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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 07 Dec 2016 16:51:28 +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/07/t1481126285k0jp17q521hql5n.htm/, Retrieved Fri, 17 May 2024 13:49:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298219, Retrieved Fri, 17 May 2024 13:49:21 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2016-12-07 15:51:28] [153c3207812fd13fe5ceee3276565119] [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=298219&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=298219&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298219&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	-0.354011	-3.5928	0.000252
2	-0.301315	-3.058	0.00142
3	0.244144	2.4778	0.007423
4	-0.108561	-1.1018	0.136565
5	0.058889	0.5977	0.27569
6	0.031792	0.3227	0.373805
7	-0.11575	-1.1747	0.121406
8	0.105241	1.0681	0.14399
9	-0.096303	-0.9774	0.165338
10	0.084905	0.8617	0.19543
11	0.221429	2.2473	0.013378
12	-0.444811	-4.5143	8e-06
13	0.190793	1.9363	0.027783
14	0.10147	1.0298	0.152755
15	-0.177988	-1.8064	0.03689
16	0.082961	0.842	0.200881
17	0.050987	0.5175	0.302973
18	-0.158876	-1.6124	0.054966
19	0.181289	1.8399	0.034333
20	-0.078195	-0.7936	0.214628

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.354011 & -3.5928 & 0.000252 \tabularnewline
2 & -0.301315 & -3.058 & 0.00142 \tabularnewline
3 & 0.244144 & 2.4778 & 0.007423 \tabularnewline
4 & -0.108561 & -1.1018 & 0.136565 \tabularnewline
5 & 0.058889 & 0.5977 & 0.27569 \tabularnewline
6 & 0.031792 & 0.3227 & 0.373805 \tabularnewline
7 & -0.11575 & -1.1747 & 0.121406 \tabularnewline
8 & 0.105241 & 1.0681 & 0.14399 \tabularnewline
9 & -0.096303 & -0.9774 & 0.165338 \tabularnewline
10 & 0.084905 & 0.8617 & 0.19543 \tabularnewline
11 & 0.221429 & 2.2473 & 0.013378 \tabularnewline
12 & -0.444811 & -4.5143 & 8e-06 \tabularnewline
13 & 0.190793 & 1.9363 & 0.027783 \tabularnewline
14 & 0.10147 & 1.0298 & 0.152755 \tabularnewline
15 & -0.177988 & -1.8064 & 0.03689 \tabularnewline
16 & 0.082961 & 0.842 & 0.200881 \tabularnewline
17 & 0.050987 & 0.5175 & 0.302973 \tabularnewline
18 & -0.158876 & -1.6124 & 0.054966 \tabularnewline
19 & 0.181289 & 1.8399 & 0.034333 \tabularnewline
20 & -0.078195 & -0.7936 & 0.214628 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298219&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]-0.354011[/C][C]-3.5928[/C][C]0.000252[/C][/ROW]
[ROW][C]2[/C][C]-0.301315[/C][C]-3.058[/C][C]0.00142[/C][/ROW]
[ROW][C]3[/C][C]0.244144[/C][C]2.4778[/C][C]0.007423[/C][/ROW]
[ROW][C]4[/C][C]-0.108561[/C][C]-1.1018[/C][C]0.136565[/C][/ROW]
[ROW][C]5[/C][C]0.058889[/C][C]0.5977[/C][C]0.27569[/C][/ROW]
[ROW][C]6[/C][C]0.031792[/C][C]0.3227[/C][C]0.373805[/C][/ROW]
[ROW][C]7[/C][C]-0.11575[/C][C]-1.1747[/C][C]0.121406[/C][/ROW]
[ROW][C]8[/C][C]0.105241[/C][C]1.0681[/C][C]0.14399[/C][/ROW]
[ROW][C]9[/C][C]-0.096303[/C][C]-0.9774[/C][C]0.165338[/C][/ROW]
[ROW][C]10[/C][C]0.084905[/C][C]0.8617[/C][C]0.19543[/C][/ROW]
[ROW][C]11[/C][C]0.221429[/C][C]2.2473[/C][C]0.013378[/C][/ROW]
[ROW][C]12[/C][C]-0.444811[/C][C]-4.5143[/C][C]8e-06[/C][/ROW]
[ROW][C]13[/C][C]0.190793[/C][C]1.9363[/C][C]0.027783[/C][/ROW]
[ROW][C]14[/C][C]0.10147[/C][C]1.0298[/C][C]0.152755[/C][/ROW]
[ROW][C]15[/C][C]-0.177988[/C][C]-1.8064[/C][C]0.03689[/C][/ROW]
[ROW][C]16[/C][C]0.082961[/C][C]0.842[/C][C]0.200881[/C][/ROW]
[ROW][C]17[/C][C]0.050987[/C][C]0.5175[/C][C]0.302973[/C][/ROW]
[ROW][C]18[/C][C]-0.158876[/C][C]-1.6124[/C][C]0.054966[/C][/ROW]
[ROW][C]19[/C][C]0.181289[/C][C]1.8399[/C][C]0.034333[/C][/ROW]
[ROW][C]20[/C][C]-0.078195[/C][C]-0.7936[/C][C]0.214628[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298219&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298219&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	-0.354011	-3.5928	0.000252
2	-0.301315	-3.058	0.00142
3	0.244144	2.4778	0.007423
4	-0.108561	-1.1018	0.136565
5	0.058889	0.5977	0.27569
6	0.031792	0.3227	0.373805
7	-0.11575	-1.1747	0.121406
8	0.105241	1.0681	0.14399
9	-0.096303	-0.9774	0.165338
10	0.084905	0.8617	0.19543
11	0.221429	2.2473	0.013378
12	-0.444811	-4.5143	8e-06
13	0.190793	1.9363	0.027783
14	0.10147	1.0298	0.152755
15	-0.177988	-1.8064	0.03689
16	0.082961	0.842	0.200881
17	0.050987	0.5175	0.302973
18	-0.158876	-1.6124	0.054966
19	0.181289	1.8399	0.034333
20	-0.078195	-0.7936	0.214628

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.354011	-3.5928	0.000252
2	-0.487768	-4.9503	1e-06
3	-0.130863	-1.3281	0.093539
4	-0.272384	-2.7644	0.003379
5	-0.033761	-0.3426	0.366285
6	-0.052974	-0.5376	0.295996
7	-0.076936	-0.7808	0.218351
8	0.015131	0.1536	0.439127
9	-0.146311	-1.4849	0.070313
10	0.05599	0.5682	0.285554
11	0.325009	3.2985	0.000668
12	-0.155188	-1.575	0.059163
13	0.116747	1.1848	0.119402
14	-0.098031	-0.9949	0.161056
15	-0.0243	-0.2466	0.402847
16	-0.138629	-1.4069	0.081229
17	0.052127	0.529	0.298962
18	-0.189794	-1.9262	0.028418
19	0.086578	0.8787	0.190812
20	-0.098608	-1.0008	0.159644

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.354011 & -3.5928 & 0.000252 \tabularnewline
2 & -0.487768 & -4.9503 & 1e-06 \tabularnewline
3 & -0.130863 & -1.3281 & 0.093539 \tabularnewline
4 & -0.272384 & -2.7644 & 0.003379 \tabularnewline
5 & -0.033761 & -0.3426 & 0.366285 \tabularnewline
6 & -0.052974 & -0.5376 & 0.295996 \tabularnewline
7 & -0.076936 & -0.7808 & 0.218351 \tabularnewline
8 & 0.015131 & 0.1536 & 0.439127 \tabularnewline
9 & -0.146311 & -1.4849 & 0.070313 \tabularnewline
10 & 0.05599 & 0.5682 & 0.285554 \tabularnewline
11 & 0.325009 & 3.2985 & 0.000668 \tabularnewline
12 & -0.155188 & -1.575 & 0.059163 \tabularnewline
13 & 0.116747 & 1.1848 & 0.119402 \tabularnewline
14 & -0.098031 & -0.9949 & 0.161056 \tabularnewline
15 & -0.0243 & -0.2466 & 0.402847 \tabularnewline
16 & -0.138629 & -1.4069 & 0.081229 \tabularnewline
17 & 0.052127 & 0.529 & 0.298962 \tabularnewline
18 & -0.189794 & -1.9262 & 0.028418 \tabularnewline
19 & 0.086578 & 0.8787 & 0.190812 \tabularnewline
20 & -0.098608 & -1.0008 & 0.159644 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298219&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]-0.354011[/C][C]-3.5928[/C][C]0.000252[/C][/ROW]
[ROW][C]2[/C][C]-0.487768[/C][C]-4.9503[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.130863[/C][C]-1.3281[/C][C]0.093539[/C][/ROW]
[ROW][C]4[/C][C]-0.272384[/C][C]-2.7644[/C][C]0.003379[/C][/ROW]
[ROW][C]5[/C][C]-0.033761[/C][C]-0.3426[/C][C]0.366285[/C][/ROW]
[ROW][C]6[/C][C]-0.052974[/C][C]-0.5376[/C][C]0.295996[/C][/ROW]
[ROW][C]7[/C][C]-0.076936[/C][C]-0.7808[/C][C]0.218351[/C][/ROW]
[ROW][C]8[/C][C]0.015131[/C][C]0.1536[/C][C]0.439127[/C][/ROW]
[ROW][C]9[/C][C]-0.146311[/C][C]-1.4849[/C][C]0.070313[/C][/ROW]
[ROW][C]10[/C][C]0.05599[/C][C]0.5682[/C][C]0.285554[/C][/ROW]
[ROW][C]11[/C][C]0.325009[/C][C]3.2985[/C][C]0.000668[/C][/ROW]
[ROW][C]12[/C][C]-0.155188[/C][C]-1.575[/C][C]0.059163[/C][/ROW]
[ROW][C]13[/C][C]0.116747[/C][C]1.1848[/C][C]0.119402[/C][/ROW]
[ROW][C]14[/C][C]-0.098031[/C][C]-0.9949[/C][C]0.161056[/C][/ROW]
[ROW][C]15[/C][C]-0.0243[/C][C]-0.2466[/C][C]0.402847[/C][/ROW]
[ROW][C]16[/C][C]-0.138629[/C][C]-1.4069[/C][C]0.081229[/C][/ROW]
[ROW][C]17[/C][C]0.052127[/C][C]0.529[/C][C]0.298962[/C][/ROW]
[ROW][C]18[/C][C]-0.189794[/C][C]-1.9262[/C][C]0.028418[/C][/ROW]
[ROW][C]19[/C][C]0.086578[/C][C]0.8787[/C][C]0.190812[/C][/ROW]
[ROW][C]20[/C][C]-0.098608[/C][C]-1.0008[/C][C]0.159644[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298219&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298219&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	-0.354011	-3.5928	0.000252
2	-0.487768	-4.9503	1e-06
3	-0.130863	-1.3281	0.093539
4	-0.272384	-2.7644	0.003379
5	-0.033761	-0.3426	0.366285
6	-0.052974	-0.5376	0.295996
7	-0.076936	-0.7808	0.218351
8	0.015131	0.1536	0.439127
9	-0.146311	-1.4849	0.070313
10	0.05599	0.5682	0.285554
11	0.325009	3.2985	0.000668
12	-0.155188	-1.575	0.059163
13	0.116747	1.1848	0.119402
14	-0.098031	-0.9949	0.161056
15	-0.0243	-0.2466	0.402847
16	-0.138629	-1.4069	0.081229
17	0.052127	0.529	0.298962
18	-0.189794	-1.9262	0.028418
19	0.086578	0.8787	0.190812
20	-0.098608	-1.0008	0.159644

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

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PDF link

Parameters (Session):

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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