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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 01 Dec 2016 11:04:14 +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/01/t1480586747t4q55hl5ii498ah.htm/, Retrieved Thu, 02 May 2024 12:14:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297506, Retrieved Thu, 02 May 2024 12:14:52 +0000

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No (this computation is public)

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Estimated Impact

115

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2016-12-01 10:04:14] [2322cf848a5cbdeb3105c2829b69db5d] [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=297506&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=297506&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297506&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	0.868183	5.1362	5e-06
2	0.688927	4.0757	0.000125
3	0.476591	2.8195	0.003932
4	0.250128	1.4798	0.073939
5	0.020685	0.1224	0.451652
6	-0.167476	-0.9908	0.164291
7	-0.283894	-1.6795	0.050977
8	-0.343292	-2.0309	0.024955
9	-0.369968	-2.1888	0.017688
10	-0.328856	-1.9455	0.029888
11	-0.265077	-1.5682	0.062914
12	-0.192028	-1.1361	0.131827
13	-0.133816	-0.7917	0.216945
14	-0.091786	-0.543	0.295281
15	-0.060724	-0.3592	0.360784

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.868183 & 5.1362 & 5e-06 \tabularnewline
2 & 0.688927 & 4.0757 & 0.000125 \tabularnewline
3 & 0.476591 & 2.8195 & 0.003932 \tabularnewline
4 & 0.250128 & 1.4798 & 0.073939 \tabularnewline
5 & 0.020685 & 0.1224 & 0.451652 \tabularnewline
6 & -0.167476 & -0.9908 & 0.164291 \tabularnewline
7 & -0.283894 & -1.6795 & 0.050977 \tabularnewline
8 & -0.343292 & -2.0309 & 0.024955 \tabularnewline
9 & -0.369968 & -2.1888 & 0.017688 \tabularnewline
10 & -0.328856 & -1.9455 & 0.029888 \tabularnewline
11 & -0.265077 & -1.5682 & 0.062914 \tabularnewline
12 & -0.192028 & -1.1361 & 0.131827 \tabularnewline
13 & -0.133816 & -0.7917 & 0.216945 \tabularnewline
14 & -0.091786 & -0.543 & 0.295281 \tabularnewline
15 & -0.060724 & -0.3592 & 0.360784 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297506&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]0.868183[/C][C]5.1362[/C][C]5e-06[/C][/ROW]
[ROW][C]2[/C][C]0.688927[/C][C]4.0757[/C][C]0.000125[/C][/ROW]
[ROW][C]3[/C][C]0.476591[/C][C]2.8195[/C][C]0.003932[/C][/ROW]
[ROW][C]4[/C][C]0.250128[/C][C]1.4798[/C][C]0.073939[/C][/ROW]
[ROW][C]5[/C][C]0.020685[/C][C]0.1224[/C][C]0.451652[/C][/ROW]
[ROW][C]6[/C][C]-0.167476[/C][C]-0.9908[/C][C]0.164291[/C][/ROW]
[ROW][C]7[/C][C]-0.283894[/C][C]-1.6795[/C][C]0.050977[/C][/ROW]
[ROW][C]8[/C][C]-0.343292[/C][C]-2.0309[/C][C]0.024955[/C][/ROW]
[ROW][C]9[/C][C]-0.369968[/C][C]-2.1888[/C][C]0.017688[/C][/ROW]
[ROW][C]10[/C][C]-0.328856[/C][C]-1.9455[/C][C]0.029888[/C][/ROW]
[ROW][C]11[/C][C]-0.265077[/C][C]-1.5682[/C][C]0.062914[/C][/ROW]
[ROW][C]12[/C][C]-0.192028[/C][C]-1.1361[/C][C]0.131827[/C][/ROW]
[ROW][C]13[/C][C]-0.133816[/C][C]-0.7917[/C][C]0.216945[/C][/ROW]
[ROW][C]14[/C][C]-0.091786[/C][C]-0.543[/C][C]0.295281[/C][/ROW]
[ROW][C]15[/C][C]-0.060724[/C][C]-0.3592[/C][C]0.360784[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297506&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297506&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	0.868183	5.1362	5e-06
2	0.688927	4.0757	0.000125
3	0.476591	2.8195	0.003932
4	0.250128	1.4798	0.073939
5	0.020685	0.1224	0.451652
6	-0.167476	-0.9908	0.164291
7	-0.283894	-1.6795	0.050977
8	-0.343292	-2.0309	0.024955
9	-0.369968	-2.1888	0.017688
10	-0.328856	-1.9455	0.029888
11	-0.265077	-1.5682	0.062914
12	-0.192028	-1.1361	0.131827
13	-0.133816	-0.7917	0.216945
14	-0.091786	-0.543	0.295281
15	-0.060724	-0.3592	0.360784

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.868183	5.1362	5e-06
2	-0.263204	-1.5571	0.064218
3	-0.220076	-1.302	0.100712
4	-0.177996	-1.053	0.149769
5	-0.181389	-1.0731	0.145282
6	-0.025793	-0.1526	0.439797
7	0.084229	0.4983	0.310692
8	0.00292	0.0173	0.493159
9	-0.100289	-0.5933	0.278392
10	0.098605	0.5834	0.281697
11	-0.064732	-0.383	0.352032
12	-0.042352	-0.2506	0.401809
13	-0.077539	-0.4587	0.324632
14	-0.079166	-0.4684	0.321219
15	-0.012996	-0.0769	0.469577

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.868183 & 5.1362 & 5e-06 \tabularnewline
2 & -0.263204 & -1.5571 & 0.064218 \tabularnewline
3 & -0.220076 & -1.302 & 0.100712 \tabularnewline
4 & -0.177996 & -1.053 & 0.149769 \tabularnewline
5 & -0.181389 & -1.0731 & 0.145282 \tabularnewline
6 & -0.025793 & -0.1526 & 0.439797 \tabularnewline
7 & 0.084229 & 0.4983 & 0.310692 \tabularnewline
8 & 0.00292 & 0.0173 & 0.493159 \tabularnewline
9 & -0.100289 & -0.5933 & 0.278392 \tabularnewline
10 & 0.098605 & 0.5834 & 0.281697 \tabularnewline
11 & -0.064732 & -0.383 & 0.352032 \tabularnewline
12 & -0.042352 & -0.2506 & 0.401809 \tabularnewline
13 & -0.077539 & -0.4587 & 0.324632 \tabularnewline
14 & -0.079166 & -0.4684 & 0.321219 \tabularnewline
15 & -0.012996 & -0.0769 & 0.469577 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297506&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]0.868183[/C][C]5.1362[/C][C]5e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.263204[/C][C]-1.5571[/C][C]0.064218[/C][/ROW]
[ROW][C]3[/C][C]-0.220076[/C][C]-1.302[/C][C]0.100712[/C][/ROW]
[ROW][C]4[/C][C]-0.177996[/C][C]-1.053[/C][C]0.149769[/C][/ROW]
[ROW][C]5[/C][C]-0.181389[/C][C]-1.0731[/C][C]0.145282[/C][/ROW]
[ROW][C]6[/C][C]-0.025793[/C][C]-0.1526[/C][C]0.439797[/C][/ROW]
[ROW][C]7[/C][C]0.084229[/C][C]0.4983[/C][C]0.310692[/C][/ROW]
[ROW][C]8[/C][C]0.00292[/C][C]0.0173[/C][C]0.493159[/C][/ROW]
[ROW][C]9[/C][C]-0.100289[/C][C]-0.5933[/C][C]0.278392[/C][/ROW]
[ROW][C]10[/C][C]0.098605[/C][C]0.5834[/C][C]0.281697[/C][/ROW]
[ROW][C]11[/C][C]-0.064732[/C][C]-0.383[/C][C]0.352032[/C][/ROW]
[ROW][C]12[/C][C]-0.042352[/C][C]-0.2506[/C][C]0.401809[/C][/ROW]
[ROW][C]13[/C][C]-0.077539[/C][C]-0.4587[/C][C]0.324632[/C][/ROW]
[ROW][C]14[/C][C]-0.079166[/C][C]-0.4684[/C][C]0.321219[/C][/ROW]
[ROW][C]15[/C][C]-0.012996[/C][C]-0.0769[/C][C]0.469577[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297506&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297506&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	0.868183	5.1362	5e-06
2	-0.263204	-1.5571	0.064218
3	-0.220076	-1.302	0.100712
4	-0.177996	-1.053	0.149769
5	-0.181389	-1.0731	0.145282
6	-0.025793	-0.1526	0.439797
7	0.084229	0.4983	0.310692
8	0.00292	0.0173	0.493159
9	-0.100289	-0.5933	0.278392
10	0.098605	0.5834	0.281697
11	-0.064732	-0.383	0.352032
12	-0.042352	-0.2506	0.401809
13	-0.077539	-0.4587	0.324632
14	-0.079166	-0.4684	0.321219
15	-0.012996	-0.0769	0.469577

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 = 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