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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2016 16:52:56 +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/20/t14822493696jgw1wndnwo5ztg.htm/, Retrieved Fri, 01 Nov 2024 03:44:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301723, Retrieved Fri, 01 Nov 2024 03:44:20 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-20 15:52:56] [b7216e4bc5ee29192acbe9c506cee18c] [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=301723&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=301723&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301723&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	-0.570167	-5.7866	0
2	-0.077829	-0.7899	0.215708
3	0.380367	3.8603	9.9e-05
4	-0.364565	-3.6999	0.000174
5	0.086366	0.8765	0.191395
6	0.199404	2.0237	0.022794
7	-0.264865	-2.6881	0.004191
8	0.116787	1.1853	0.119321
9	0.116107	1.1784	0.120685
10	-0.293432	-2.978	0.001809
11	0.301505	3.0599	0.001411
12	-0.098633	-1.001	0.159583
13	-0.18541	-1.8817	0.031349
14	0.216845	2.2007	0.014994
15	0.06096	0.6187	0.268746
16	-0.290615	-2.9494	0.00197
17	0.269931	2.7395	0.003627
18	-0.048813	-0.4954	0.310687
19	-0.236285	-2.398	0.009142
20	0.33742	3.4244	0.000443

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.570167 & -5.7866 & 0 \tabularnewline
2 & -0.077829 & -0.7899 & 0.215708 \tabularnewline
3 & 0.380367 & 3.8603 & 9.9e-05 \tabularnewline
4 & -0.364565 & -3.6999 & 0.000174 \tabularnewline
5 & 0.086366 & 0.8765 & 0.191395 \tabularnewline
6 & 0.199404 & 2.0237 & 0.022794 \tabularnewline
7 & -0.264865 & -2.6881 & 0.004191 \tabularnewline
8 & 0.116787 & 1.1853 & 0.119321 \tabularnewline
9 & 0.116107 & 1.1784 & 0.120685 \tabularnewline
10 & -0.293432 & -2.978 & 0.001809 \tabularnewline
11 & 0.301505 & 3.0599 & 0.001411 \tabularnewline
12 & -0.098633 & -1.001 & 0.159583 \tabularnewline
13 & -0.18541 & -1.8817 & 0.031349 \tabularnewline
14 & 0.216845 & 2.2007 & 0.014994 \tabularnewline
15 & 0.06096 & 0.6187 & 0.268746 \tabularnewline
16 & -0.290615 & -2.9494 & 0.00197 \tabularnewline
17 & 0.269931 & 2.7395 & 0.003627 \tabularnewline
18 & -0.048813 & -0.4954 & 0.310687 \tabularnewline
19 & -0.236285 & -2.398 & 0.009142 \tabularnewline
20 & 0.33742 & 3.4244 & 0.000443 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301723&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]-0.570167[/C][C]-5.7866[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.077829[/C][C]-0.7899[/C][C]0.215708[/C][/ROW]
[ROW][C]3[/C][C]0.380367[/C][C]3.8603[/C][C]9.9e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.364565[/C][C]-3.6999[/C][C]0.000174[/C][/ROW]
[ROW][C]5[/C][C]0.086366[/C][C]0.8765[/C][C]0.191395[/C][/ROW]
[ROW][C]6[/C][C]0.199404[/C][C]2.0237[/C][C]0.022794[/C][/ROW]
[ROW][C]7[/C][C]-0.264865[/C][C]-2.6881[/C][C]0.004191[/C][/ROW]
[ROW][C]8[/C][C]0.116787[/C][C]1.1853[/C][C]0.119321[/C][/ROW]
[ROW][C]9[/C][C]0.116107[/C][C]1.1784[/C][C]0.120685[/C][/ROW]
[ROW][C]10[/C][C]-0.293432[/C][C]-2.978[/C][C]0.001809[/C][/ROW]
[ROW][C]11[/C][C]0.301505[/C][C]3.0599[/C][C]0.001411[/C][/ROW]
[ROW][C]12[/C][C]-0.098633[/C][C]-1.001[/C][C]0.159583[/C][/ROW]
[ROW][C]13[/C][C]-0.18541[/C][C]-1.8817[/C][C]0.031349[/C][/ROW]
[ROW][C]14[/C][C]0.216845[/C][C]2.2007[/C][C]0.014994[/C][/ROW]
[ROW][C]15[/C][C]0.06096[/C][C]0.6187[/C][C]0.268746[/C][/ROW]
[ROW][C]16[/C][C]-0.290615[/C][C]-2.9494[/C][C]0.00197[/C][/ROW]
[ROW][C]17[/C][C]0.269931[/C][C]2.7395[/C][C]0.003627[/C][/ROW]
[ROW][C]18[/C][C]-0.048813[/C][C]-0.4954[/C][C]0.310687[/C][/ROW]
[ROW][C]19[/C][C]-0.236285[/C][C]-2.398[/C][C]0.009142[/C][/ROW]
[ROW][C]20[/C][C]0.33742[/C][C]3.4244[/C][C]0.000443[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301723&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301723&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	-0.570167	-5.7866	0
2	-0.077829	-0.7899	0.215708
3	0.380367	3.8603	9.9e-05
4	-0.364565	-3.6999	0.000174
5	0.086366	0.8765	0.191395
6	0.199404	2.0237	0.022794
7	-0.264865	-2.6881	0.004191
8	0.116787	1.1853	0.119321
9	0.116107	1.1784	0.120685
10	-0.293432	-2.978	0.001809
11	0.301505	3.0599	0.001411
12	-0.098633	-1.001	0.159583
13	-0.18541	-1.8817	0.031349
14	0.216845	2.2007	0.014994
15	0.06096	0.6187	0.268746
16	-0.290615	-2.9494	0.00197
17	0.269931	2.7395	0.003627
18	-0.048813	-0.4954	0.310687
19	-0.236285	-2.398	0.009142
20	0.33742	3.4244	0.000443

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.570167	-5.7866	0
2	-0.596997	-6.0589	0
3	-0.071112	-0.7217	0.236056
4	-0.217785	-2.2103	0.014649
5	-0.257607	-2.6144	0.005139
6	-0.078981	-0.8016	0.212323
7	-0.09442	-0.9583	0.170088
8	-0.114281	-1.1598	0.124401
9	0.034761	0.3528	0.362487
10	-0.180593	-1.8328	0.034859
11	0.045921	0.466	0.321083
12	0.039087	0.3967	0.346209
13	-0.105648	-1.0722	0.143065
14	-0.271243	-2.7528	0.003492
15	0.161872	1.6428	0.051735
16	-0.024651	-0.2502	0.401472
17	-0.023884	-0.2424	0.404476
18	0.040064	0.4066	0.342573
19	-0.093558	-0.9495	0.172292
20	-0.041445	-0.4206	0.337454

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.570167 & -5.7866 & 0 \tabularnewline
2 & -0.596997 & -6.0589 & 0 \tabularnewline
3 & -0.071112 & -0.7217 & 0.236056 \tabularnewline
4 & -0.217785 & -2.2103 & 0.014649 \tabularnewline
5 & -0.257607 & -2.6144 & 0.005139 \tabularnewline
6 & -0.078981 & -0.8016 & 0.212323 \tabularnewline
7 & -0.09442 & -0.9583 & 0.170088 \tabularnewline
8 & -0.114281 & -1.1598 & 0.124401 \tabularnewline
9 & 0.034761 & 0.3528 & 0.362487 \tabularnewline
10 & -0.180593 & -1.8328 & 0.034859 \tabularnewline
11 & 0.045921 & 0.466 & 0.321083 \tabularnewline
12 & 0.039087 & 0.3967 & 0.346209 \tabularnewline
13 & -0.105648 & -1.0722 & 0.143065 \tabularnewline
14 & -0.271243 & -2.7528 & 0.003492 \tabularnewline
15 & 0.161872 & 1.6428 & 0.051735 \tabularnewline
16 & -0.024651 & -0.2502 & 0.401472 \tabularnewline
17 & -0.023884 & -0.2424 & 0.404476 \tabularnewline
18 & 0.040064 & 0.4066 & 0.342573 \tabularnewline
19 & -0.093558 & -0.9495 & 0.172292 \tabularnewline
20 & -0.041445 & -0.4206 & 0.337454 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301723&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]-0.570167[/C][C]-5.7866[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.596997[/C][C]-6.0589[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.071112[/C][C]-0.7217[/C][C]0.236056[/C][/ROW]
[ROW][C]4[/C][C]-0.217785[/C][C]-2.2103[/C][C]0.014649[/C][/ROW]
[ROW][C]5[/C][C]-0.257607[/C][C]-2.6144[/C][C]0.005139[/C][/ROW]
[ROW][C]6[/C][C]-0.078981[/C][C]-0.8016[/C][C]0.212323[/C][/ROW]
[ROW][C]7[/C][C]-0.09442[/C][C]-0.9583[/C][C]0.170088[/C][/ROW]
[ROW][C]8[/C][C]-0.114281[/C][C]-1.1598[/C][C]0.124401[/C][/ROW]
[ROW][C]9[/C][C]0.034761[/C][C]0.3528[/C][C]0.362487[/C][/ROW]
[ROW][C]10[/C][C]-0.180593[/C][C]-1.8328[/C][C]0.034859[/C][/ROW]
[ROW][C]11[/C][C]0.045921[/C][C]0.466[/C][C]0.321083[/C][/ROW]
[ROW][C]12[/C][C]0.039087[/C][C]0.3967[/C][C]0.346209[/C][/ROW]
[ROW][C]13[/C][C]-0.105648[/C][C]-1.0722[/C][C]0.143065[/C][/ROW]
[ROW][C]14[/C][C]-0.271243[/C][C]-2.7528[/C][C]0.003492[/C][/ROW]
[ROW][C]15[/C][C]0.161872[/C][C]1.6428[/C][C]0.051735[/C][/ROW]
[ROW][C]16[/C][C]-0.024651[/C][C]-0.2502[/C][C]0.401472[/C][/ROW]
[ROW][C]17[/C][C]-0.023884[/C][C]-0.2424[/C][C]0.404476[/C][/ROW]
[ROW][C]18[/C][C]0.040064[/C][C]0.4066[/C][C]0.342573[/C][/ROW]
[ROW][C]19[/C][C]-0.093558[/C][C]-0.9495[/C][C]0.172292[/C][/ROW]
[ROW][C]20[/C][C]-0.041445[/C][C]-0.4206[/C][C]0.337454[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301723&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301723&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	-0.570167	-5.7866	0
2	-0.596997	-6.0589	0
3	-0.071112	-0.7217	0.236056
4	-0.217785	-2.2103	0.014649
5	-0.257607	-2.6144	0.005139
6	-0.078981	-0.8016	0.212323
7	-0.09442	-0.9583	0.170088
8	-0.114281	-1.1598	0.124401
9	0.034761	0.3528	0.362487
10	-0.180593	-1.8328	0.034859
11	0.045921	0.466	0.321083
12	0.039087	0.3967	0.346209
13	-0.105648	-1.0722	0.143065
14	-0.271243	-2.7528	0.003492
15	0.161872	1.6428	0.051735
16	-0.024651	-0.2502	0.401472
17	-0.023884	-0.2424	0.404476
18	0.040064	0.4066	0.342573
19	-0.093558	-0.9495	0.172292
20	-0.041445	-0.4206	0.337454

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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Parameters (Session):

par1 = Default ; par2 = -0.4 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = -0.4 ; 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 <- '2'
par3 <- '1'
par2 <- '-0.4'
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