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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 11 Mar 2016 10:20:03 +0000

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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/Mar/11/t1457691682vehny2jrql8i106.htm/, Retrieved Sat, 18 May 2024 14:49:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293846, Retrieved Sat, 18 May 2024 14:49:35 +0000

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168

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-       [(Partial) Autocorrelation Function] [] [2016-03-11 10:20:03] [4c0c83f68a39c2484f611b00ec7d20d3] [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	'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293846&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]1 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=293846&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293846&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.846375	7.1817	0
2	0.625969	5.3115	1e-06
3	0.521926	4.4287	1.7e-05
4	0.538564	4.5699	1e-05
5	0.630811	5.3526	0
6	0.67779	5.7512	0
7	0.591769	5.0213	2e-06
8	0.460771	3.9098	0.000103
9	0.391086	3.3185	0.000711
10	0.423538	3.5938	0.000296
11	0.557315	4.729	5e-06
12	0.639981	5.4304	0
13	0.496043	4.2091	3.7e-05
14	0.288365	2.4469	0.008426
15	0.166314	1.4112	0.081244
16	0.144592	1.2269	0.111928
17	0.19424	1.6482	0.051837
18	0.212788	1.8056	0.037583

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.846375 & 7.1817 & 0 \tabularnewline
2 & 0.625969 & 5.3115 & 1e-06 \tabularnewline
3 & 0.521926 & 4.4287 & 1.7e-05 \tabularnewline
4 & 0.538564 & 4.5699 & 1e-05 \tabularnewline
5 & 0.630811 & 5.3526 & 0 \tabularnewline
6 & 0.67779 & 5.7512 & 0 \tabularnewline
7 & 0.591769 & 5.0213 & 2e-06 \tabularnewline
8 & 0.460771 & 3.9098 & 0.000103 \tabularnewline
9 & 0.391086 & 3.3185 & 0.000711 \tabularnewline
10 & 0.423538 & 3.5938 & 0.000296 \tabularnewline
11 & 0.557315 & 4.729 & 5e-06 \tabularnewline
12 & 0.639981 & 5.4304 & 0 \tabularnewline
13 & 0.496043 & 4.2091 & 3.7e-05 \tabularnewline
14 & 0.288365 & 2.4469 & 0.008426 \tabularnewline
15 & 0.166314 & 1.4112 & 0.081244 \tabularnewline
16 & 0.144592 & 1.2269 & 0.111928 \tabularnewline
17 & 0.19424 & 1.6482 & 0.051837 \tabularnewline
18 & 0.212788 & 1.8056 & 0.037583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293846&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]0.846375[/C][C]7.1817[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.625969[/C][C]5.3115[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.521926[/C][C]4.4287[/C][C]1.7e-05[/C][/ROW]
[ROW][C]4[/C][C]0.538564[/C][C]4.5699[/C][C]1e-05[/C][/ROW]
[ROW][C]5[/C][C]0.630811[/C][C]5.3526[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.67779[/C][C]5.7512[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.591769[/C][C]5.0213[/C][C]2e-06[/C][/ROW]
[ROW][C]8[/C][C]0.460771[/C][C]3.9098[/C][C]0.000103[/C][/ROW]
[ROW][C]9[/C][C]0.391086[/C][C]3.3185[/C][C]0.000711[/C][/ROW]
[ROW][C]10[/C][C]0.423538[/C][C]3.5938[/C][C]0.000296[/C][/ROW]
[ROW][C]11[/C][C]0.557315[/C][C]4.729[/C][C]5e-06[/C][/ROW]
[ROW][C]12[/C][C]0.639981[/C][C]5.4304[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.496043[/C][C]4.2091[/C][C]3.7e-05[/C][/ROW]
[ROW][C]14[/C][C]0.288365[/C][C]2.4469[/C][C]0.008426[/C][/ROW]
[ROW][C]15[/C][C]0.166314[/C][C]1.4112[/C][C]0.081244[/C][/ROW]
[ROW][C]16[/C][C]0.144592[/C][C]1.2269[/C][C]0.111928[/C][/ROW]
[ROW][C]17[/C][C]0.19424[/C][C]1.6482[/C][C]0.051837[/C][/ROW]
[ROW][C]18[/C][C]0.212788[/C][C]1.8056[/C][C]0.037583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293846&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293846&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	0.846375	7.1817	0
2	0.625969	5.3115	1e-06
3	0.521926	4.4287	1.7e-05
4	0.538564	4.5699	1e-05
5	0.630811	5.3526	0
6	0.67779	5.7512	0
7	0.591769	5.0213	2e-06
8	0.460771	3.9098	0.000103
9	0.391086	3.3185	0.000711
10	0.423538	3.5938	0.000296
11	0.557315	4.729	5e-06
12	0.639981	5.4304	0
13	0.496043	4.2091	3.7e-05
14	0.288365	2.4469	0.008426
15	0.166314	1.4112	0.081244
16	0.144592	1.2269	0.111928
17	0.19424	1.6482	0.051837
18	0.212788	1.8056	0.037583

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.846375	7.1817	0
2	-0.31864	-2.7038	0.004274
3	0.364895	3.0962	0.001396
4	0.185231	1.5717	0.060198
5	0.327671	2.7804	0.003462
6	-0.015007	-0.1273	0.449514
7	-0.171242	-1.453	0.075279
8	0.015633	0.1326	0.447421
9	0.006371	0.0541	0.478517
10	0.136172	1.1555	0.125862
11	0.321123	2.7248	0.004035
12	-0.05374	-0.456	0.324882
13	-0.55389	-4.6999	6e-06
14	0.026242	0.2227	0.412213
15	-0.191113	-1.6216	0.054625
16	-0.170671	-1.4482	0.075952
17	-0.145583	-1.2353	0.110366
18	-0.067755	-0.5749	0.28357

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.846375 & 7.1817 & 0 \tabularnewline
2 & -0.31864 & -2.7038 & 0.004274 \tabularnewline
3 & 0.364895 & 3.0962 & 0.001396 \tabularnewline
4 & 0.185231 & 1.5717 & 0.060198 \tabularnewline
5 & 0.327671 & 2.7804 & 0.003462 \tabularnewline
6 & -0.015007 & -0.1273 & 0.449514 \tabularnewline
7 & -0.171242 & -1.453 & 0.075279 \tabularnewline
8 & 0.015633 & 0.1326 & 0.447421 \tabularnewline
9 & 0.006371 & 0.0541 & 0.478517 \tabularnewline
10 & 0.136172 & 1.1555 & 0.125862 \tabularnewline
11 & 0.321123 & 2.7248 & 0.004035 \tabularnewline
12 & -0.05374 & -0.456 & 0.324882 \tabularnewline
13 & -0.55389 & -4.6999 & 6e-06 \tabularnewline
14 & 0.026242 & 0.2227 & 0.412213 \tabularnewline
15 & -0.191113 & -1.6216 & 0.054625 \tabularnewline
16 & -0.170671 & -1.4482 & 0.075952 \tabularnewline
17 & -0.145583 & -1.2353 & 0.110366 \tabularnewline
18 & -0.067755 & -0.5749 & 0.28357 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293846&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]0.846375[/C][C]7.1817[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.31864[/C][C]-2.7038[/C][C]0.004274[/C][/ROW]
[ROW][C]3[/C][C]0.364895[/C][C]3.0962[/C][C]0.001396[/C][/ROW]
[ROW][C]4[/C][C]0.185231[/C][C]1.5717[/C][C]0.060198[/C][/ROW]
[ROW][C]5[/C][C]0.327671[/C][C]2.7804[/C][C]0.003462[/C][/ROW]
[ROW][C]6[/C][C]-0.015007[/C][C]-0.1273[/C][C]0.449514[/C][/ROW]
[ROW][C]7[/C][C]-0.171242[/C][C]-1.453[/C][C]0.075279[/C][/ROW]
[ROW][C]8[/C][C]0.015633[/C][C]0.1326[/C][C]0.447421[/C][/ROW]
[ROW][C]9[/C][C]0.006371[/C][C]0.0541[/C][C]0.478517[/C][/ROW]
[ROW][C]10[/C][C]0.136172[/C][C]1.1555[/C][C]0.125862[/C][/ROW]
[ROW][C]11[/C][C]0.321123[/C][C]2.7248[/C][C]0.004035[/C][/ROW]
[ROW][C]12[/C][C]-0.05374[/C][C]-0.456[/C][C]0.324882[/C][/ROW]
[ROW][C]13[/C][C]-0.55389[/C][C]-4.6999[/C][C]6e-06[/C][/ROW]
[ROW][C]14[/C][C]0.026242[/C][C]0.2227[/C][C]0.412213[/C][/ROW]
[ROW][C]15[/C][C]-0.191113[/C][C]-1.6216[/C][C]0.054625[/C][/ROW]
[ROW][C]16[/C][C]-0.170671[/C][C]-1.4482[/C][C]0.075952[/C][/ROW]
[ROW][C]17[/C][C]-0.145583[/C][C]-1.2353[/C][C]0.110366[/C][/ROW]
[ROW][C]18[/C][C]-0.067755[/C][C]-0.5749[/C][C]0.28357[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293846&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293846&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	0.846375	7.1817	0
2	-0.31864	-2.7038	0.004274
3	0.364895	3.0962	0.001396
4	0.185231	1.5717	0.060198
5	0.327671	2.7804	0.003462
6	-0.015007	-0.1273	0.449514
7	-0.171242	-1.453	0.075279
8	0.015633	0.1326	0.447421
9	0.006371	0.0541	0.478517
10	0.136172	1.1555	0.125862
11	0.321123	2.7248	0.004035
12	-0.05374	-0.456	0.324882
13	-0.55389	-4.6999	6e-06
14	0.026242	0.2227	0.412213
15	-0.191113	-1.6216	0.054625
16	-0.170671	-1.4482	0.075952
17	-0.145583	-1.2353	0.110366
18	-0.067755	-0.5749	0.28357

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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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Input Parameters & R Code