363 \tabularnewline
7 & -0.115337 & -1.1705 & 0.122242 \tabularnewline
8 & 0.066872 & 0.6787 & 0.249432 \tabularnewline
9 & 0.119038 & 1.2081 & 0.114887 \tabularnewline
10 & 0.102074 & 1.0359 & 0.151328 \tabularnewline
11 & -0.033444 & -0.3394 & 0.367492 \tabularnewline
12 & -0.332672 & -3.3762 & 0.000519 \tabularnewline
13 & 0.006006 & 0.061 & 0.475756 \tabularnewline
14 & 0.063297 & 0.6424 & 0.261021 \tabularnewline
15 & -0.05551 & -0.5634 & 0.287206 \tabularnewline
16 & 0.075371 & 0.7649 & 0.22303 \tabularnewline
17 & -0.015842 & -0.1608 & 0.436291 \tabularnewline
18 & 0.073473 & 0.7457 & 0.228782 \tabularnewline
19 & 0.057676 & 0.5853 & 0.279798 \tabularnewline
20 & -0.005882 & -0.0597 & 0.476255 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302818&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]0.143191[/C][C]1.4532[/C][C]0.074601[/C][/ROW]
[ROW][C]2[/C][C]-0.058745[/C][C]-0.5962[/C][C]0.276176[/C][/ROW]
[ROW][C]3[/C][C]0.18803[/C][C]1.9083[/C][C]0.029569[/C][/ROW]
[ROW][C]4[/C][C]0.055458[/C][C]0.5628[/C][C]0.287385[/C][/ROW]
[ROW][C]5[/C][C]0.23064[/C][C]2.3407[/C][C]0.010586[/C][/ROW]
[ROW][C]6[/C][C]0.096293[/C][C]0.9773[/C][C]0.165363[/C][/ROW]
[ROW][C]7[/C][C]-0.115337[/C][C]-1.1705[/C][C]0.122242[/C][/ROW]
[ROW][C]8[/C][C]0.066872[/C][C]0.6787[/C][C]0.249432[/C][/ROW]
[ROW][C]9[/C][C]0.119038[/C][C]1.2081[/C][C]0.114887[/C][/ROW]
[ROW][C]10[/C][C]0.102074[/C][C]1.0359[/C][C]0.151328[/C][/ROW]
[ROW][C]11[/C][C]-0.033444[/C][C]-0.3394[/C][C]0.367492[/C][/ROW]
[ROW][C]12[/C][C]-0.332672[/C][C]-3.3762[/C][C]0.000519[/C][/ROW]
[ROW][C]13[/C][C]0.006006[/C][C]0.061[/C][C]0.475756[/C][/ROW]
[ROW][C]14[/C][C]0.063297[/C][C]0.6424[/C][C]0.261021[/C][/ROW]
[ROW][C]15[/C][C]-0.05551[/C][C]-0.5634[/C][C]0.287206[/C][/ROW]
[ROW][C]16[/C][C]0.075371[/C][C]0.7649[/C][C]0.22303[/C][/ROW]
[ROW][C]17[/C][C]-0.015842[/C][C]-0.1608[/C][C]0.436291[/C][/ROW]
[ROW][C]18[/C][C]0.073473[/C][C]0.7457[/C][C]0.228782[/C][/ROW]
[ROW][C]19[/C][C]0.057676[/C][C]0.5853[/C][C]0.279798[/C][/ROW]
[ROW][C]20[/C][C]-0.005882[/C][C]-0.0597[/C][C]0.476255[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302818&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302818&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	0.143191	1.4532	0.074601
2	-0.058745	-0.5962	0.276176
3	0.18803	1.9083	0.029569
4	0.055458	0.5628	0.287385
5	0.23064	2.3407	0.010586
6	0.096293	0.9773	0.165363
7	-0.115337	-1.1705	0.122242
8	0.066872	0.6787	0.249432
9	0.119038	1.2081	0.114887
10	0.102074	1.0359	0.151328
11	-0.033444	-0.3394	0.367492
12	-0.332672	-3.3762	0.000519
13	0.006006	0.061	0.475756
14	0.063297	0.6424	0.261021
15	-0.05551	-0.5634	0.287206
16	0.075371	0.7649	0.22303
17	-0.015842	-0.1608	0.436291
18	0.073473	0.7457	0.228782
19	0.057676	0.5853	0.279798
20	-0.005882	-0.0597	0.476255

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.143191	1.4532	0.074601
2	-0.080907	-0.8211	0.206737
3	0.21448	2.1767	0.015892
4	-0.015428	-0.1566	0.437943
5	0.277622	2.8176	0.002901
6	-0.030103	-0.3055	0.380295
7	-0.084862	-0.8613	0.195548
8	0.01038	0.1053	0.458152
9	0.066932	0.6793	0.249239
10	0.081832	0.8305	0.204086
11	-0.09754	-0.9899	0.162266
12	-0.330179	-3.3509	0.000563
13	0.064989	0.6596	0.255501
14	-0.054313	-0.5512	0.29134
15	0.07599	0.7712	0.221172
16	0.119426	1.212	0.114134
17	0.129327	1.3125	0.09613
18	0.116487	1.1822	0.119922
19	-0.115197	-1.1691	0.122527
20	0.047396	0.481	0.315762

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.143191 & 1.4532 & 0.074601 \tabularnewline
2 & -0.080907 & -0.8211 & 0.206737 \tabularnewline
3 & 0.21448 & 2.1767 & 0.015892 \tabularnewline
4 & -0.015428 & -0.1566 & 0.437943 \tabularnewline
5 & 0.277622 & 2.8176 & 0.002901 \tabularnewline
6 & -0.030103 & -0.3055 & 0.380295 \tabularnewline
7 & -0.084862 & -0.8613 & 0.195548 \tabularnewline
8 & 0.01038 & 0.1053 & 0.458152 \tabularnewline
9 & 0.066932 & 0.6793 & 0.249239 \tabularnewline
10 & 0.081832 & 0.8305 & 0.204086 \tabularnewline
11 & -0.09754 & -0.9899 & 0.162266 \tabularnewline
12 & -0.330179 & -3.3509 & 0.000563 \tabularnewline
13 & 0.064989 & 0.6596 & 0.255501 \tabularnewline
14 & -0.054313 & -0.5512 & 0.29134 \tabularnewline
15 & 0.07599 & 0.7712 & 0.221172 \tabularnewline
16 & 0.119426 & 1.212 & 0.114134 \tabularnewline
17 & 0.129327 & 1.3125 & 0.09613 \tabularnewline
18 & 0.116487 & 1.1822 & 0.119922 \tabularnewline
19 & -0.115197 & -1.1691 & 0.122527 \tabularnewline
20 & 0.047396 & 0.481 & 0.315762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302818&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]0.143191[/C][C]1.4532[/C][C]0.074601[/C][/ROW]
[ROW][C]2[/C][C]-0.080907[/C][C]-0.8211[/C][C]0.206737[/C][/ROW]
[ROW][C]3[/C][C]0.21448[/C][C]2.1767[/C][C]0.015892[/C][/ROW]
[ROW][C]4[/C][C]-0.015428[/C][C]-0.1566[/C][C]0.437943[/C][/ROW]
[ROW][C]5[/C][C]0.277622[/C][C]2.8176[/C][C]0.002901[/C][/ROW]
[ROW][C]6[/C][C]-0.030103[/C][C]-0.3055[/C][C]0.380295[/C][/ROW]
[ROW][C]7[/C][C]-0.084862[/C][C]-0.8613[/C][C]0.195548[/C][/ROW]
[ROW][C]8[/C][C]0.01038[/C][C]0.1053[/C][C]0.458152[/C][/ROW]
[ROW][C]9[/C][C]0.066932[/C][C]0.6793[/C][C]0.249239[/C][/ROW]
[ROW][C]10[/C][C]0.081832[/C][C]0.8305[/C][C]0.204086[/C][/ROW]
[ROW][C]11[/C][C]-0.09754[/C][C]-0.9899[/C][C]0.162266[/C][/ROW]
[ROW][C]12[/C][C]-0.330179[/C][C]-3.3509[/C][C]0.000563[/C][/ROW]
[ROW][C]13[/C][C]0.064989[/C][C]0.6596[/C][C]0.255501[/C][/ROW]
[ROW][C]14[/C][C]-0.054313[/C][C]-0.5512[/C][C]0.29134[/C][/ROW]
[ROW][C]15[/C][C]0.07599[/C][C]0.7712[/C][C]0.221172[/C][/ROW]
[ROW][C]16[/C][C]0.119426[/C][C]1.212[/C][C]0.114134[/C][/ROW]
[ROW][C]17[/C][C]0.129327[/C][C]1.3125[/C][C]0.09613[/C][/ROW]
[ROW][C]18[/C][C]0.116487[/C][C]1.1822[/C][C]0.119922[/C][/ROW]
[ROW][C]19[/C][C]-0.115197[/C][C]-1.1691[/C][C]0.122527[/C][/ROW]
[ROW][C]20[/C][C]0.047396[/C][C]0.481[/C][C]0.315762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302818&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302818&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	0.143191	1.4532	0.074601
2	-0.080907	-0.8211	0.206737
3	0.21448	2.1767	0.015892
4	-0.015428	-0.1566	0.437943
5	0.277622	2.8176	0.002901
6	-0.030103	-0.3055	0.380295
7	-0.084862	-0.8613	0.195548
8	0.01038	0.1053	0.458152
9	0.066932	0.6793	0.249239
10	0.081832	0.8305	0.204086
11	-0.09754	-0.9899	0.162266
12	-0.330179	-3.3509	0.000563
13	0.064989	0.6596	0.255501
14	-0.054313	-0.5512	0.29134
15	0.07599	0.7712	0.221172
16	0.119426	1.212	0.114134
17	0.129327	1.3125	0.09613
18	0.116487	1.1822	0.119922
19	-0.115197	-1.1691	0.122527
20	0.047396	0.481	0.315762

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

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PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code