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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 18 May 2017 13:23:25 +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/2017/May/18/t1495110250gp579zl2ra0drd3.htm/, Retrieved Fri, 17 May 2024 04:29:30 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 17 May 2024 04:29:30 +0200

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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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.40377	3.4022	0.000551
2	0.123478	1.0404	0.150832
3	-0.010648	-0.0897	0.464381
4	0.126266	1.0639	0.145482
5	0.174446	1.4699	0.073002
6	0.085758	0.7226	0.236148
7	0.040138	0.3382	0.368102
8	-0.070645	-0.5953	0.276779
9	0.188428	1.5877	0.058397
10	0.207519	1.7486	0.042342
11	0.004621	0.0389	0.484523
12	-0.13517	-1.139	0.129273
13	-0.200291	-1.6877	0.047931
14	-0.035899	-0.3025	0.381582
15	-0.084353	-0.7108	0.239777
16	-0.020573	-0.1734	0.431434
17	-0.129282	-1.0893	0.139842
18	-0.090674	-0.764	0.223689

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.40377 & 3.4022 & 0.000551 \tabularnewline
2 & 0.123478 & 1.0404 & 0.150832 \tabularnewline
3 & -0.010648 & -0.0897 & 0.464381 \tabularnewline
4 & 0.126266 & 1.0639 & 0.145482 \tabularnewline
5 & 0.174446 & 1.4699 & 0.073002 \tabularnewline
6 & 0.085758 & 0.7226 & 0.236148 \tabularnewline
7 & 0.040138 & 0.3382 & 0.368102 \tabularnewline
8 & -0.070645 & -0.5953 & 0.276779 \tabularnewline
9 & 0.188428 & 1.5877 & 0.058397 \tabularnewline
10 & 0.207519 & 1.7486 & 0.042342 \tabularnewline
11 & 0.004621 & 0.0389 & 0.484523 \tabularnewline
12 & -0.13517 & -1.139 & 0.129273 \tabularnewline
13 & -0.200291 & -1.6877 & 0.047931 \tabularnewline
14 & -0.035899 & -0.3025 & 0.381582 \tabularnewline
15 & -0.084353 & -0.7108 & 0.239777 \tabularnewline
16 & -0.020573 & -0.1734 & 0.431434 \tabularnewline
17 & -0.129282 & -1.0893 & 0.139842 \tabularnewline
18 & -0.090674 & -0.764 & 0.223689 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.40377[/C][C]3.4022[/C][C]0.000551[/C][/ROW]
[ROW][C]2[/C][C]0.123478[/C][C]1.0404[/C][C]0.150832[/C][/ROW]
[ROW][C]3[/C][C]-0.010648[/C][C]-0.0897[/C][C]0.464381[/C][/ROW]
[ROW][C]4[/C][C]0.126266[/C][C]1.0639[/C][C]0.145482[/C][/ROW]
[ROW][C]5[/C][C]0.174446[/C][C]1.4699[/C][C]0.073002[/C][/ROW]
[ROW][C]6[/C][C]0.085758[/C][C]0.7226[/C][C]0.236148[/C][/ROW]
[ROW][C]7[/C][C]0.040138[/C][C]0.3382[/C][C]0.368102[/C][/ROW]
[ROW][C]8[/C][C]-0.070645[/C][C]-0.5953[/C][C]0.276779[/C][/ROW]
[ROW][C]9[/C][C]0.188428[/C][C]1.5877[/C][C]0.058397[/C][/ROW]
[ROW][C]10[/C][C]0.207519[/C][C]1.7486[/C][C]0.042342[/C][/ROW]
[ROW][C]11[/C][C]0.004621[/C][C]0.0389[/C][C]0.484523[/C][/ROW]
[ROW][C]12[/C][C]-0.13517[/C][C]-1.139[/C][C]0.129273[/C][/ROW]
[ROW][C]13[/C][C]-0.200291[/C][C]-1.6877[/C][C]0.047931[/C][/ROW]
[ROW][C]14[/C][C]-0.035899[/C][C]-0.3025[/C][C]0.381582[/C][/ROW]
[ROW][C]15[/C][C]-0.084353[/C][C]-0.7108[/C][C]0.239777[/C][/ROW]
[ROW][C]16[/C][C]-0.020573[/C][C]-0.1734[/C][C]0.431434[/C][/ROW]
[ROW][C]17[/C][C]-0.129282[/C][C]-1.0893[/C][C]0.139842[/C][/ROW]
[ROW][C]18[/C][C]-0.090674[/C][C]-0.764[/C][C]0.223689[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.40377	3.4022	0.000551
2	0.123478	1.0404	0.150832
3	-0.010648	-0.0897	0.464381
4	0.126266	1.0639	0.145482
5	0.174446	1.4699	0.073002
6	0.085758	0.7226	0.236148
7	0.040138	0.3382	0.368102
8	-0.070645	-0.5953	0.276779
9	0.188428	1.5877	0.058397
10	0.207519	1.7486	0.042342
11	0.004621	0.0389	0.484523
12	-0.13517	-1.139	0.129273
13	-0.200291	-1.6877	0.047931
14	-0.035899	-0.3025	0.381582
15	-0.084353	-0.7108	0.239777
16	-0.020573	-0.1734	0.431434
17	-0.129282	-1.0893	0.139842
18	-0.090674	-0.764	0.223689

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.40377	3.4022	0.000551
2	-0.047257	-0.3982	0.345841
3	-0.052424	-0.4417	0.330011
4	0.186127	1.5683	0.060625
5	0.075751	0.6383	0.26267
6	-0.045549	-0.3838	0.351135
7	0.037801	0.3185	0.375513
8	-0.111763	-0.9417	0.174762
9	0.284173	2.3945	0.009643
10	0.031919	0.269	0.394374
11	-0.213764	-1.8012	0.037958
12	-0.021075	-0.1776	0.42978
13	-0.145099	-1.2226	0.112757
14	0.026733	0.2253	0.411214
15	-0.108469	-0.914	0.181912
16	0.02215	0.1866	0.426236
17	-0.018719	-0.1577	0.437559
18	-0.012742	-0.1074	0.457402

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.40377 & 3.4022 & 0.000551 \tabularnewline
2 & -0.047257 & -0.3982 & 0.345841 \tabularnewline
3 & -0.052424 & -0.4417 & 0.330011 \tabularnewline
4 & 0.186127 & 1.5683 & 0.060625 \tabularnewline
5 & 0.075751 & 0.6383 & 0.26267 \tabularnewline
6 & -0.045549 & -0.3838 & 0.351135 \tabularnewline
7 & 0.037801 & 0.3185 & 0.375513 \tabularnewline
8 & -0.111763 & -0.9417 & 0.174762 \tabularnewline
9 & 0.284173 & 2.3945 & 0.009643 \tabularnewline
10 & 0.031919 & 0.269 & 0.394374 \tabularnewline
11 & -0.213764 & -1.8012 & 0.037958 \tabularnewline
12 & -0.021075 & -0.1776 & 0.42978 \tabularnewline
13 & -0.145099 & -1.2226 & 0.112757 \tabularnewline
14 & 0.026733 & 0.2253 & 0.411214 \tabularnewline
15 & -0.108469 & -0.914 & 0.181912 \tabularnewline
16 & 0.02215 & 0.1866 & 0.426236 \tabularnewline
17 & -0.018719 & -0.1577 & 0.437559 \tabularnewline
18 & -0.012742 & -0.1074 & 0.457402 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.40377[/C][C]3.4022[/C][C]0.000551[/C][/ROW]
[ROW][C]2[/C][C]-0.047257[/C][C]-0.3982[/C][C]0.345841[/C][/ROW]
[ROW][C]3[/C][C]-0.052424[/C][C]-0.4417[/C][C]0.330011[/C][/ROW]
[ROW][C]4[/C][C]0.186127[/C][C]1.5683[/C][C]0.060625[/C][/ROW]
[ROW][C]5[/C][C]0.075751[/C][C]0.6383[/C][C]0.26267[/C][/ROW]
[ROW][C]6[/C][C]-0.045549[/C][C]-0.3838[/C][C]0.351135[/C][/ROW]
[ROW][C]7[/C][C]0.037801[/C][C]0.3185[/C][C]0.375513[/C][/ROW]
[ROW][C]8[/C][C]-0.111763[/C][C]-0.9417[/C][C]0.174762[/C][/ROW]
[ROW][C]9[/C][C]0.284173[/C][C]2.3945[/C][C]0.009643[/C][/ROW]
[ROW][C]10[/C][C]0.031919[/C][C]0.269[/C][C]0.394374[/C][/ROW]
[ROW][C]11[/C][C]-0.213764[/C][C]-1.8012[/C][C]0.037958[/C][/ROW]
[ROW][C]12[/C][C]-0.021075[/C][C]-0.1776[/C][C]0.42978[/C][/ROW]
[ROW][C]13[/C][C]-0.145099[/C][C]-1.2226[/C][C]0.112757[/C][/ROW]
[ROW][C]14[/C][C]0.026733[/C][C]0.2253[/C][C]0.411214[/C][/ROW]
[ROW][C]15[/C][C]-0.108469[/C][C]-0.914[/C][C]0.181912[/C][/ROW]
[ROW][C]16[/C][C]0.02215[/C][C]0.1866[/C][C]0.426236[/C][/ROW]
[ROW][C]17[/C][C]-0.018719[/C][C]-0.1577[/C][C]0.437559[/C][/ROW]
[ROW][C]18[/C][C]-0.012742[/C][C]-0.1074[/C][C]0.457402[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	0.40377	3.4022	0.000551
2	-0.047257	-0.3982	0.345841
3	-0.052424	-0.4417	0.330011
4	0.186127	1.5683	0.060625
5	0.075751	0.6383	0.26267
6	-0.045549	-0.3838	0.351135
7	0.037801	0.3185	0.375513
8	-0.111763	-0.9417	0.174762
9	0.284173	2.3945	0.009643
10	0.031919	0.269	0.394374
11	-0.213764	-1.8012	0.037958
12	-0.021075	-0.1776	0.42978
13	-0.145099	-1.2226	0.112757
14	0.026733	0.2253	0.411214
15	-0.108469	-0.914	0.181912
16	0.02215	0.1866	0.426236
17	-0.018719	-0.1577	0.437559
18	-0.012742	-0.1074	0.457402

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 = 24 ; par2 = grey ; par3 = FALSE ; par4 = Unknown ;

Parameters (R input):

par1 = Default ; par2 = 1 ; 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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code