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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 15:12:27 +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/19/t1482156931yjarhsqo436xty3.htm/, Retrieved Fri, 01 Nov 2024 03:30:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301362, Retrieved Fri, 01 Nov 2024 03:30:41 +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] [Auto 1 1 ] [2016-12-19 14:12:27] [06fd994a2f2098873ec640c3e39346e5] [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=301362&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=301362&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301362&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	-0.286977	-2.8841	0.002399
2	-0.121064	-1.2167	0.113281
3	-0.111195	-1.1175	0.133216
4	-0.004547	-0.0457	0.481819
5	0.018757	0.1885	0.425427
6	0.058375	0.5867	0.279369
7	-0.027747	-0.2788	0.390465
8	-0.132995	-1.3366	0.092181
9	0.216714	2.1779	0.015869
10	-0.051489	-0.5175	0.302984
11	0.286599	2.8803	0.002426
12	-0.439447	-4.4164	1.3e-05
13	-0.143605	-1.4432	0.076027
14	0.16061	1.6141	0.054812
15	0.118208	1.188	0.118816
16	-0.01211	-0.1217	0.451687
17	0.089052	0.895	0.186469
18	-0.054372	-0.5464	0.292986
19	-0.081644	-0.8205	0.20693
20	0.047104	0.4734	0.318478
21	-0.061887	-0.622	0.267686

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.286977 & -2.8841 & 0.002399 \tabularnewline
2 & -0.121064 & -1.2167 & 0.113281 \tabularnewline
3 & -0.111195 & -1.1175 & 0.133216 \tabularnewline
4 & -0.004547 & -0.0457 & 0.481819 \tabularnewline
5 & 0.018757 & 0.1885 & 0.425427 \tabularnewline
6 & 0.058375 & 0.5867 & 0.279369 \tabularnewline
7 & -0.027747 & -0.2788 & 0.390465 \tabularnewline
8 & -0.132995 & -1.3366 & 0.092181 \tabularnewline
9 & 0.216714 & 2.1779 & 0.015869 \tabularnewline
10 & -0.051489 & -0.5175 & 0.302984 \tabularnewline
11 & 0.286599 & 2.8803 & 0.002426 \tabularnewline
12 & -0.439447 & -4.4164 & 1.3e-05 \tabularnewline
13 & -0.143605 & -1.4432 & 0.076027 \tabularnewline
14 & 0.16061 & 1.6141 & 0.054812 \tabularnewline
15 & 0.118208 & 1.188 & 0.118816 \tabularnewline
16 & -0.01211 & -0.1217 & 0.451687 \tabularnewline
17 & 0.089052 & 0.895 & 0.186469 \tabularnewline
18 & -0.054372 & -0.5464 & 0.292986 \tabularnewline
19 & -0.081644 & -0.8205 & 0.20693 \tabularnewline
20 & 0.047104 & 0.4734 & 0.318478 \tabularnewline
21 & -0.061887 & -0.622 & 0.267686 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301362&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]-0.286977[/C][C]-2.8841[/C][C]0.002399[/C][/ROW]
[ROW][C]2[/C][C]-0.121064[/C][C]-1.2167[/C][C]0.113281[/C][/ROW]
[ROW][C]3[/C][C]-0.111195[/C][C]-1.1175[/C][C]0.133216[/C][/ROW]
[ROW][C]4[/C][C]-0.004547[/C][C]-0.0457[/C][C]0.481819[/C][/ROW]
[ROW][C]5[/C][C]0.018757[/C][C]0.1885[/C][C]0.425427[/C][/ROW]
[ROW][C]6[/C][C]0.058375[/C][C]0.5867[/C][C]0.279369[/C][/ROW]
[ROW][C]7[/C][C]-0.027747[/C][C]-0.2788[/C][C]0.390465[/C][/ROW]
[ROW][C]8[/C][C]-0.132995[/C][C]-1.3366[/C][C]0.092181[/C][/ROW]
[ROW][C]9[/C][C]0.216714[/C][C]2.1779[/C][C]0.015869[/C][/ROW]
[ROW][C]10[/C][C]-0.051489[/C][C]-0.5175[/C][C]0.302984[/C][/ROW]
[ROW][C]11[/C][C]0.286599[/C][C]2.8803[/C][C]0.002426[/C][/ROW]
[ROW][C]12[/C][C]-0.439447[/C][C]-4.4164[/C][C]1.3e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.143605[/C][C]-1.4432[/C][C]0.076027[/C][/ROW]
[ROW][C]14[/C][C]0.16061[/C][C]1.6141[/C][C]0.054812[/C][/ROW]
[ROW][C]15[/C][C]0.118208[/C][C]1.188[/C][C]0.118816[/C][/ROW]
[ROW][C]16[/C][C]-0.01211[/C][C]-0.1217[/C][C]0.451687[/C][/ROW]
[ROW][C]17[/C][C]0.089052[/C][C]0.895[/C][C]0.186469[/C][/ROW]
[ROW][C]18[/C][C]-0.054372[/C][C]-0.5464[/C][C]0.292986[/C][/ROW]
[ROW][C]19[/C][C]-0.081644[/C][C]-0.8205[/C][C]0.20693[/C][/ROW]
[ROW][C]20[/C][C]0.047104[/C][C]0.4734[/C][C]0.318478[/C][/ROW]
[ROW][C]21[/C][C]-0.061887[/C][C]-0.622[/C][C]0.267686[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301362&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301362&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	-0.286977	-2.8841	0.002399
2	-0.121064	-1.2167	0.113281
3	-0.111195	-1.1175	0.133216
4	-0.004547	-0.0457	0.481819
5	0.018757	0.1885	0.425427
6	0.058375	0.5867	0.279369
7	-0.027747	-0.2788	0.390465
8	-0.132995	-1.3366	0.092181
9	0.216714	2.1779	0.015869
10	-0.051489	-0.5175	0.302984
11	0.286599	2.8803	0.002426
12	-0.439447	-4.4164	1.3e-05
13	-0.143605	-1.4432	0.076027
14	0.16061	1.6141	0.054812
15	0.118208	1.188	0.118816
16	-0.01211	-0.1217	0.451687
17	0.089052	0.895	0.186469
18	-0.054372	-0.5464	0.292986
19	-0.081644	-0.8205	0.20693
20	0.047104	0.4734	0.318478
21	-0.061887	-0.622	0.267686

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.286977	-2.8841	0.002399
2	-0.221676	-2.2278	0.014056
3	-0.248988	-2.5023	0.006972
4	-0.193691	-1.9466	0.027182
5	-0.151775	-1.5253	0.065152
6	-0.068162	-0.685	0.24745
7	-0.087329	-0.8776	0.19111
8	-0.23294	-2.341	0.010598
9	0.073972	0.7434	0.22948
10	-0.015981	-0.1606	0.436363
11	0.404835	4.0685	4.7e-05
12	-0.191019	-1.9197	0.028858
13	-0.311758	-3.1331	0.001132
14	-0.104314	-1.0483	0.148491
15	-0.065404	-0.6573	0.256241
16	-0.099063	-0.9956	0.16092
17	0.107177	1.0771	0.141998
18	0.061967	0.6228	0.267421
19	0.083113	0.8353	0.202767
20	-0.191015	-1.9197	0.02886
21	-0.062822	-0.6314	0.264618

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.286977 & -2.8841 & 0.002399 \tabularnewline
2 & -0.221676 & -2.2278 & 0.014056 \tabularnewline
3 & -0.248988 & -2.5023 & 0.006972 \tabularnewline
4 & -0.193691 & -1.9466 & 0.027182 \tabularnewline
5 & -0.151775 & -1.5253 & 0.065152 \tabularnewline
6 & -0.068162 & -0.685 & 0.24745 \tabularnewline
7 & -0.087329 & -0.8776 & 0.19111 \tabularnewline
8 & -0.23294 & -2.341 & 0.010598 \tabularnewline
9 & 0.073972 & 0.7434 & 0.22948 \tabularnewline
10 & -0.015981 & -0.1606 & 0.436363 \tabularnewline
11 & 0.404835 & 4.0685 & 4.7e-05 \tabularnewline
12 & -0.191019 & -1.9197 & 0.028858 \tabularnewline
13 & -0.311758 & -3.1331 & 0.001132 \tabularnewline
14 & -0.104314 & -1.0483 & 0.148491 \tabularnewline
15 & -0.065404 & -0.6573 & 0.256241 \tabularnewline
16 & -0.099063 & -0.9956 & 0.16092 \tabularnewline
17 & 0.107177 & 1.0771 & 0.141998 \tabularnewline
18 & 0.061967 & 0.6228 & 0.267421 \tabularnewline
19 & 0.083113 & 0.8353 & 0.202767 \tabularnewline
20 & -0.191015 & -1.9197 & 0.02886 \tabularnewline
21 & -0.062822 & -0.6314 & 0.264618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301362&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]-0.286977[/C][C]-2.8841[/C][C]0.002399[/C][/ROW]
[ROW][C]2[/C][C]-0.221676[/C][C]-2.2278[/C][C]0.014056[/C][/ROW]
[ROW][C]3[/C][C]-0.248988[/C][C]-2.5023[/C][C]0.006972[/C][/ROW]
[ROW][C]4[/C][C]-0.193691[/C][C]-1.9466[/C][C]0.027182[/C][/ROW]
[ROW][C]5[/C][C]-0.151775[/C][C]-1.5253[/C][C]0.065152[/C][/ROW]
[ROW][C]6[/C][C]-0.068162[/C][C]-0.685[/C][C]0.24745[/C][/ROW]
[ROW][C]7[/C][C]-0.087329[/C][C]-0.8776[/C][C]0.19111[/C][/ROW]
[ROW][C]8[/C][C]-0.23294[/C][C]-2.341[/C][C]0.010598[/C][/ROW]
[ROW][C]9[/C][C]0.073972[/C][C]0.7434[/C][C]0.22948[/C][/ROW]
[ROW][C]10[/C][C]-0.015981[/C][C]-0.1606[/C][C]0.436363[/C][/ROW]
[ROW][C]11[/C][C]0.404835[/C][C]4.0685[/C][C]4.7e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.191019[/C][C]-1.9197[/C][C]0.028858[/C][/ROW]
[ROW][C]13[/C][C]-0.311758[/C][C]-3.1331[/C][C]0.001132[/C][/ROW]
[ROW][C]14[/C][C]-0.104314[/C][C]-1.0483[/C][C]0.148491[/C][/ROW]
[ROW][C]15[/C][C]-0.065404[/C][C]-0.6573[/C][C]0.256241[/C][/ROW]
[ROW][C]16[/C][C]-0.099063[/C][C]-0.9956[/C][C]0.16092[/C][/ROW]
[ROW][C]17[/C][C]0.107177[/C][C]1.0771[/C][C]0.141998[/C][/ROW]
[ROW][C]18[/C][C]0.061967[/C][C]0.6228[/C][C]0.267421[/C][/ROW]
[ROW][C]19[/C][C]0.083113[/C][C]0.8353[/C][C]0.202767[/C][/ROW]
[ROW][C]20[/C][C]-0.191015[/C][C]-1.9197[/C][C]0.02886[/C][/ROW]
[ROW][C]21[/C][C]-0.062822[/C][C]-0.6314[/C][C]0.264618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301362&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301362&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	-0.286977	-2.8841	0.002399
2	-0.221676	-2.2278	0.014056
3	-0.248988	-2.5023	0.006972
4	-0.193691	-1.9466	0.027182
5	-0.151775	-1.5253	0.065152
6	-0.068162	-0.685	0.24745
7	-0.087329	-0.8776	0.19111
8	-0.23294	-2.341	0.010598
9	0.073972	0.7434	0.22948
10	-0.015981	-0.1606	0.436363
11	0.404835	4.0685	4.7e-05
12	-0.191019	-1.9197	0.028858
13	-0.311758	-3.1331	0.001132
14	-0.104314	-1.0483	0.148491
15	-0.065404	-0.6573	0.256241
16	-0.099063	-0.9956	0.16092
17	0.107177	1.0771	0.141998
18	0.061967	0.6228	0.267421
19	0.083113	0.8353	0.202767
20	-0.191015	-1.9197	0.02886
21	-0.062822	-0.6314	0.264618

Figure 1

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Figure 2

PNG link

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Figure 3

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Parameters (Session):

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 2 ; 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