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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 09:45:07 +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/t1481877962x415wqmfi30wa8g.htm/, Retrieved Fri, 17 May 2024 20:03:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300132, Retrieved Fri, 17 May 2024 20:03:00 +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...] [2016-12-16 08:45:07] [d92250bd36540c2281a4ec15b45df1dd] [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=300132&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=300132&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300132&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	0.672909	4.8055	7e-06
2	0.657851	4.698	1e-05
3	0.611624	4.3679	3.1e-05
4	0.815592	5.8245	0
5	0.505383	3.6092	0.00035
6	0.495643	3.5396	0.000433
7	0.455547	3.2533	0.001014
8	0.635831	4.5407	1.7e-05
9	0.340377	2.4308	0.009311
10	0.327506	2.3389	0.01165
11	0.28496	2.035	0.023531
12	0.440453	3.1455	0.001383
13	0.167361	1.1952	0.118769
14	0.150859	1.0773	0.143198
15	0.097731	0.6979	0.244193
16	0.228041	1.6285	0.054787
17	-0.02277	-0.1626	0.435733

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.672909 & 4.8055 & 7e-06 \tabularnewline
2 & 0.657851 & 4.698 & 1e-05 \tabularnewline
3 & 0.611624 & 4.3679 & 3.1e-05 \tabularnewline
4 & 0.815592 & 5.8245 & 0 \tabularnewline
5 & 0.505383 & 3.6092 & 0.00035 \tabularnewline
6 & 0.495643 & 3.5396 & 0.000433 \tabularnewline
7 & 0.455547 & 3.2533 & 0.001014 \tabularnewline
8 & 0.635831 & 4.5407 & 1.7e-05 \tabularnewline
9 & 0.340377 & 2.4308 & 0.009311 \tabularnewline
10 & 0.327506 & 2.3389 & 0.01165 \tabularnewline
11 & 0.28496 & 2.035 & 0.023531 \tabularnewline
12 & 0.440453 & 3.1455 & 0.001383 \tabularnewline
13 & 0.167361 & 1.1952 & 0.118769 \tabularnewline
14 & 0.150859 & 1.0773 & 0.143198 \tabularnewline
15 & 0.097731 & 0.6979 & 0.244193 \tabularnewline
16 & 0.228041 & 1.6285 & 0.054787 \tabularnewline
17 & -0.02277 & -0.1626 & 0.435733 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300132&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]0.672909[/C][C]4.8055[/C][C]7e-06[/C][/ROW]
[ROW][C]2[/C][C]0.657851[/C][C]4.698[/C][C]1e-05[/C][/ROW]
[ROW][C]3[/C][C]0.611624[/C][C]4.3679[/C][C]3.1e-05[/C][/ROW]
[ROW][C]4[/C][C]0.815592[/C][C]5.8245[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.505383[/C][C]3.6092[/C][C]0.00035[/C][/ROW]
[ROW][C]6[/C][C]0.495643[/C][C]3.5396[/C][C]0.000433[/C][/ROW]
[ROW][C]7[/C][C]0.455547[/C][C]3.2533[/C][C]0.001014[/C][/ROW]
[ROW][C]8[/C][C]0.635831[/C][C]4.5407[/C][C]1.7e-05[/C][/ROW]
[ROW][C]9[/C][C]0.340377[/C][C]2.4308[/C][C]0.009311[/C][/ROW]
[ROW][C]10[/C][C]0.327506[/C][C]2.3389[/C][C]0.01165[/C][/ROW]
[ROW][C]11[/C][C]0.28496[/C][C]2.035[/C][C]0.023531[/C][/ROW]
[ROW][C]12[/C][C]0.440453[/C][C]3.1455[/C][C]0.001383[/C][/ROW]
[ROW][C]13[/C][C]0.167361[/C][C]1.1952[/C][C]0.118769[/C][/ROW]
[ROW][C]14[/C][C]0.150859[/C][C]1.0773[/C][C]0.143198[/C][/ROW]
[ROW][C]15[/C][C]0.097731[/C][C]0.6979[/C][C]0.244193[/C][/ROW]
[ROW][C]16[/C][C]0.228041[/C][C]1.6285[/C][C]0.054787[/C][/ROW]
[ROW][C]17[/C][C]-0.02277[/C][C]-0.1626[/C][C]0.435733[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300132&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300132&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	0.672909	4.8055	7e-06
2	0.657851	4.698	1e-05
3	0.611624	4.3679	3.1e-05
4	0.815592	5.8245	0
5	0.505383	3.6092	0.00035
6	0.495643	3.5396	0.000433
7	0.455547	3.2533	0.001014
8	0.635831	4.5407	1.7e-05
9	0.340377	2.4308	0.009311
10	0.327506	2.3389	0.01165
11	0.28496	2.035	0.023531
12	0.440453	3.1455	0.001383
13	0.167361	1.1952	0.118769
14	0.150859	1.0773	0.143198
15	0.097731	0.6979	0.244193
16	0.228041	1.6285	0.054787
17	-0.02277	-0.1626	0.435733

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.672909	4.8055	7e-06
2	0.37472	2.676	0.004996
3	0.175773	1.2553	0.10755
4	0.619525	4.4243	2.6e-05
5	-0.545141	-3.8931	0.000144
6	-0.066965	-0.4782	0.317268
7	0.053654	0.3832	0.351595
8	0.1788	1.2769	0.103713
9	-0.188218	-1.3441	0.092425
10	-0.133329	-0.9522	0.172754
11	-0.044121	-0.3151	0.37699
12	0.058716	0.4193	0.338374
13	-0.020493	-0.1463	0.442112
14	-0.118692	-0.8476	0.200303
15	-0.139985	-0.9997	0.16109
16	-0.03384	-0.2417	0.405003
17	0.019252	0.1375	0.445594

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.672909 & 4.8055 & 7e-06 \tabularnewline
2 & 0.37472 & 2.676 & 0.004996 \tabularnewline
3 & 0.175773 & 1.2553 & 0.10755 \tabularnewline
4 & 0.619525 & 4.4243 & 2.6e-05 \tabularnewline
5 & -0.545141 & -3.8931 & 0.000144 \tabularnewline
6 & -0.066965 & -0.4782 & 0.317268 \tabularnewline
7 & 0.053654 & 0.3832 & 0.351595 \tabularnewline
8 & 0.1788 & 1.2769 & 0.103713 \tabularnewline
9 & -0.188218 & -1.3441 & 0.092425 \tabularnewline
10 & -0.133329 & -0.9522 & 0.172754 \tabularnewline
11 & -0.044121 & -0.3151 & 0.37699 \tabularnewline
12 & 0.058716 & 0.4193 & 0.338374 \tabularnewline
13 & -0.020493 & -0.1463 & 0.442112 \tabularnewline
14 & -0.118692 & -0.8476 & 0.200303 \tabularnewline
15 & -0.139985 & -0.9997 & 0.16109 \tabularnewline
16 & -0.03384 & -0.2417 & 0.405003 \tabularnewline
17 & 0.019252 & 0.1375 & 0.445594 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300132&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]0.672909[/C][C]4.8055[/C][C]7e-06[/C][/ROW]
[ROW][C]2[/C][C]0.37472[/C][C]2.676[/C][C]0.004996[/C][/ROW]
[ROW][C]3[/C][C]0.175773[/C][C]1.2553[/C][C]0.10755[/C][/ROW]
[ROW][C]4[/C][C]0.619525[/C][C]4.4243[/C][C]2.6e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.545141[/C][C]-3.8931[/C][C]0.000144[/C][/ROW]
[ROW][C]6[/C][C]-0.066965[/C][C]-0.4782[/C][C]0.317268[/C][/ROW]
[ROW][C]7[/C][C]0.053654[/C][C]0.3832[/C][C]0.351595[/C][/ROW]
[ROW][C]8[/C][C]0.1788[/C][C]1.2769[/C][C]0.103713[/C][/ROW]
[ROW][C]9[/C][C]-0.188218[/C][C]-1.3441[/C][C]0.092425[/C][/ROW]
[ROW][C]10[/C][C]-0.133329[/C][C]-0.9522[/C][C]0.172754[/C][/ROW]
[ROW][C]11[/C][C]-0.044121[/C][C]-0.3151[/C][C]0.37699[/C][/ROW]
[ROW][C]12[/C][C]0.058716[/C][C]0.4193[/C][C]0.338374[/C][/ROW]
[ROW][C]13[/C][C]-0.020493[/C][C]-0.1463[/C][C]0.442112[/C][/ROW]
[ROW][C]14[/C][C]-0.118692[/C][C]-0.8476[/C][C]0.200303[/C][/ROW]
[ROW][C]15[/C][C]-0.139985[/C][C]-0.9997[/C][C]0.16109[/C][/ROW]
[ROW][C]16[/C][C]-0.03384[/C][C]-0.2417[/C][C]0.405003[/C][/ROW]
[ROW][C]17[/C][C]0.019252[/C][C]0.1375[/C][C]0.445594[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300132&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300132&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	0.672909	4.8055	7e-06
2	0.37472	2.676	0.004996
3	0.175773	1.2553	0.10755
4	0.619525	4.4243	2.6e-05
5	-0.545141	-3.8931	0.000144
6	-0.066965	-0.4782	0.317268
7	0.053654	0.3832	0.351595
8	0.1788	1.2769	0.103713
9	-0.188218	-1.3441	0.092425
10	-0.133329	-0.9522	0.172754
11	-0.044121	-0.3151	0.37699
12	0.058716	0.4193	0.338374
13	-0.020493	-0.1463	0.442112
14	-0.118692	-0.8476	0.200303
15	-0.139985	-0.9997	0.16109
16	-0.03384	-0.2417	0.405003
17	0.019252	0.1375	0.445594

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):

par4 = 12 ;

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)

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Input Parameters & R Code