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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 15:58:42 +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/16/t1481900336v570jvgtsi7yqzb.htm/, Retrieved Fri, 03 May 2024 01:52:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300337, Retrieved Fri, 03 May 2024 01:52:42 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-16 14:58:42] [1a4fa2544711480e714211476e711237] [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=300337&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=300337&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300337&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	0.658826	6.8467	0
2	0.663449	6.8948	0
3	0.630805	6.5555	0
4	0.570468	5.9285	0
5	0.547353	5.6883	0
6	0.476516	4.9521	1e-06
7	0.552253	5.7392	0
8	0.506021	5.2587	0
9	0.487084	5.0619	1e-06
10	0.578436	6.0113	0
11	0.491679	5.1097	1e-06
12	0.533939	5.5489	0
13	0.433403	4.5041	8e-06
14	0.470658	4.8912	2e-06
15	0.429333	4.4618	1e-05
16	0.381425	3.9639	6.6e-05
17	0.411709	4.2786	2e-05
18	0.330951	3.4393	0.000415
19	0.306833	3.1887	0.000935
20	0.316251	3.2866	0.000684

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.658826 & 6.8467 & 0 \tabularnewline
2 & 0.663449 & 6.8948 & 0 \tabularnewline
3 & 0.630805 & 6.5555 & 0 \tabularnewline
4 & 0.570468 & 5.9285 & 0 \tabularnewline
5 & 0.547353 & 5.6883 & 0 \tabularnewline
6 & 0.476516 & 4.9521 & 1e-06 \tabularnewline
7 & 0.552253 & 5.7392 & 0 \tabularnewline
8 & 0.506021 & 5.2587 & 0 \tabularnewline
9 & 0.487084 & 5.0619 & 1e-06 \tabularnewline
10 & 0.578436 & 6.0113 & 0 \tabularnewline
11 & 0.491679 & 5.1097 & 1e-06 \tabularnewline
12 & 0.533939 & 5.5489 & 0 \tabularnewline
13 & 0.433403 & 4.5041 & 8e-06 \tabularnewline
14 & 0.470658 & 4.8912 & 2e-06 \tabularnewline
15 & 0.429333 & 4.4618 & 1e-05 \tabularnewline
16 & 0.381425 & 3.9639 & 6.6e-05 \tabularnewline
17 & 0.411709 & 4.2786 & 2e-05 \tabularnewline
18 & 0.330951 & 3.4393 & 0.000415 \tabularnewline
19 & 0.306833 & 3.1887 & 0.000935 \tabularnewline
20 & 0.316251 & 3.2866 & 0.000684 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300337&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]0.658826[/C][C]6.8467[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.663449[/C][C]6.8948[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.630805[/C][C]6.5555[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.570468[/C][C]5.9285[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.547353[/C][C]5.6883[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.476516[/C][C]4.9521[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.552253[/C][C]5.7392[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.506021[/C][C]5.2587[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.487084[/C][C]5.0619[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.578436[/C][C]6.0113[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.491679[/C][C]5.1097[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]0.533939[/C][C]5.5489[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.433403[/C][C]4.5041[/C][C]8e-06[/C][/ROW]
[ROW][C]14[/C][C]0.470658[/C][C]4.8912[/C][C]2e-06[/C][/ROW]
[ROW][C]15[/C][C]0.429333[/C][C]4.4618[/C][C]1e-05[/C][/ROW]
[ROW][C]16[/C][C]0.381425[/C][C]3.9639[/C][C]6.6e-05[/C][/ROW]
[ROW][C]17[/C][C]0.411709[/C][C]4.2786[/C][C]2e-05[/C][/ROW]
[ROW][C]18[/C][C]0.330951[/C][C]3.4393[/C][C]0.000415[/C][/ROW]
[ROW][C]19[/C][C]0.306833[/C][C]3.1887[/C][C]0.000935[/C][/ROW]
[ROW][C]20[/C][C]0.316251[/C][C]3.2866[/C][C]0.000684[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300337&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300337&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	0.658826	6.8467	0
2	0.663449	6.8948	0
3	0.630805	6.5555	0
4	0.570468	5.9285	0
5	0.547353	5.6883	0
6	0.476516	4.9521	1e-06
7	0.552253	5.7392	0
8	0.506021	5.2587	0
9	0.487084	5.0619	1e-06
10	0.578436	6.0113	0
11	0.491679	5.1097	1e-06
12	0.533939	5.5489	0
13	0.433403	4.5041	8e-06
14	0.470658	4.8912	2e-06
15	0.429333	4.4618	1e-05
16	0.381425	3.9639	6.6e-05
17	0.411709	4.2786	2e-05
18	0.330951	3.4393	0.000415
19	0.306833	3.1887	0.000935
20	0.316251	3.2866	0.000684

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.658826	6.8467	0
2	0.405334	4.2124	2.6e-05
3	0.219538	2.2815	0.01224
4	0.051028	0.5303	0.298496
5	0.046407	0.4823	0.315293
6	-0.054854	-0.5701	0.28491
7	0.219573	2.2819	0.012229
8	0.073025	0.7589	0.224783
9	0.010399	0.1081	0.45707
10	0.229422	2.3842	0.00943
11	-0.05112	-0.5313	0.298165
12	0.059993	0.6235	0.267146
13	-0.146939	-1.527	0.064838
14	0.042921	0.446	0.328227
15	-0.024789	-0.2576	0.398597
16	-0.006138	-0.0638	0.474628
17	0.00061	0.0063	0.497478
18	-0.103508	-1.0757	0.142232
19	-0.12995	-1.3505	0.089842
20	0.014714	0.1529	0.439378

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.658826 & 6.8467 & 0 \tabularnewline
2 & 0.405334 & 4.2124 & 2.6e-05 \tabularnewline
3 & 0.219538 & 2.2815 & 0.01224 \tabularnewline
4 & 0.051028 & 0.5303 & 0.298496 \tabularnewline
5 & 0.046407 & 0.4823 & 0.315293 \tabularnewline
6 & -0.054854 & -0.5701 & 0.28491 \tabularnewline
7 & 0.219573 & 2.2819 & 0.012229 \tabularnewline
8 & 0.073025 & 0.7589 & 0.224783 \tabularnewline
9 & 0.010399 & 0.1081 & 0.45707 \tabularnewline
10 & 0.229422 & 2.3842 & 0.00943 \tabularnewline
11 & -0.05112 & -0.5313 & 0.298165 \tabularnewline
12 & 0.059993 & 0.6235 & 0.267146 \tabularnewline
13 & -0.146939 & -1.527 & 0.064838 \tabularnewline
14 & 0.042921 & 0.446 & 0.328227 \tabularnewline
15 & -0.024789 & -0.2576 & 0.398597 \tabularnewline
16 & -0.006138 & -0.0638 & 0.474628 \tabularnewline
17 & 0.00061 & 0.0063 & 0.497478 \tabularnewline
18 & -0.103508 & -1.0757 & 0.142232 \tabularnewline
19 & -0.12995 & -1.3505 & 0.089842 \tabularnewline
20 & 0.014714 & 0.1529 & 0.439378 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300337&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]0.658826[/C][C]6.8467[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.405334[/C][C]4.2124[/C][C]2.6e-05[/C][/ROW]
[ROW][C]3[/C][C]0.219538[/C][C]2.2815[/C][C]0.01224[/C][/ROW]
[ROW][C]4[/C][C]0.051028[/C][C]0.5303[/C][C]0.298496[/C][/ROW]
[ROW][C]5[/C][C]0.046407[/C][C]0.4823[/C][C]0.315293[/C][/ROW]
[ROW][C]6[/C][C]-0.054854[/C][C]-0.5701[/C][C]0.28491[/C][/ROW]
[ROW][C]7[/C][C]0.219573[/C][C]2.2819[/C][C]0.012229[/C][/ROW]
[ROW][C]8[/C][C]0.073025[/C][C]0.7589[/C][C]0.224783[/C][/ROW]
[ROW][C]9[/C][C]0.010399[/C][C]0.1081[/C][C]0.45707[/C][/ROW]
[ROW][C]10[/C][C]0.229422[/C][C]2.3842[/C][C]0.00943[/C][/ROW]
[ROW][C]11[/C][C]-0.05112[/C][C]-0.5313[/C][C]0.298165[/C][/ROW]
[ROW][C]12[/C][C]0.059993[/C][C]0.6235[/C][C]0.267146[/C][/ROW]
[ROW][C]13[/C][C]-0.146939[/C][C]-1.527[/C][C]0.064838[/C][/ROW]
[ROW][C]14[/C][C]0.042921[/C][C]0.446[/C][C]0.328227[/C][/ROW]
[ROW][C]15[/C][C]-0.024789[/C][C]-0.2576[/C][C]0.398597[/C][/ROW]
[ROW][C]16[/C][C]-0.006138[/C][C]-0.0638[/C][C]0.474628[/C][/ROW]
[ROW][C]17[/C][C]0.00061[/C][C]0.0063[/C][C]0.497478[/C][/ROW]
[ROW][C]18[/C][C]-0.103508[/C][C]-1.0757[/C][C]0.142232[/C][/ROW]
[ROW][C]19[/C][C]-0.12995[/C][C]-1.3505[/C][C]0.089842[/C][/ROW]
[ROW][C]20[/C][C]0.014714[/C][C]0.1529[/C][C]0.439378[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300337&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300337&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	0.658826	6.8467	0
2	0.405334	4.2124	2.6e-05
3	0.219538	2.2815	0.01224
4	0.051028	0.5303	0.298496
5	0.046407	0.4823	0.315293
6	-0.054854	-0.5701	0.28491
7	0.219573	2.2819	0.012229
8	0.073025	0.7589	0.224783
9	0.010399	0.1081	0.45707
10	0.229422	2.3842	0.00943
11	-0.05112	-0.5313	0.298165
12	0.059993	0.6235	0.267146
13	-0.146939	-1.527	0.064838
14	0.042921	0.446	0.328227
15	-0.024789	-0.2576	0.398597
16	-0.006138	-0.0638	0.474628
17	0.00061	0.0063	0.497478
18	-0.103508	-1.0757	0.142232
19	-0.12995	-1.3505	0.089842
20	0.014714	0.1529	0.439378

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):

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code