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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 16:14:42 +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/t1481901356bwga7nc22fbvz2z.htm/, Retrieved Thu, 02 May 2024 22:55:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300351, Retrieved Thu, 02 May 2024 22:55:58 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-16 15:14:42] [9b171b8beffcb53bb49a1e7c02b89c12] [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=300351&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=300351&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300351&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	-0.347073	-3.0653	0.001493
2	0.085557	0.7556	0.226076
3	0.12387	1.094	0.138663
4	-0.247955	-2.1899	0.015761
5	0.206199	1.8211	0.036213
6	0.091907	0.8117	0.209717
7	-0.105467	-0.9315	0.177245
8	0.04251	0.3754	0.354178
9	-0.022277	-0.1967	0.422269
10	0.044016	0.3887	0.349263
11	-0.08136	-0.7186	0.237281
12	0.057254	0.5056	0.307264
13	-0.036053	-0.3184	0.375514
14	-0.221588	-1.957	0.026962
15	0.187043	1.6519	0.051286
16	-0.333728	-2.9474	0.002113
17	0.176388	1.5578	0.061662
18	0.041756	0.3688	0.356645
19	-0.103099	-0.9105	0.182669

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.347073 & -3.0653 & 0.001493 \tabularnewline
2 & 0.085557 & 0.7556 & 0.226076 \tabularnewline
3 & 0.12387 & 1.094 & 0.138663 \tabularnewline
4 & -0.247955 & -2.1899 & 0.015761 \tabularnewline
5 & 0.206199 & 1.8211 & 0.036213 \tabularnewline
6 & 0.091907 & 0.8117 & 0.209717 \tabularnewline
7 & -0.105467 & -0.9315 & 0.177245 \tabularnewline
8 & 0.04251 & 0.3754 & 0.354178 \tabularnewline
9 & -0.022277 & -0.1967 & 0.422269 \tabularnewline
10 & 0.044016 & 0.3887 & 0.349263 \tabularnewline
11 & -0.08136 & -0.7186 & 0.237281 \tabularnewline
12 & 0.057254 & 0.5056 & 0.307264 \tabularnewline
13 & -0.036053 & -0.3184 & 0.375514 \tabularnewline
14 & -0.221588 & -1.957 & 0.026962 \tabularnewline
15 & 0.187043 & 1.6519 & 0.051286 \tabularnewline
16 & -0.333728 & -2.9474 & 0.002113 \tabularnewline
17 & 0.176388 & 1.5578 & 0.061662 \tabularnewline
18 & 0.041756 & 0.3688 & 0.356645 \tabularnewline
19 & -0.103099 & -0.9105 & 0.182669 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300351&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]-0.347073[/C][C]-3.0653[/C][C]0.001493[/C][/ROW]
[ROW][C]2[/C][C]0.085557[/C][C]0.7556[/C][C]0.226076[/C][/ROW]
[ROW][C]3[/C][C]0.12387[/C][C]1.094[/C][C]0.138663[/C][/ROW]
[ROW][C]4[/C][C]-0.247955[/C][C]-2.1899[/C][C]0.015761[/C][/ROW]
[ROW][C]5[/C][C]0.206199[/C][C]1.8211[/C][C]0.036213[/C][/ROW]
[ROW][C]6[/C][C]0.091907[/C][C]0.8117[/C][C]0.209717[/C][/ROW]
[ROW][C]7[/C][C]-0.105467[/C][C]-0.9315[/C][C]0.177245[/C][/ROW]
[ROW][C]8[/C][C]0.04251[/C][C]0.3754[/C][C]0.354178[/C][/ROW]
[ROW][C]9[/C][C]-0.022277[/C][C]-0.1967[/C][C]0.422269[/C][/ROW]
[ROW][C]10[/C][C]0.044016[/C][C]0.3887[/C][C]0.349263[/C][/ROW]
[ROW][C]11[/C][C]-0.08136[/C][C]-0.7186[/C][C]0.237281[/C][/ROW]
[ROW][C]12[/C][C]0.057254[/C][C]0.5056[/C][C]0.307264[/C][/ROW]
[ROW][C]13[/C][C]-0.036053[/C][C]-0.3184[/C][C]0.375514[/C][/ROW]
[ROW][C]14[/C][C]-0.221588[/C][C]-1.957[/C][C]0.026962[/C][/ROW]
[ROW][C]15[/C][C]0.187043[/C][C]1.6519[/C][C]0.051286[/C][/ROW]
[ROW][C]16[/C][C]-0.333728[/C][C]-2.9474[/C][C]0.002113[/C][/ROW]
[ROW][C]17[/C][C]0.176388[/C][C]1.5578[/C][C]0.061662[/C][/ROW]
[ROW][C]18[/C][C]0.041756[/C][C]0.3688[/C][C]0.356645[/C][/ROW]
[ROW][C]19[/C][C]-0.103099[/C][C]-0.9105[/C][C]0.182669[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300351&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300351&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	-0.347073	-3.0653	0.001493
2	0.085557	0.7556	0.226076
3	0.12387	1.094	0.138663
4	-0.247955	-2.1899	0.015761
5	0.206199	1.8211	0.036213
6	0.091907	0.8117	0.209717
7	-0.105467	-0.9315	0.177245
8	0.04251	0.3754	0.354178
9	-0.022277	-0.1967	0.422269
10	0.044016	0.3887	0.349263
11	-0.08136	-0.7186	0.237281
12	0.057254	0.5056	0.307264
13	-0.036053	-0.3184	0.375514
14	-0.221588	-1.957	0.026962
15	0.187043	1.6519	0.051286
16	-0.333728	-2.9474	0.002113
17	0.176388	1.5578	0.061662
18	0.041756	0.3688	0.356645
19	-0.103099	-0.9105	0.182669

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.347073	-3.0653	0.001493
2	-0.039682	-0.3505	0.363468
3	0.16053	1.4178	0.080121
4	-0.175204	-1.5474	0.062912
5	0.064386	0.5686	0.285615
6	0.222973	1.9692	0.026238
7	0.023814	0.2103	0.416983
8	-0.103142	-0.9109	0.18257
9	-0.002578	-0.0228	0.490947
10	0.126668	1.1187	0.13335
11	-0.138957	-1.2272	0.111713
12	-0.061168	-0.5402	0.295292
13	0.037982	0.3355	0.369093
14	-0.243949	-2.1545	0.017144
15	-0.043186	-0.3814	0.35197
16	-0.275449	-2.4327	0.008638
17	0.073566	0.6497	0.258891
18	0.060568	0.5349	0.297114
19	0.071527	0.6317	0.264712

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.347073 & -3.0653 & 0.001493 \tabularnewline
2 & -0.039682 & -0.3505 & 0.363468 \tabularnewline
3 & 0.16053 & 1.4178 & 0.080121 \tabularnewline
4 & -0.175204 & -1.5474 & 0.062912 \tabularnewline
5 & 0.064386 & 0.5686 & 0.285615 \tabularnewline
6 & 0.222973 & 1.9692 & 0.026238 \tabularnewline
7 & 0.023814 & 0.2103 & 0.416983 \tabularnewline
8 & -0.103142 & -0.9109 & 0.18257 \tabularnewline
9 & -0.002578 & -0.0228 & 0.490947 \tabularnewline
10 & 0.126668 & 1.1187 & 0.13335 \tabularnewline
11 & -0.138957 & -1.2272 & 0.111713 \tabularnewline
12 & -0.061168 & -0.5402 & 0.295292 \tabularnewline
13 & 0.037982 & 0.3355 & 0.369093 \tabularnewline
14 & -0.243949 & -2.1545 & 0.017144 \tabularnewline
15 & -0.043186 & -0.3814 & 0.35197 \tabularnewline
16 & -0.275449 & -2.4327 & 0.008638 \tabularnewline
17 & 0.073566 & 0.6497 & 0.258891 \tabularnewline
18 & 0.060568 & 0.5349 & 0.297114 \tabularnewline
19 & 0.071527 & 0.6317 & 0.264712 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300351&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]-0.347073[/C][C]-3.0653[/C][C]0.001493[/C][/ROW]
[ROW][C]2[/C][C]-0.039682[/C][C]-0.3505[/C][C]0.363468[/C][/ROW]
[ROW][C]3[/C][C]0.16053[/C][C]1.4178[/C][C]0.080121[/C][/ROW]
[ROW][C]4[/C][C]-0.175204[/C][C]-1.5474[/C][C]0.062912[/C][/ROW]
[ROW][C]5[/C][C]0.064386[/C][C]0.5686[/C][C]0.285615[/C][/ROW]
[ROW][C]6[/C][C]0.222973[/C][C]1.9692[/C][C]0.026238[/C][/ROW]
[ROW][C]7[/C][C]0.023814[/C][C]0.2103[/C][C]0.416983[/C][/ROW]
[ROW][C]8[/C][C]-0.103142[/C][C]-0.9109[/C][C]0.18257[/C][/ROW]
[ROW][C]9[/C][C]-0.002578[/C][C]-0.0228[/C][C]0.490947[/C][/ROW]
[ROW][C]10[/C][C]0.126668[/C][C]1.1187[/C][C]0.13335[/C][/ROW]
[ROW][C]11[/C][C]-0.138957[/C][C]-1.2272[/C][C]0.111713[/C][/ROW]
[ROW][C]12[/C][C]-0.061168[/C][C]-0.5402[/C][C]0.295292[/C][/ROW]
[ROW][C]13[/C][C]0.037982[/C][C]0.3355[/C][C]0.369093[/C][/ROW]
[ROW][C]14[/C][C]-0.243949[/C][C]-2.1545[/C][C]0.017144[/C][/ROW]
[ROW][C]15[/C][C]-0.043186[/C][C]-0.3814[/C][C]0.35197[/C][/ROW]
[ROW][C]16[/C][C]-0.275449[/C][C]-2.4327[/C][C]0.008638[/C][/ROW]
[ROW][C]17[/C][C]0.073566[/C][C]0.6497[/C][C]0.258891[/C][/ROW]
[ROW][C]18[/C][C]0.060568[/C][C]0.5349[/C][C]0.297114[/C][/ROW]
[ROW][C]19[/C][C]0.071527[/C][C]0.6317[/C][C]0.264712[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300351&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300351&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	-0.347073	-3.0653	0.001493
2	-0.039682	-0.3505	0.363468
3	0.16053	1.4178	0.080121
4	-0.175204	-1.5474	0.062912
5	0.064386	0.5686	0.285615
6	0.222973	1.9692	0.026238
7	0.023814	0.2103	0.416983
8	-0.103142	-0.9109	0.18257
9	-0.002578	-0.0228	0.490947
10	0.126668	1.1187	0.13335
11	-0.138957	-1.2272	0.111713
12	-0.061168	-0.5402	0.295292
13	0.037982	0.3355	0.369093
14	-0.243949	-2.1545	0.017144
15	-0.043186	-0.3814	0.35197
16	-0.275449	-2.4327	0.008638
17	0.073566	0.6497	0.258891
18	0.060568	0.5349	0.297114
19	0.071527	0.6317	0.264712

Figure 1

PNG link

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 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 0 ; 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 <- '1'
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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code