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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 16 Oct 2014 16:37:29 +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/2014/Oct/16/t1413473876rm045rij67vmjuj.htm/, Retrieved Mon, 13 May 2024 09:29:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=242492, Retrieved Mon, 13 May 2024 09:29:09 +0000

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-       [(Partial) Autocorrelation Function] [] [2014-10-16 15:37:29] [5d8373a1f2ebce02db7a575ae6fdba0f] [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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=242492&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=242492&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=242492&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.085004	0.7163	0.238092
2	0.125844	1.0604	0.146283
3	0.164114	1.3829	0.085522
4	-0.173939	-1.4656	0.073581
5	-0.041476	-0.3495	0.36388
6	-0.11216	-0.9451	0.173913
7	-0.219855	-1.8525	0.034053
8	-0.036299	-0.3059	0.380304
9	0.109051	0.9189	0.180634
10	0.006817	0.0574	0.477179
11	0.006074	0.0512	0.479664
12	0.042255	0.356	0.361431
13	0.018323	0.1544	0.43887
14	-0.003981	-0.0335	0.486667
15	0.062836	0.5295	0.299066
16	-0.032888	-0.2771	0.391248
17	-0.029617	-0.2496	0.401826
18	0.029987	0.2527	0.400623

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.085004 & 0.7163 & 0.238092 \tabularnewline
2 & 0.125844 & 1.0604 & 0.146283 \tabularnewline
3 & 0.164114 & 1.3829 & 0.085522 \tabularnewline
4 & -0.173939 & -1.4656 & 0.073581 \tabularnewline
5 & -0.041476 & -0.3495 & 0.36388 \tabularnewline
6 & -0.11216 & -0.9451 & 0.173913 \tabularnewline
7 & -0.219855 & -1.8525 & 0.034053 \tabularnewline
8 & -0.036299 & -0.3059 & 0.380304 \tabularnewline
9 & 0.109051 & 0.9189 & 0.180634 \tabularnewline
10 & 0.006817 & 0.0574 & 0.477179 \tabularnewline
11 & 0.006074 & 0.0512 & 0.479664 \tabularnewline
12 & 0.042255 & 0.356 & 0.361431 \tabularnewline
13 & 0.018323 & 0.1544 & 0.43887 \tabularnewline
14 & -0.003981 & -0.0335 & 0.486667 \tabularnewline
15 & 0.062836 & 0.5295 & 0.299066 \tabularnewline
16 & -0.032888 & -0.2771 & 0.391248 \tabularnewline
17 & -0.029617 & -0.2496 & 0.401826 \tabularnewline
18 & 0.029987 & 0.2527 & 0.400623 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=242492&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]0.085004[/C][C]0.7163[/C][C]0.238092[/C][/ROW]
[ROW][C]2[/C][C]0.125844[/C][C]1.0604[/C][C]0.146283[/C][/ROW]
[ROW][C]3[/C][C]0.164114[/C][C]1.3829[/C][C]0.085522[/C][/ROW]
[ROW][C]4[/C][C]-0.173939[/C][C]-1.4656[/C][C]0.073581[/C][/ROW]
[ROW][C]5[/C][C]-0.041476[/C][C]-0.3495[/C][C]0.36388[/C][/ROW]
[ROW][C]6[/C][C]-0.11216[/C][C]-0.9451[/C][C]0.173913[/C][/ROW]
[ROW][C]7[/C][C]-0.219855[/C][C]-1.8525[/C][C]0.034053[/C][/ROW]
[ROW][C]8[/C][C]-0.036299[/C][C]-0.3059[/C][C]0.380304[/C][/ROW]
[ROW][C]9[/C][C]0.109051[/C][C]0.9189[/C][C]0.180634[/C][/ROW]
[ROW][C]10[/C][C]0.006817[/C][C]0.0574[/C][C]0.477179[/C][/ROW]
[ROW][C]11[/C][C]0.006074[/C][C]0.0512[/C][C]0.479664[/C][/ROW]
[ROW][C]12[/C][C]0.042255[/C][C]0.356[/C][C]0.361431[/C][/ROW]
[ROW][C]13[/C][C]0.018323[/C][C]0.1544[/C][C]0.43887[/C][/ROW]
[ROW][C]14[/C][C]-0.003981[/C][C]-0.0335[/C][C]0.486667[/C][/ROW]
[ROW][C]15[/C][C]0.062836[/C][C]0.5295[/C][C]0.299066[/C][/ROW]
[ROW][C]16[/C][C]-0.032888[/C][C]-0.2771[/C][C]0.391248[/C][/ROW]
[ROW][C]17[/C][C]-0.029617[/C][C]-0.2496[/C][C]0.401826[/C][/ROW]
[ROW][C]18[/C][C]0.029987[/C][C]0.2527[/C][C]0.400623[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=242492&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=242492&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	0.085004	0.7163	0.238092
2	0.125844	1.0604	0.146283
3	0.164114	1.3829	0.085522
4	-0.173939	-1.4656	0.073581
5	-0.041476	-0.3495	0.36388
6	-0.11216	-0.9451	0.173913
7	-0.219855	-1.8525	0.034053
8	-0.036299	-0.3059	0.380304
9	0.109051	0.9189	0.180634
10	0.006817	0.0574	0.477179
11	0.006074	0.0512	0.479664
12	0.042255	0.356	0.361431
13	0.018323	0.1544	0.43887
14	-0.003981	-0.0335	0.486667
15	0.062836	0.5295	0.299066
16	-0.032888	-0.2771	0.391248
17	-0.029617	-0.2496	0.401826
18	0.029987	0.2527	0.400623

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.085004	0.7163	0.238092
2	0.119482	1.0068	0.158732
3	0.1477	1.2445	0.108697
4	-0.218883	-1.8443	0.034653
5	-0.053928	-0.4544	0.325461
6	-0.088461	-0.7454	0.22925
7	-0.142418	-1.2	0.117057
8	-0.008488	-0.0715	0.471593
9	0.195293	1.6456	0.052136
10	0.020732	0.1747	0.43091
11	-0.11313	-0.9533	0.171848
12	-0.040469	-0.341	0.367056
13	0.045988	0.3875	0.349772
14	-0.02471	-0.2082	0.41783
15	0.076444	0.6441	0.260783
16	0.02641	0.2225	0.412268
17	-0.038544	-0.3248	0.373151
18	-0.046784	-0.3942	0.347305

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.085004 & 0.7163 & 0.238092 \tabularnewline
2 & 0.119482 & 1.0068 & 0.158732 \tabularnewline
3 & 0.1477 & 1.2445 & 0.108697 \tabularnewline
4 & -0.218883 & -1.8443 & 0.034653 \tabularnewline
5 & -0.053928 & -0.4544 & 0.325461 \tabularnewline
6 & -0.088461 & -0.7454 & 0.22925 \tabularnewline
7 & -0.142418 & -1.2 & 0.117057 \tabularnewline
8 & -0.008488 & -0.0715 & 0.471593 \tabularnewline
9 & 0.195293 & 1.6456 & 0.052136 \tabularnewline
10 & 0.020732 & 0.1747 & 0.43091 \tabularnewline
11 & -0.11313 & -0.9533 & 0.171848 \tabularnewline
12 & -0.040469 & -0.341 & 0.367056 \tabularnewline
13 & 0.045988 & 0.3875 & 0.349772 \tabularnewline
14 & -0.02471 & -0.2082 & 0.41783 \tabularnewline
15 & 0.076444 & 0.6441 & 0.260783 \tabularnewline
16 & 0.02641 & 0.2225 & 0.412268 \tabularnewline
17 & -0.038544 & -0.3248 & 0.373151 \tabularnewline
18 & -0.046784 & -0.3942 & 0.347305 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=242492&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]0.085004[/C][C]0.7163[/C][C]0.238092[/C][/ROW]
[ROW][C]2[/C][C]0.119482[/C][C]1.0068[/C][C]0.158732[/C][/ROW]
[ROW][C]3[/C][C]0.1477[/C][C]1.2445[/C][C]0.108697[/C][/ROW]
[ROW][C]4[/C][C]-0.218883[/C][C]-1.8443[/C][C]0.034653[/C][/ROW]
[ROW][C]5[/C][C]-0.053928[/C][C]-0.4544[/C][C]0.325461[/C][/ROW]
[ROW][C]6[/C][C]-0.088461[/C][C]-0.7454[/C][C]0.22925[/C][/ROW]
[ROW][C]7[/C][C]-0.142418[/C][C]-1.2[/C][C]0.117057[/C][/ROW]
[ROW][C]8[/C][C]-0.008488[/C][C]-0.0715[/C][C]0.471593[/C][/ROW]
[ROW][C]9[/C][C]0.195293[/C][C]1.6456[/C][C]0.052136[/C][/ROW]
[ROW][C]10[/C][C]0.020732[/C][C]0.1747[/C][C]0.43091[/C][/ROW]
[ROW][C]11[/C][C]-0.11313[/C][C]-0.9533[/C][C]0.171848[/C][/ROW]
[ROW][C]12[/C][C]-0.040469[/C][C]-0.341[/C][C]0.367056[/C][/ROW]
[ROW][C]13[/C][C]0.045988[/C][C]0.3875[/C][C]0.349772[/C][/ROW]
[ROW][C]14[/C][C]-0.02471[/C][C]-0.2082[/C][C]0.41783[/C][/ROW]
[ROW][C]15[/C][C]0.076444[/C][C]0.6441[/C][C]0.260783[/C][/ROW]
[ROW][C]16[/C][C]0.02641[/C][C]0.2225[/C][C]0.412268[/C][/ROW]
[ROW][C]17[/C][C]-0.038544[/C][C]-0.3248[/C][C]0.373151[/C][/ROW]
[ROW][C]18[/C][C]-0.046784[/C][C]-0.3942[/C][C]0.347305[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=242492&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=242492&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	0.085004	0.7163	0.238092
2	0.119482	1.0068	0.158732
3	0.1477	1.2445	0.108697
4	-0.218883	-1.8443	0.034653
5	-0.053928	-0.4544	0.325461
6	-0.088461	-0.7454	0.22925
7	-0.142418	-1.2	0.117057
8	-0.008488	-0.0715	0.471593
9	0.195293	1.6456	0.052136
10	0.020732	0.1747	0.43091
11	-0.11313	-0.9533	0.171848
12	-0.040469	-0.341	0.367056
13	0.045988	0.3875	0.349772
14	-0.02471	-0.2082	0.41783
15	0.076444	0.6441	0.260783
16	0.02641	0.2225	0.412268
17	-0.038544	-0.3248	0.373151
18	-0.046784	-0.3942	0.347305

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 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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)
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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Input Parameters & R Code