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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 08 Dec 2016 20:52:18 +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/08/t1481226780ny4gfgfe02hr2k7.htm/, Retrieved Sun, 28 Apr 2024 14:14:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298382, Retrieved Sun, 28 Apr 2024 14:14:23 +0000

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-       [(Partial) Autocorrelation Function] [autocorrelatie] [2016-12-08 19:52:18] [d900f94b3f64e304b47af1531cb36401] [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	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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298382&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298382&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298382&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.97685	10.521	0
2	0.953862	10.2734	0
3	0.930637	10.0233	0
4	0.90703	9.769	0
5	0.883056	9.5108	0
6	0.858518	9.2465	0
7	0.833576	8.9779	0
8	0.808552	8.7084	0
9	0.783348	8.4369	0
10	0.758041	8.1644	0
11	0.732897	7.8935	0
12	0.707757	7.6228	0
13	0.68228	7.3484	0
14	0.656706	7.0729	0
15	0.631102	6.7972	0
16	0.605589	6.5224	0
17	0.580148	6.2484	0
18	0.554695	5.9742	0
19	0.529313	5.7009	0
20	0.50398	5.428	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.97685 & 10.521 & 0 \tabularnewline
2 & 0.953862 & 10.2734 & 0 \tabularnewline
3 & 0.930637 & 10.0233 & 0 \tabularnewline
4 & 0.90703 & 9.769 & 0 \tabularnewline
5 & 0.883056 & 9.5108 & 0 \tabularnewline
6 & 0.858518 & 9.2465 & 0 \tabularnewline
7 & 0.833576 & 8.9779 & 0 \tabularnewline
8 & 0.808552 & 8.7084 & 0 \tabularnewline
9 & 0.783348 & 8.4369 & 0 \tabularnewline
10 & 0.758041 & 8.1644 & 0 \tabularnewline
11 & 0.732897 & 7.8935 & 0 \tabularnewline
12 & 0.707757 & 7.6228 & 0 \tabularnewline
13 & 0.68228 & 7.3484 & 0 \tabularnewline
14 & 0.656706 & 7.0729 & 0 \tabularnewline
15 & 0.631102 & 6.7972 & 0 \tabularnewline
16 & 0.605589 & 6.5224 & 0 \tabularnewline
17 & 0.580148 & 6.2484 & 0 \tabularnewline
18 & 0.554695 & 5.9742 & 0 \tabularnewline
19 & 0.529313 & 5.7009 & 0 \tabularnewline
20 & 0.50398 & 5.428 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298382&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]0.97685[/C][C]10.521[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.953862[/C][C]10.2734[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.930637[/C][C]10.0233[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.90703[/C][C]9.769[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.883056[/C][C]9.5108[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.858518[/C][C]9.2465[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.833576[/C][C]8.9779[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.808552[/C][C]8.7084[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.783348[/C][C]8.4369[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.758041[/C][C]8.1644[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.732897[/C][C]7.8935[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.707757[/C][C]7.6228[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.68228[/C][C]7.3484[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.656706[/C][C]7.0729[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.631102[/C][C]6.7972[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.605589[/C][C]6.5224[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.580148[/C][C]6.2484[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.554695[/C][C]5.9742[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.529313[/C][C]5.7009[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.50398[/C][C]5.428[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298382&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298382&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	0.97685	10.521	0
2	0.953862	10.2734	0
3	0.930637	10.0233	0
4	0.90703	9.769	0
5	0.883056	9.5108	0
6	0.858518	9.2465	0
7	0.833576	8.9779	0
8	0.808552	8.7084	0
9	0.783348	8.4369	0
10	0.758041	8.1644	0
11	0.732897	7.8935	0
12	0.707757	7.6228	0
13	0.68228	7.3484	0
14	0.656706	7.0729	0
15	0.631102	6.7972	0
16	0.605589	6.5224	0
17	0.580148	6.2484	0
18	0.554695	5.9742	0
19	0.529313	5.7009	0
20	0.50398	5.428	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.97685	10.521	0
2	-0.008197	-0.0883	0.464903
3	-0.016918	-0.1822	0.427867
4	-0.020399	-0.2197	0.413246
5	-0.020462	-0.2204	0.412982
6	-0.025041	-0.2697	0.393937
7	-0.022025	-0.2372	0.406452
8	-0.01522	-0.1639	0.435039
9	-0.017489	-0.1884	0.425462
10	-0.016099	-0.1734	0.431323
11	-0.010521	-0.1133	0.454987
12	-0.01409	-0.1518	0.439821
13	-0.021942	-0.2363	0.406799
14	-0.017245	-0.1857	0.42649
15	-0.016035	-0.1727	0.431593
16	-0.013614	-0.1466	0.441839
17	-0.014229	-0.1532	0.439234
18	-0.016163	-0.1741	0.431053
19	-0.0147	-0.1583	0.437238
20	-0.015496	-0.1669	0.433869

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.97685 & 10.521 & 0 \tabularnewline
2 & -0.008197 & -0.0883 & 0.464903 \tabularnewline
3 & -0.016918 & -0.1822 & 0.427867 \tabularnewline
4 & -0.020399 & -0.2197 & 0.413246 \tabularnewline
5 & -0.020462 & -0.2204 & 0.412982 \tabularnewline
6 & -0.025041 & -0.2697 & 0.393937 \tabularnewline
7 & -0.022025 & -0.2372 & 0.406452 \tabularnewline
8 & -0.01522 & -0.1639 & 0.435039 \tabularnewline
9 & -0.017489 & -0.1884 & 0.425462 \tabularnewline
10 & -0.016099 & -0.1734 & 0.431323 \tabularnewline
11 & -0.010521 & -0.1133 & 0.454987 \tabularnewline
12 & -0.01409 & -0.1518 & 0.439821 \tabularnewline
13 & -0.021942 & -0.2363 & 0.406799 \tabularnewline
14 & -0.017245 & -0.1857 & 0.42649 \tabularnewline
15 & -0.016035 & -0.1727 & 0.431593 \tabularnewline
16 & -0.013614 & -0.1466 & 0.441839 \tabularnewline
17 & -0.014229 & -0.1532 & 0.439234 \tabularnewline
18 & -0.016163 & -0.1741 & 0.431053 \tabularnewline
19 & -0.0147 & -0.1583 & 0.437238 \tabularnewline
20 & -0.015496 & -0.1669 & 0.433869 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298382&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]0.97685[/C][C]10.521[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.008197[/C][C]-0.0883[/C][C]0.464903[/C][/ROW]
[ROW][C]3[/C][C]-0.016918[/C][C]-0.1822[/C][C]0.427867[/C][/ROW]
[ROW][C]4[/C][C]-0.020399[/C][C]-0.2197[/C][C]0.413246[/C][/ROW]
[ROW][C]5[/C][C]-0.020462[/C][C]-0.2204[/C][C]0.412982[/C][/ROW]
[ROW][C]6[/C][C]-0.025041[/C][C]-0.2697[/C][C]0.393937[/C][/ROW]
[ROW][C]7[/C][C]-0.022025[/C][C]-0.2372[/C][C]0.406452[/C][/ROW]
[ROW][C]8[/C][C]-0.01522[/C][C]-0.1639[/C][C]0.435039[/C][/ROW]
[ROW][C]9[/C][C]-0.017489[/C][C]-0.1884[/C][C]0.425462[/C][/ROW]
[ROW][C]10[/C][C]-0.016099[/C][C]-0.1734[/C][C]0.431323[/C][/ROW]
[ROW][C]11[/C][C]-0.010521[/C][C]-0.1133[/C][C]0.454987[/C][/ROW]
[ROW][C]12[/C][C]-0.01409[/C][C]-0.1518[/C][C]0.439821[/C][/ROW]
[ROW][C]13[/C][C]-0.021942[/C][C]-0.2363[/C][C]0.406799[/C][/ROW]
[ROW][C]14[/C][C]-0.017245[/C][C]-0.1857[/C][C]0.42649[/C][/ROW]
[ROW][C]15[/C][C]-0.016035[/C][C]-0.1727[/C][C]0.431593[/C][/ROW]
[ROW][C]16[/C][C]-0.013614[/C][C]-0.1466[/C][C]0.441839[/C][/ROW]
[ROW][C]17[/C][C]-0.014229[/C][C]-0.1532[/C][C]0.439234[/C][/ROW]
[ROW][C]18[/C][C]-0.016163[/C][C]-0.1741[/C][C]0.431053[/C][/ROW]
[ROW][C]19[/C][C]-0.0147[/C][C]-0.1583[/C][C]0.437238[/C][/ROW]
[ROW][C]20[/C][C]-0.015496[/C][C]-0.1669[/C][C]0.433869[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298382&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298382&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	0.97685	10.521	0
2	-0.008197	-0.0883	0.464903
3	-0.016918	-0.1822	0.427867
4	-0.020399	-0.2197	0.413246
5	-0.020462	-0.2204	0.412982
6	-0.025041	-0.2697	0.393937
7	-0.022025	-0.2372	0.406452
8	-0.01522	-0.1639	0.435039
9	-0.017489	-0.1884	0.425462
10	-0.016099	-0.1734	0.431323
11	-0.010521	-0.1133	0.454987
12	-0.01409	-0.1518	0.439821
13	-0.021942	-0.2363	0.406799
14	-0.017245	-0.1857	0.42649
15	-0.016035	-0.1727	0.431593
16	-0.013614	-0.1466	0.441839
17	-0.014229	-0.1532	0.439234
18	-0.016163	-0.1741	0.431053
19	-0.0147	-0.1583	0.437238
20	-0.015496	-0.1669	0.433869

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

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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,'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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code