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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Dec 2016 22:05:51 +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/18/t1482095188epm50i3t9t06pd8.htm/, Retrieved Wed, 08 May 2024 04:05:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301244, Retrieved Wed, 08 May 2024 04:05:12 +0000

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-     [(Partial) Autocorrelation Function] [autocorrelation N247] [2016-12-16 08:48:05] [5ad8e5538a25411d3c3b0ec85050bd51]
- R P   [(Partial) Autocorrelation Function] [Autocorrelation N...] [2016-12-16 13:04:03] [d1d385d9b7e195437bdc484ddbefdda4]
- R         [(Partial) Autocorrelation Function] [1x d] [2016-12-18 21:05:51] [b95f76f605693b3a3343a287ab24f42a] [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=301244&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=301244&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301244&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	-0.443182	-4.7111	4e-06
2	-0.16021	-1.7031	0.045654
3	0.098138	1.0432	0.149536
4	0.028864	0.3068	0.37977
5	-0.020628	-0.2193	0.413415
6	-0.035844	-0.381	0.35195
7	0.063065	0.6704	0.251989
8	-0.036799	-0.3912	0.3482
9	0.12892	1.3704	0.086633
10	-0.195382	-2.0769	0.020037
11	-0.230177	-2.4468	0.007977
12	0.641429	6.8185	0
13	-0.277196	-2.9466	0.001951
14	-0.146621	-1.5586	0.060943
15	0.120698	1.283	0.101052
16	-0.066957	-0.7118	0.239039
17	0.026594	0.2827	0.388962
18	0.001934	0.0206	0.491815
19	0.028803	0.3062	0.380015
20	-0.024455	-0.26	0.397682

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.443182 & -4.7111 & 4e-06 \tabularnewline
2 & -0.16021 & -1.7031 & 0.045654 \tabularnewline
3 & 0.098138 & 1.0432 & 0.149536 \tabularnewline
4 & 0.028864 & 0.3068 & 0.37977 \tabularnewline
5 & -0.020628 & -0.2193 & 0.413415 \tabularnewline
6 & -0.035844 & -0.381 & 0.35195 \tabularnewline
7 & 0.063065 & 0.6704 & 0.251989 \tabularnewline
8 & -0.036799 & -0.3912 & 0.3482 \tabularnewline
9 & 0.12892 & 1.3704 & 0.086633 \tabularnewline
10 & -0.195382 & -2.0769 & 0.020037 \tabularnewline
11 & -0.230177 & -2.4468 & 0.007977 \tabularnewline
12 & 0.641429 & 6.8185 & 0 \tabularnewline
13 & -0.277196 & -2.9466 & 0.001951 \tabularnewline
14 & -0.146621 & -1.5586 & 0.060943 \tabularnewline
15 & 0.120698 & 1.283 & 0.101052 \tabularnewline
16 & -0.066957 & -0.7118 & 0.239039 \tabularnewline
17 & 0.026594 & 0.2827 & 0.388962 \tabularnewline
18 & 0.001934 & 0.0206 & 0.491815 \tabularnewline
19 & 0.028803 & 0.3062 & 0.380015 \tabularnewline
20 & -0.024455 & -0.26 & 0.397682 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301244&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]-0.443182[/C][C]-4.7111[/C][C]4e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.16021[/C][C]-1.7031[/C][C]0.045654[/C][/ROW]
[ROW][C]3[/C][C]0.098138[/C][C]1.0432[/C][C]0.149536[/C][/ROW]
[ROW][C]4[/C][C]0.028864[/C][C]0.3068[/C][C]0.37977[/C][/ROW]
[ROW][C]5[/C][C]-0.020628[/C][C]-0.2193[/C][C]0.413415[/C][/ROW]
[ROW][C]6[/C][C]-0.035844[/C][C]-0.381[/C][C]0.35195[/C][/ROW]
[ROW][C]7[/C][C]0.063065[/C][C]0.6704[/C][C]0.251989[/C][/ROW]
[ROW][C]8[/C][C]-0.036799[/C][C]-0.3912[/C][C]0.3482[/C][/ROW]
[ROW][C]9[/C][C]0.12892[/C][C]1.3704[/C][C]0.086633[/C][/ROW]
[ROW][C]10[/C][C]-0.195382[/C][C]-2.0769[/C][C]0.020037[/C][/ROW]
[ROW][C]11[/C][C]-0.230177[/C][C]-2.4468[/C][C]0.007977[/C][/ROW]
[ROW][C]12[/C][C]0.641429[/C][C]6.8185[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.277196[/C][C]-2.9466[/C][C]0.001951[/C][/ROW]
[ROW][C]14[/C][C]-0.146621[/C][C]-1.5586[/C][C]0.060943[/C][/ROW]
[ROW][C]15[/C][C]0.120698[/C][C]1.283[/C][C]0.101052[/C][/ROW]
[ROW][C]16[/C][C]-0.066957[/C][C]-0.7118[/C][C]0.239039[/C][/ROW]
[ROW][C]17[/C][C]0.026594[/C][C]0.2827[/C][C]0.388962[/C][/ROW]
[ROW][C]18[/C][C]0.001934[/C][C]0.0206[/C][C]0.491815[/C][/ROW]
[ROW][C]19[/C][C]0.028803[/C][C]0.3062[/C][C]0.380015[/C][/ROW]
[ROW][C]20[/C][C]-0.024455[/C][C]-0.26[/C][C]0.397682[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301244&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301244&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	-0.443182	-4.7111	4e-06
2	-0.16021	-1.7031	0.045654
3	0.098138	1.0432	0.149536
4	0.028864	0.3068	0.37977
5	-0.020628	-0.2193	0.413415
6	-0.035844	-0.381	0.35195
7	0.063065	0.6704	0.251989
8	-0.036799	-0.3912	0.3482
9	0.12892	1.3704	0.086633
10	-0.195382	-2.0769	0.020037
11	-0.230177	-2.4468	0.007977
12	0.641429	6.8185	0
13	-0.277196	-2.9466	0.001951
14	-0.146621	-1.5586	0.060943
15	0.120698	1.283	0.101052
16	-0.066957	-0.7118	0.239039
17	0.026594	0.2827	0.388962
18	0.001934	0.0206	0.491815
19	0.028803	0.3062	0.380015
20	-0.024455	-0.26	0.397682

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.443182	-4.7111	4e-06
2	-0.443784	-4.7175	3e-06
3	-0.311548	-3.3118	0.000623
4	-0.233196	-2.4789	0.007328
5	-0.182521	-1.9402	0.027422
6	-0.205242	-2.1817	0.015599
7	-0.120806	-1.2842	0.100852
8	-0.135045	-1.4356	0.076946
9	0.148561	1.5792	0.05854
10	-0.010891	-0.1158	0.454019
11	-0.575554	-6.1182	0
12	0.136733	1.4535	0.07443
13	0.163347	1.7364	0.042609
14	0.130354	1.3857	0.084287
15	0.243797	2.5916	0.005407
16	-0.081338	-0.8646	0.194535
17	-0.053275	-0.5663	0.286148
18	0.042994	0.457	0.324264
19	-0.043084	-0.458	0.32392
20	0.040894	0.4347	0.332302

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.443182 & -4.7111 & 4e-06 \tabularnewline
2 & -0.443784 & -4.7175 & 3e-06 \tabularnewline
3 & -0.311548 & -3.3118 & 0.000623 \tabularnewline
4 & -0.233196 & -2.4789 & 0.007328 \tabularnewline
5 & -0.182521 & -1.9402 & 0.027422 \tabularnewline
6 & -0.205242 & -2.1817 & 0.015599 \tabularnewline
7 & -0.120806 & -1.2842 & 0.100852 \tabularnewline
8 & -0.135045 & -1.4356 & 0.076946 \tabularnewline
9 & 0.148561 & 1.5792 & 0.05854 \tabularnewline
10 & -0.010891 & -0.1158 & 0.454019 \tabularnewline
11 & -0.575554 & -6.1182 & 0 \tabularnewline
12 & 0.136733 & 1.4535 & 0.07443 \tabularnewline
13 & 0.163347 & 1.7364 & 0.042609 \tabularnewline
14 & 0.130354 & 1.3857 & 0.084287 \tabularnewline
15 & 0.243797 & 2.5916 & 0.005407 \tabularnewline
16 & -0.081338 & -0.8646 & 0.194535 \tabularnewline
17 & -0.053275 & -0.5663 & 0.286148 \tabularnewline
18 & 0.042994 & 0.457 & 0.324264 \tabularnewline
19 & -0.043084 & -0.458 & 0.32392 \tabularnewline
20 & 0.040894 & 0.4347 & 0.332302 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301244&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]-0.443182[/C][C]-4.7111[/C][C]4e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.443784[/C][C]-4.7175[/C][C]3e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.311548[/C][C]-3.3118[/C][C]0.000623[/C][/ROW]
[ROW][C]4[/C][C]-0.233196[/C][C]-2.4789[/C][C]0.007328[/C][/ROW]
[ROW][C]5[/C][C]-0.182521[/C][C]-1.9402[/C][C]0.027422[/C][/ROW]
[ROW][C]6[/C][C]-0.205242[/C][C]-2.1817[/C][C]0.015599[/C][/ROW]
[ROW][C]7[/C][C]-0.120806[/C][C]-1.2842[/C][C]0.100852[/C][/ROW]
[ROW][C]8[/C][C]-0.135045[/C][C]-1.4356[/C][C]0.076946[/C][/ROW]
[ROW][C]9[/C][C]0.148561[/C][C]1.5792[/C][C]0.05854[/C][/ROW]
[ROW][C]10[/C][C]-0.010891[/C][C]-0.1158[/C][C]0.454019[/C][/ROW]
[ROW][C]11[/C][C]-0.575554[/C][C]-6.1182[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.136733[/C][C]1.4535[/C][C]0.07443[/C][/ROW]
[ROW][C]13[/C][C]0.163347[/C][C]1.7364[/C][C]0.042609[/C][/ROW]
[ROW][C]14[/C][C]0.130354[/C][C]1.3857[/C][C]0.084287[/C][/ROW]
[ROW][C]15[/C][C]0.243797[/C][C]2.5916[/C][C]0.005407[/C][/ROW]
[ROW][C]16[/C][C]-0.081338[/C][C]-0.8646[/C][C]0.194535[/C][/ROW]
[ROW][C]17[/C][C]-0.053275[/C][C]-0.5663[/C][C]0.286148[/C][/ROW]
[ROW][C]18[/C][C]0.042994[/C][C]0.457[/C][C]0.324264[/C][/ROW]
[ROW][C]19[/C][C]-0.043084[/C][C]-0.458[/C][C]0.32392[/C][/ROW]
[ROW][C]20[/C][C]0.040894[/C][C]0.4347[/C][C]0.332302[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301244&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301244&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	-0.443182	-4.7111	4e-06
2	-0.443784	-4.7175	3e-06
3	-0.311548	-3.3118	0.000623
4	-0.233196	-2.4789	0.007328
5	-0.182521	-1.9402	0.027422
6	-0.205242	-2.1817	0.015599
7	-0.120806	-1.2842	0.100852
8	-0.135045	-1.4356	0.076946
9	0.148561	1.5792	0.05854
10	-0.010891	-0.1158	0.454019
11	-0.575554	-6.1182	0
12	0.136733	1.4535	0.07443
13	0.163347	1.7364	0.042609
14	0.130354	1.3857	0.084287
15	0.243797	2.5916	0.005407
16	-0.081338	-0.8646	0.194535
17	-0.053275	-0.5663	0.286148
18	0.042994	0.457	0.324264
19	-0.043084	-0.458	0.32392
20	0.040894	0.4347	0.332302

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = -0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code