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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 16:11:21 +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/t1481901207kbx3n68yf6txwrn.htm/, Retrieved Thu, 02 May 2024 14:33:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300348, Retrieved Thu, 02 May 2024 14:33:06 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-16 15:11:21] [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=300348&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=300348&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300348&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	0.965875	8.6391	0
2	0.929393	8.3127	0
3	0.890332	7.9634	0
4	0.8497	7.5999	0
5	0.807994	7.2269	0
6	0.765583	6.8476	0
7	0.722408	6.4614	0
8	0.679686	6.0793	0
9	0.637166	5.699	0
10	0.595166	5.3233	0
11	0.553902	4.9543	2e-06
12	0.513578	4.5936	8e-06
13	0.474849	4.2472	2.9e-05
14	0.437565	3.9137	9.5e-05
15	0.402471	3.5998	0.000275
16	0.367195	3.2843	0.000759
17	0.33337	2.9818	0.001898
18	0.297105	2.6574	0.004753
19	0.256246	2.2919	0.012269

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.965875 & 8.6391 & 0 \tabularnewline
2 & 0.929393 & 8.3127 & 0 \tabularnewline
3 & 0.890332 & 7.9634 & 0 \tabularnewline
4 & 0.8497 & 7.5999 & 0 \tabularnewline
5 & 0.807994 & 7.2269 & 0 \tabularnewline
6 & 0.765583 & 6.8476 & 0 \tabularnewline
7 & 0.722408 & 6.4614 & 0 \tabularnewline
8 & 0.679686 & 6.0793 & 0 \tabularnewline
9 & 0.637166 & 5.699 & 0 \tabularnewline
10 & 0.595166 & 5.3233 & 0 \tabularnewline
11 & 0.553902 & 4.9543 & 2e-06 \tabularnewline
12 & 0.513578 & 4.5936 & 8e-06 \tabularnewline
13 & 0.474849 & 4.2472 & 2.9e-05 \tabularnewline
14 & 0.437565 & 3.9137 & 9.5e-05 \tabularnewline
15 & 0.402471 & 3.5998 & 0.000275 \tabularnewline
16 & 0.367195 & 3.2843 & 0.000759 \tabularnewline
17 & 0.33337 & 2.9818 & 0.001898 \tabularnewline
18 & 0.297105 & 2.6574 & 0.004753 \tabularnewline
19 & 0.256246 & 2.2919 & 0.012269 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300348&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]0.965875[/C][C]8.6391[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.929393[/C][C]8.3127[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.890332[/C][C]7.9634[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.8497[/C][C]7.5999[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.807994[/C][C]7.2269[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.765583[/C][C]6.8476[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.722408[/C][C]6.4614[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.679686[/C][C]6.0793[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.637166[/C][C]5.699[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.595166[/C][C]5.3233[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.553902[/C][C]4.9543[/C][C]2e-06[/C][/ROW]
[ROW][C]12[/C][C]0.513578[/C][C]4.5936[/C][C]8e-06[/C][/ROW]
[ROW][C]13[/C][C]0.474849[/C][C]4.2472[/C][C]2.9e-05[/C][/ROW]
[ROW][C]14[/C][C]0.437565[/C][C]3.9137[/C][C]9.5e-05[/C][/ROW]
[ROW][C]15[/C][C]0.402471[/C][C]3.5998[/C][C]0.000275[/C][/ROW]
[ROW][C]16[/C][C]0.367195[/C][C]3.2843[/C][C]0.000759[/C][/ROW]
[ROW][C]17[/C][C]0.33337[/C][C]2.9818[/C][C]0.001898[/C][/ROW]
[ROW][C]18[/C][C]0.297105[/C][C]2.6574[/C][C]0.004753[/C][/ROW]
[ROW][C]19[/C][C]0.256246[/C][C]2.2919[/C][C]0.012269[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300348&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300348&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	0.965875	8.6391	0
2	0.929393	8.3127	0
3	0.890332	7.9634	0
4	0.8497	7.5999	0
5	0.807994	7.2269	0
6	0.765583	6.8476	0
7	0.722408	6.4614	0
8	0.679686	6.0793	0
9	0.637166	5.699	0
10	0.595166	5.3233	0
11	0.553902	4.9543	2e-06
12	0.513578	4.5936	8e-06
13	0.474849	4.2472	2.9e-05
14	0.437565	3.9137	9.5e-05
15	0.402471	3.5998	0.000275
16	0.367195	3.2843	0.000759
17	0.33337	2.9818	0.001898
18	0.297105	2.6574	0.004753
19	0.256246	2.2919	0.012269

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.965875	8.6391	0
2	-0.052495	-0.4695	0.319984
3	-0.056296	-0.5035	0.307988
4	-0.041776	-0.3737	0.354824
5	-0.035431	-0.3169	0.37607
6	-0.031292	-0.2799	0.390144
7	-0.033558	-0.3001	0.382421
8	-0.016517	-0.1477	0.441463
9	-0.021595	-0.1932	0.423665
10	-0.018217	-0.1629	0.435488
11	-0.015845	-0.1417	0.443828
12	-0.01364	-0.122	0.451603
13	-0.004451	-0.0398	0.484172
14	-0.007484	-0.0669	0.473398
15	0.003423	0.0306	0.487827
16	-0.032635	-0.2919	0.385559
17	-0.00765	-0.0684	0.472809
18	-0.065767	-0.5882	0.279014
19	-0.09842	-0.8803	0.190668

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.965875 & 8.6391 & 0 \tabularnewline
2 & -0.052495 & -0.4695 & 0.319984 \tabularnewline
3 & -0.056296 & -0.5035 & 0.307988 \tabularnewline
4 & -0.041776 & -0.3737 & 0.354824 \tabularnewline
5 & -0.035431 & -0.3169 & 0.37607 \tabularnewline
6 & -0.031292 & -0.2799 & 0.390144 \tabularnewline
7 & -0.033558 & -0.3001 & 0.382421 \tabularnewline
8 & -0.016517 & -0.1477 & 0.441463 \tabularnewline
9 & -0.021595 & -0.1932 & 0.423665 \tabularnewline
10 & -0.018217 & -0.1629 & 0.435488 \tabularnewline
11 & -0.015845 & -0.1417 & 0.443828 \tabularnewline
12 & -0.01364 & -0.122 & 0.451603 \tabularnewline
13 & -0.004451 & -0.0398 & 0.484172 \tabularnewline
14 & -0.007484 & -0.0669 & 0.473398 \tabularnewline
15 & 0.003423 & 0.0306 & 0.487827 \tabularnewline
16 & -0.032635 & -0.2919 & 0.385559 \tabularnewline
17 & -0.00765 & -0.0684 & 0.472809 \tabularnewline
18 & -0.065767 & -0.5882 & 0.279014 \tabularnewline
19 & -0.09842 & -0.8803 & 0.190668 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300348&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]0.965875[/C][C]8.6391[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.052495[/C][C]-0.4695[/C][C]0.319984[/C][/ROW]
[ROW][C]3[/C][C]-0.056296[/C][C]-0.5035[/C][C]0.307988[/C][/ROW]
[ROW][C]4[/C][C]-0.041776[/C][C]-0.3737[/C][C]0.354824[/C][/ROW]
[ROW][C]5[/C][C]-0.035431[/C][C]-0.3169[/C][C]0.37607[/C][/ROW]
[ROW][C]6[/C][C]-0.031292[/C][C]-0.2799[/C][C]0.390144[/C][/ROW]
[ROW][C]7[/C][C]-0.033558[/C][C]-0.3001[/C][C]0.382421[/C][/ROW]
[ROW][C]8[/C][C]-0.016517[/C][C]-0.1477[/C][C]0.441463[/C][/ROW]
[ROW][C]9[/C][C]-0.021595[/C][C]-0.1932[/C][C]0.423665[/C][/ROW]
[ROW][C]10[/C][C]-0.018217[/C][C]-0.1629[/C][C]0.435488[/C][/ROW]
[ROW][C]11[/C][C]-0.015845[/C][C]-0.1417[/C][C]0.443828[/C][/ROW]
[ROW][C]12[/C][C]-0.01364[/C][C]-0.122[/C][C]0.451603[/C][/ROW]
[ROW][C]13[/C][C]-0.004451[/C][C]-0.0398[/C][C]0.484172[/C][/ROW]
[ROW][C]14[/C][C]-0.007484[/C][C]-0.0669[/C][C]0.473398[/C][/ROW]
[ROW][C]15[/C][C]0.003423[/C][C]0.0306[/C][C]0.487827[/C][/ROW]
[ROW][C]16[/C][C]-0.032635[/C][C]-0.2919[/C][C]0.385559[/C][/ROW]
[ROW][C]17[/C][C]-0.00765[/C][C]-0.0684[/C][C]0.472809[/C][/ROW]
[ROW][C]18[/C][C]-0.065767[/C][C]-0.5882[/C][C]0.279014[/C][/ROW]
[ROW][C]19[/C][C]-0.09842[/C][C]-0.8803[/C][C]0.190668[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300348&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300348&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	0.965875	8.6391	0
2	-0.052495	-0.4695	0.319984
3	-0.056296	-0.5035	0.307988
4	-0.041776	-0.3737	0.354824
5	-0.035431	-0.3169	0.37607
6	-0.031292	-0.2799	0.390144
7	-0.033558	-0.3001	0.382421
8	-0.016517	-0.1477	0.441463
9	-0.021595	-0.1932	0.423665
10	-0.018217	-0.1629	0.435488
11	-0.015845	-0.1417	0.443828
12	-0.01364	-0.122	0.451603
13	-0.004451	-0.0398	0.484172
14	-0.007484	-0.0669	0.473398
15	0.003423	0.0306	0.487827
16	-0.032635	-0.2919	0.385559
17	-0.00765	-0.0684	0.472809
18	-0.065767	-0.5882	0.279014
19	-0.09842	-0.8803	0.190668

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code