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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 18:32:40 +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/17/t1481995994ehzadtfwmbvoid0.htm/, Retrieved Thu, 02 May 2024 01:23:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300897, Retrieved Thu, 02 May 2024 01:23:03 +0000

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-     [ML Fitting and QQ Plot- Normal Distribution] [Histogram] [2016-12-02 11:39:44] [937b9e6718912fc8986df66e31b6c342]
- RMP   [Histogram] [HISTO&FREQ STATPAP] [2016-12-11 13:44:30] [937b9e6718912fc8986df66e31b6c342]
- RMP       [(Partial) Autocorrelation Function] [] [2016-12-17 17:32:40] [863feeaf19a0ddfce7bd9c25059c4d8a] [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	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300897&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300897&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300897&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.243121	-1.4587	0.076656
2	0.061364	0.3682	0.357447
3	0.079202	0.4752	0.318753
4	0.077432	0.4646	0.322511
5	0.074215	0.4453	0.329388
6	-0.155542	-0.9333	0.178454
7	-0.065032	-0.3902	0.349348
8	0.029003	0.174	0.431413
9	0.049455	0.2967	0.384188
10	-0.091442	-0.5487	0.293316
11	0.073035	0.4382	0.331926
12	-0.285374	-1.7122	0.047727
13	0.207372	1.2442	0.110727
14	-0.086491	-0.5189	0.303488
15	-0.001408	-0.0084	0.496653
16	-0.008757	-0.0525	0.479194
17	-0.060281	-0.3617	0.35985

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.243121 & -1.4587 & 0.076656 \tabularnewline
2 & 0.061364 & 0.3682 & 0.357447 \tabularnewline
3 & 0.079202 & 0.4752 & 0.318753 \tabularnewline
4 & 0.077432 & 0.4646 & 0.322511 \tabularnewline
5 & 0.074215 & 0.4453 & 0.329388 \tabularnewline
6 & -0.155542 & -0.9333 & 0.178454 \tabularnewline
7 & -0.065032 & -0.3902 & 0.349348 \tabularnewline
8 & 0.029003 & 0.174 & 0.431413 \tabularnewline
9 & 0.049455 & 0.2967 & 0.384188 \tabularnewline
10 & -0.091442 & -0.5487 & 0.293316 \tabularnewline
11 & 0.073035 & 0.4382 & 0.331926 \tabularnewline
12 & -0.285374 & -1.7122 & 0.047727 \tabularnewline
13 & 0.207372 & 1.2442 & 0.110727 \tabularnewline
14 & -0.086491 & -0.5189 & 0.303488 \tabularnewline
15 & -0.001408 & -0.0084 & 0.496653 \tabularnewline
16 & -0.008757 & -0.0525 & 0.479194 \tabularnewline
17 & -0.060281 & -0.3617 & 0.35985 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300897&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]-0.243121[/C][C]-1.4587[/C][C]0.076656[/C][/ROW]
[ROW][C]2[/C][C]0.061364[/C][C]0.3682[/C][C]0.357447[/C][/ROW]
[ROW][C]3[/C][C]0.079202[/C][C]0.4752[/C][C]0.318753[/C][/ROW]
[ROW][C]4[/C][C]0.077432[/C][C]0.4646[/C][C]0.322511[/C][/ROW]
[ROW][C]5[/C][C]0.074215[/C][C]0.4453[/C][C]0.329388[/C][/ROW]
[ROW][C]6[/C][C]-0.155542[/C][C]-0.9333[/C][C]0.178454[/C][/ROW]
[ROW][C]7[/C][C]-0.065032[/C][C]-0.3902[/C][C]0.349348[/C][/ROW]
[ROW][C]8[/C][C]0.029003[/C][C]0.174[/C][C]0.431413[/C][/ROW]
[ROW][C]9[/C][C]0.049455[/C][C]0.2967[/C][C]0.384188[/C][/ROW]
[ROW][C]10[/C][C]-0.091442[/C][C]-0.5487[/C][C]0.293316[/C][/ROW]
[ROW][C]11[/C][C]0.073035[/C][C]0.4382[/C][C]0.331926[/C][/ROW]
[ROW][C]12[/C][C]-0.285374[/C][C]-1.7122[/C][C]0.047727[/C][/ROW]
[ROW][C]13[/C][C]0.207372[/C][C]1.2442[/C][C]0.110727[/C][/ROW]
[ROW][C]14[/C][C]-0.086491[/C][C]-0.5189[/C][C]0.303488[/C][/ROW]
[ROW][C]15[/C][C]-0.001408[/C][C]-0.0084[/C][C]0.496653[/C][/ROW]
[ROW][C]16[/C][C]-0.008757[/C][C]-0.0525[/C][C]0.479194[/C][/ROW]
[ROW][C]17[/C][C]-0.060281[/C][C]-0.3617[/C][C]0.35985[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300897&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300897&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	-0.243121	-1.4587	0.076656
2	0.061364	0.3682	0.357447
3	0.079202	0.4752	0.318753
4	0.077432	0.4646	0.322511
5	0.074215	0.4453	0.329388
6	-0.155542	-0.9333	0.178454
7	-0.065032	-0.3902	0.349348
8	0.029003	0.174	0.431413
9	0.049455	0.2967	0.384188
10	-0.091442	-0.5487	0.293316
11	0.073035	0.4382	0.331926
12	-0.285374	-1.7122	0.047727
13	0.207372	1.2442	0.110727
14	-0.086491	-0.5189	0.303488
15	-0.001408	-0.0084	0.496653
16	-0.008757	-0.0525	0.479194
17	-0.060281	-0.3617	0.35985

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.243121	-1.4587	0.076656
2	0.002398	0.0144	0.494301
3	0.100616	0.6037	0.274916
4	0.128282	0.7697	0.223251
5	0.125832	0.755	0.227583
6	-0.139041	-0.8342	0.204821
7	-0.1924	-1.1544	0.127971
8	-0.061843	-0.3711	0.356384
9	0.092203	0.5532	0.291768
10	0.017543	0.1053	0.458377
11	0.115374	0.6922	0.246612
12	-0.317379	-1.9043	0.032445
13	-0.007545	-0.0453	0.482071
14	-0.028507	-0.171	0.432574
15	0.106183	0.6371	0.264046
16	0.07164	0.4298	0.334936
17	-0.049483	-0.2969	0.384126

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.243121 & -1.4587 & 0.076656 \tabularnewline
2 & 0.002398 & 0.0144 & 0.494301 \tabularnewline
3 & 0.100616 & 0.6037 & 0.274916 \tabularnewline
4 & 0.128282 & 0.7697 & 0.223251 \tabularnewline
5 & 0.125832 & 0.755 & 0.227583 \tabularnewline
6 & -0.139041 & -0.8342 & 0.204821 \tabularnewline
7 & -0.1924 & -1.1544 & 0.127971 \tabularnewline
8 & -0.061843 & -0.3711 & 0.356384 \tabularnewline
9 & 0.092203 & 0.5532 & 0.291768 \tabularnewline
10 & 0.017543 & 0.1053 & 0.458377 \tabularnewline
11 & 0.115374 & 0.6922 & 0.246612 \tabularnewline
12 & -0.317379 & -1.9043 & 0.032445 \tabularnewline
13 & -0.007545 & -0.0453 & 0.482071 \tabularnewline
14 & -0.028507 & -0.171 & 0.432574 \tabularnewline
15 & 0.106183 & 0.6371 & 0.264046 \tabularnewline
16 & 0.07164 & 0.4298 & 0.334936 \tabularnewline
17 & -0.049483 & -0.2969 & 0.384126 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300897&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]-0.243121[/C][C]-1.4587[/C][C]0.076656[/C][/ROW]
[ROW][C]2[/C][C]0.002398[/C][C]0.0144[/C][C]0.494301[/C][/ROW]
[ROW][C]3[/C][C]0.100616[/C][C]0.6037[/C][C]0.274916[/C][/ROW]
[ROW][C]4[/C][C]0.128282[/C][C]0.7697[/C][C]0.223251[/C][/ROW]
[ROW][C]5[/C][C]0.125832[/C][C]0.755[/C][C]0.227583[/C][/ROW]
[ROW][C]6[/C][C]-0.139041[/C][C]-0.8342[/C][C]0.204821[/C][/ROW]
[ROW][C]7[/C][C]-0.1924[/C][C]-1.1544[/C][C]0.127971[/C][/ROW]
[ROW][C]8[/C][C]-0.061843[/C][C]-0.3711[/C][C]0.356384[/C][/ROW]
[ROW][C]9[/C][C]0.092203[/C][C]0.5532[/C][C]0.291768[/C][/ROW]
[ROW][C]10[/C][C]0.017543[/C][C]0.1053[/C][C]0.458377[/C][/ROW]
[ROW][C]11[/C][C]0.115374[/C][C]0.6922[/C][C]0.246612[/C][/ROW]
[ROW][C]12[/C][C]-0.317379[/C][C]-1.9043[/C][C]0.032445[/C][/ROW]
[ROW][C]13[/C][C]-0.007545[/C][C]-0.0453[/C][C]0.482071[/C][/ROW]
[ROW][C]14[/C][C]-0.028507[/C][C]-0.171[/C][C]0.432574[/C][/ROW]
[ROW][C]15[/C][C]0.106183[/C][C]0.6371[/C][C]0.264046[/C][/ROW]
[ROW][C]16[/C][C]0.07164[/C][C]0.4298[/C][C]0.334936[/C][/ROW]
[ROW][C]17[/C][C]-0.049483[/C][C]-0.2969[/C][C]0.384126[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300897&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300897&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	-0.243121	-1.4587	0.076656
2	0.002398	0.0144	0.494301
3	0.100616	0.6037	0.274916
4	0.128282	0.7697	0.223251
5	0.125832	0.755	0.227583
6	-0.139041	-0.8342	0.204821
7	-0.1924	-1.1544	0.127971
8	-0.061843	-0.3711	0.356384
9	0.092203	0.5532	0.291768
10	0.017543	0.1053	0.458377
11	0.115374	0.6922	0.246612
12	-0.317379	-1.9043	0.032445
13	-0.007545	-0.0453	0.482071
14	-0.028507	-0.171	0.432574
15	0.106183	0.6371	0.264046
16	0.07164	0.4298	0.334936
17	-0.049483	-0.2969	0.384126

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1.4 ; par3 = 1 ; par4 = 2 ; 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 <- '0'
par2 <- '1.4'
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')

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Input Parameters & R Code