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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Oct 2014 16:58:16 +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/2014/Oct/19/t141373434492su9ulk9ktl4sh.htm/, Retrieved Sat, 11 May 2024 06:14:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243691, Retrieved Sat, 11 May 2024 06:14:39 +0000

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Original text written by user:

IsPrivate?

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User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [] [2014-10-19 15:58:16] [517bf63cbd197750110a40d4d2cd39d6] [Current]

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Dataseries X:

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Histogram

Boxplots

1,38
1,96
1,36
1,24
1,35
1,23
1,09
1,08
1,33
1,35
1,38
1,5
1,47
2,09
1,52
1,29
1,52
1,27
1,35
1,29
1,41
1,39
1,45
1,53
1,45
2,11
1,53
1,38
1,54
1,35
1,29
1,33
1,47
1,47
1,54
1,59
1,5
2
1,51
1,4
1,62
1,44
1,29
1,28
1,4
1,39
1,46
1,49
1,45
2,05
1,59
1,42
1,73
1,39
1,23
1,37
1,51
1,47
1,5
1,54
1,54
2,15
1,62
1,4
1,65
1,49
1,45
1,45
1,51
1,48
1,56
1,57
1,57
2,28
1,7
1,56
1,8
1,56
1,51
1,46
1,51
1,55
1,57
1,64
1,58
2,16
1,77
1,54
1,64
1,53
1,49
1,43
1,52
1,56
1,59
1,64

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	'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243691&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243691&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243691&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.273835	2.683	0.004296
2	0.135548	1.3281	0.093649
3	0.24795	2.4294	0.008492
4	-0.052642	-0.5158	0.303594
5	-0.146387	-1.4343	0.07737
6	-0.258389	-2.5317	0.006488
7	-0.170622	-1.6717	0.048916
8	-0.096155	-0.9421	0.174248

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.273835 & 2.683 & 0.004296 \tabularnewline
2 & 0.135548 & 1.3281 & 0.093649 \tabularnewline
3 & 0.24795 & 2.4294 & 0.008492 \tabularnewline
4 & -0.052642 & -0.5158 & 0.303594 \tabularnewline
5 & -0.146387 & -1.4343 & 0.07737 \tabularnewline
6 & -0.258389 & -2.5317 & 0.006488 \tabularnewline
7 & -0.170622 & -1.6717 & 0.048916 \tabularnewline
8 & -0.096155 & -0.9421 & 0.174248 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243691&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]0.273835[/C][C]2.683[/C][C]0.004296[/C][/ROW]
[ROW][C]2[/C][C]0.135548[/C][C]1.3281[/C][C]0.093649[/C][/ROW]
[ROW][C]3[/C][C]0.24795[/C][C]2.4294[/C][C]0.008492[/C][/ROW]
[ROW][C]4[/C][C]-0.052642[/C][C]-0.5158[/C][C]0.303594[/C][/ROW]
[ROW][C]5[/C][C]-0.146387[/C][C]-1.4343[/C][C]0.07737[/C][/ROW]
[ROW][C]6[/C][C]-0.258389[/C][C]-2.5317[/C][C]0.006488[/C][/ROW]
[ROW][C]7[/C][C]-0.170622[/C][C]-1.6717[/C][C]0.048916[/C][/ROW]
[ROW][C]8[/C][C]-0.096155[/C][C]-0.9421[/C][C]0.174248[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243691&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243691&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	0.273835	2.683	0.004296
2	0.135548	1.3281	0.093649
3	0.24795	2.4294	0.008492
4	-0.052642	-0.5158	0.303594
5	-0.146387	-1.4343	0.07737
6	-0.258389	-2.5317	0.006488
7	-0.170622	-1.6717	0.048916
8	-0.096155	-0.9421	0.174248

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.273835	2.683	0.004296
2	0.065471	0.6415	0.261368
3	0.212078	2.0779	0.020192
4	-0.195815	-1.9186	0.029003
5	-0.137523	-1.3474	0.090505
6	-0.270054	-2.646	0.00476
7	0.030337	0.2972	0.383463
8	0.041973	0.4112	0.340905

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.273835 & 2.683 & 0.004296 \tabularnewline
2 & 0.065471 & 0.6415 & 0.261368 \tabularnewline
3 & 0.212078 & 2.0779 & 0.020192 \tabularnewline
4 & -0.195815 & -1.9186 & 0.029003 \tabularnewline
5 & -0.137523 & -1.3474 & 0.090505 \tabularnewline
6 & -0.270054 & -2.646 & 0.00476 \tabularnewline
7 & 0.030337 & 0.2972 & 0.383463 \tabularnewline
8 & 0.041973 & 0.4112 & 0.340905 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243691&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]0.273835[/C][C]2.683[/C][C]0.004296[/C][/ROW]
[ROW][C]2[/C][C]0.065471[/C][C]0.6415[/C][C]0.261368[/C][/ROW]
[ROW][C]3[/C][C]0.212078[/C][C]2.0779[/C][C]0.020192[/C][/ROW]
[ROW][C]4[/C][C]-0.195815[/C][C]-1.9186[/C][C]0.029003[/C][/ROW]
[ROW][C]5[/C][C]-0.137523[/C][C]-1.3474[/C][C]0.090505[/C][/ROW]
[ROW][C]6[/C][C]-0.270054[/C][C]-2.646[/C][C]0.00476[/C][/ROW]
[ROW][C]7[/C][C]0.030337[/C][C]0.2972[/C][C]0.383463[/C][/ROW]
[ROW][C]8[/C][C]0.041973[/C][C]0.4112[/C][C]0.340905[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243691&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243691&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	0.273835	2.683	0.004296
2	0.065471	0.6415	0.261368
3	0.212078	2.0779	0.020192
4	-0.195815	-1.9186	0.029003
5	-0.137523	-1.3474	0.090505
6	-0.270054	-2.646	0.00476
7	0.030337	0.2972	0.383463
8	0.041973	0.4112	0.340905

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 = 8 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 8 ; 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)
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,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),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,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code