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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 01 Dec 2016 11:20:08 +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/01/t1480587698wmfbtejpg3x7nk5.htm/, Retrieved Wed, 01 May 2024 23:24:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=297511, Retrieved Wed, 01 May 2024 23:24:38 +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] [(Partial) Autocor...] [2016-12-01 10:20:08] [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=297511&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=297511&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297511&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	0.033586	0.1575	0.438132
2	0.171525	0.8045	0.214852
3	0.181466	0.8512	0.201927
4	0.0587	0.2753	0.392818
5	0.191358	0.8975	0.189572
6	-0.150309	-0.705	0.2441
7	0.040803	0.1914	0.42499
8	0.000746	0.0035	0.498621
9	-0.113811	-0.5338	0.299409
10	-0.108424	-0.5086	0.308064
11	-0.078064	-0.3662	0.358875
12	-0.446669	-2.0951	0.023948
13	0.017816	0.0836	0.46708
14	-0.065814	-0.3087	0.380229
15	-0.124769	-0.5852	0.282179

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.033586 & 0.1575 & 0.438132 \tabularnewline
2 & 0.171525 & 0.8045 & 0.214852 \tabularnewline
3 & 0.181466 & 0.8512 & 0.201927 \tabularnewline
4 & 0.0587 & 0.2753 & 0.392818 \tabularnewline
5 & 0.191358 & 0.8975 & 0.189572 \tabularnewline
6 & -0.150309 & -0.705 & 0.2441 \tabularnewline
7 & 0.040803 & 0.1914 & 0.42499 \tabularnewline
8 & 0.000746 & 0.0035 & 0.498621 \tabularnewline
9 & -0.113811 & -0.5338 & 0.299409 \tabularnewline
10 & -0.108424 & -0.5086 & 0.308064 \tabularnewline
11 & -0.078064 & -0.3662 & 0.358875 \tabularnewline
12 & -0.446669 & -2.0951 & 0.023948 \tabularnewline
13 & 0.017816 & 0.0836 & 0.46708 \tabularnewline
14 & -0.065814 & -0.3087 & 0.380229 \tabularnewline
15 & -0.124769 & -0.5852 & 0.282179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297511&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]0.033586[/C][C]0.1575[/C][C]0.438132[/C][/ROW]
[ROW][C]2[/C][C]0.171525[/C][C]0.8045[/C][C]0.214852[/C][/ROW]
[ROW][C]3[/C][C]0.181466[/C][C]0.8512[/C][C]0.201927[/C][/ROW]
[ROW][C]4[/C][C]0.0587[/C][C]0.2753[/C][C]0.392818[/C][/ROW]
[ROW][C]5[/C][C]0.191358[/C][C]0.8975[/C][C]0.189572[/C][/ROW]
[ROW][C]6[/C][C]-0.150309[/C][C]-0.705[/C][C]0.2441[/C][/ROW]
[ROW][C]7[/C][C]0.040803[/C][C]0.1914[/C][C]0.42499[/C][/ROW]
[ROW][C]8[/C][C]0.000746[/C][C]0.0035[/C][C]0.498621[/C][/ROW]
[ROW][C]9[/C][C]-0.113811[/C][C]-0.5338[/C][C]0.299409[/C][/ROW]
[ROW][C]10[/C][C]-0.108424[/C][C]-0.5086[/C][C]0.308064[/C][/ROW]
[ROW][C]11[/C][C]-0.078064[/C][C]-0.3662[/C][C]0.358875[/C][/ROW]
[ROW][C]12[/C][C]-0.446669[/C][C]-2.0951[/C][C]0.023948[/C][/ROW]
[ROW][C]13[/C][C]0.017816[/C][C]0.0836[/C][C]0.46708[/C][/ROW]
[ROW][C]14[/C][C]-0.065814[/C][C]-0.3087[/C][C]0.380229[/C][/ROW]
[ROW][C]15[/C][C]-0.124769[/C][C]-0.5852[/C][C]0.282179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297511&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297511&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	0.033586	0.1575	0.438132
2	0.171525	0.8045	0.214852
3	0.181466	0.8512	0.201927
4	0.0587	0.2753	0.392818
5	0.191358	0.8975	0.189572
6	-0.150309	-0.705	0.2441
7	0.040803	0.1914	0.42499
8	0.000746	0.0035	0.498621
9	-0.113811	-0.5338	0.299409
10	-0.108424	-0.5086	0.308064
11	-0.078064	-0.3662	0.358875
12	-0.446669	-2.0951	0.023948
13	0.017816	0.0836	0.46708
14	-0.065814	-0.3087	0.380229
15	-0.124769	-0.5852	0.282179

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.033586	0.1575	0.438132
2	0.170589	0.8001	0.216095
3	0.176282	0.8268	0.208604
4	0.026353	0.1236	0.451374
5	0.139888	0.6561	0.259272
6	-0.210288	-0.9863	0.167345
7	-0.024155	-0.1133	0.455412
8	-0.006989	-0.0328	0.487073
9	-0.078639	-0.3689	0.357882
10	-0.130484	-0.612	0.273398
11	0.013226	0.062	0.475548
12	-0.480371	-2.2531	0.017278
13	0.13948	0.6542	0.259876
14	0.12703	0.5958	0.278687
15	0.006234	0.0292	0.488469

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.033586 & 0.1575 & 0.438132 \tabularnewline
2 & 0.170589 & 0.8001 & 0.216095 \tabularnewline
3 & 0.176282 & 0.8268 & 0.208604 \tabularnewline
4 & 0.026353 & 0.1236 & 0.451374 \tabularnewline
5 & 0.139888 & 0.6561 & 0.259272 \tabularnewline
6 & -0.210288 & -0.9863 & 0.167345 \tabularnewline
7 & -0.024155 & -0.1133 & 0.455412 \tabularnewline
8 & -0.006989 & -0.0328 & 0.487073 \tabularnewline
9 & -0.078639 & -0.3689 & 0.357882 \tabularnewline
10 & -0.130484 & -0.612 & 0.273398 \tabularnewline
11 & 0.013226 & 0.062 & 0.475548 \tabularnewline
12 & -0.480371 & -2.2531 & 0.017278 \tabularnewline
13 & 0.13948 & 0.6542 & 0.259876 \tabularnewline
14 & 0.12703 & 0.5958 & 0.278687 \tabularnewline
15 & 0.006234 & 0.0292 & 0.488469 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=297511&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]0.033586[/C][C]0.1575[/C][C]0.438132[/C][/ROW]
[ROW][C]2[/C][C]0.170589[/C][C]0.8001[/C][C]0.216095[/C][/ROW]
[ROW][C]3[/C][C]0.176282[/C][C]0.8268[/C][C]0.208604[/C][/ROW]
[ROW][C]4[/C][C]0.026353[/C][C]0.1236[/C][C]0.451374[/C][/ROW]
[ROW][C]5[/C][C]0.139888[/C][C]0.6561[/C][C]0.259272[/C][/ROW]
[ROW][C]6[/C][C]-0.210288[/C][C]-0.9863[/C][C]0.167345[/C][/ROW]
[ROW][C]7[/C][C]-0.024155[/C][C]-0.1133[/C][C]0.455412[/C][/ROW]
[ROW][C]8[/C][C]-0.006989[/C][C]-0.0328[/C][C]0.487073[/C][/ROW]
[ROW][C]9[/C][C]-0.078639[/C][C]-0.3689[/C][C]0.357882[/C][/ROW]
[ROW][C]10[/C][C]-0.130484[/C][C]-0.612[/C][C]0.273398[/C][/ROW]
[ROW][C]11[/C][C]0.013226[/C][C]0.062[/C][C]0.475548[/C][/ROW]
[ROW][C]12[/C][C]-0.480371[/C][C]-2.2531[/C][C]0.017278[/C][/ROW]
[ROW][C]13[/C][C]0.13948[/C][C]0.6542[/C][C]0.259876[/C][/ROW]
[ROW][C]14[/C][C]0.12703[/C][C]0.5958[/C][C]0.278687[/C][/ROW]
[ROW][C]15[/C][C]0.006234[/C][C]0.0292[/C][C]0.488469[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=297511&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=297511&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	0.033586	0.1575	0.438132
2	0.170589	0.8001	0.216095
3	0.176282	0.8268	0.208604
4	0.026353	0.1236	0.451374
5	0.139888	0.6561	0.259272
6	-0.210288	-0.9863	0.167345
7	-0.024155	-0.1133	0.455412
8	-0.006989	-0.0328	0.487073
9	-0.078639	-0.3689	0.357882
10	-0.130484	-0.612	0.273398
11	0.013226	0.062	0.475548
12	-0.480371	-2.2531	0.017278
13	0.13948	0.6542	0.259876
14	0.12703	0.5958	0.278687
15	0.006234	0.0292	0.488469

Figure 1

PNG link

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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Input Parameters & R Code