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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 14 Dec 2015 22:46:34 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/14/t1450133242w6ltgukgsqdyed2.htm/, Retrieved Thu, 31 Oct 2024 23:04:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286421, Retrieved Thu, 31 Oct 2024 23:04:18 +0000

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-       [(Partial) Autocorrelation Function] [paper35] [2015-12-14 22:46:34] [1e67203134127d491eaf7d256835640d] [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	'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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286421&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]2 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=286421&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286421&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.362259	2.017	0.026215
2	-0.186443	-1.0381	0.153633
3	-0.239563	-1.3338	0.095989
4	-0.177242	-0.9868	0.16568
5	-0.256755	-1.4295	0.081424
6	-0.164435	-0.9155	0.183489
7	-0.188999	-1.0523	0.150397
8	-0.085577	-0.4765	0.318539
9	0.092391	0.5144	0.305307
10	0.314775	1.7526	0.044779
11	0.291616	1.6236	0.057289
12	0.193931	1.0798	0.144288
13	-0.026203	-0.1459	0.442476
14	-0.249693	-1.3902	0.08718
15	-0.215473	-1.1997	0.119672

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.362259 & 2.017 & 0.026215 \tabularnewline
2 & -0.186443 & -1.0381 & 0.153633 \tabularnewline
3 & -0.239563 & -1.3338 & 0.095989 \tabularnewline
4 & -0.177242 & -0.9868 & 0.16568 \tabularnewline
5 & -0.256755 & -1.4295 & 0.081424 \tabularnewline
6 & -0.164435 & -0.9155 & 0.183489 \tabularnewline
7 & -0.188999 & -1.0523 & 0.150397 \tabularnewline
8 & -0.085577 & -0.4765 & 0.318539 \tabularnewline
9 & 0.092391 & 0.5144 & 0.305307 \tabularnewline
10 & 0.314775 & 1.7526 & 0.044779 \tabularnewline
11 & 0.291616 & 1.6236 & 0.057289 \tabularnewline
12 & 0.193931 & 1.0798 & 0.144288 \tabularnewline
13 & -0.026203 & -0.1459 & 0.442476 \tabularnewline
14 & -0.249693 & -1.3902 & 0.08718 \tabularnewline
15 & -0.215473 & -1.1997 & 0.119672 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286421&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]0.362259[/C][C]2.017[/C][C]0.026215[/C][/ROW]
[ROW][C]2[/C][C]-0.186443[/C][C]-1.0381[/C][C]0.153633[/C][/ROW]
[ROW][C]3[/C][C]-0.239563[/C][C]-1.3338[/C][C]0.095989[/C][/ROW]
[ROW][C]4[/C][C]-0.177242[/C][C]-0.9868[/C][C]0.16568[/C][/ROW]
[ROW][C]5[/C][C]-0.256755[/C][C]-1.4295[/C][C]0.081424[/C][/ROW]
[ROW][C]6[/C][C]-0.164435[/C][C]-0.9155[/C][C]0.183489[/C][/ROW]
[ROW][C]7[/C][C]-0.188999[/C][C]-1.0523[/C][C]0.150397[/C][/ROW]
[ROW][C]8[/C][C]-0.085577[/C][C]-0.4765[/C][C]0.318539[/C][/ROW]
[ROW][C]9[/C][C]0.092391[/C][C]0.5144[/C][C]0.305307[/C][/ROW]
[ROW][C]10[/C][C]0.314775[/C][C]1.7526[/C][C]0.044779[/C][/ROW]
[ROW][C]11[/C][C]0.291616[/C][C]1.6236[/C][C]0.057289[/C][/ROW]
[ROW][C]12[/C][C]0.193931[/C][C]1.0798[/C][C]0.144288[/C][/ROW]
[ROW][C]13[/C][C]-0.026203[/C][C]-0.1459[/C][C]0.442476[/C][/ROW]
[ROW][C]14[/C][C]-0.249693[/C][C]-1.3902[/C][C]0.08718[/C][/ROW]
[ROW][C]15[/C][C]-0.215473[/C][C]-1.1997[/C][C]0.119672[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286421&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286421&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	0.362259	2.017	0.026215
2	-0.186443	-1.0381	0.153633
3	-0.239563	-1.3338	0.095989
4	-0.177242	-0.9868	0.16568
5	-0.256755	-1.4295	0.081424
6	-0.164435	-0.9155	0.183489
7	-0.188999	-1.0523	0.150397
8	-0.085577	-0.4765	0.318539
9	0.092391	0.5144	0.305307
10	0.314775	1.7526	0.044779
11	0.291616	1.6236	0.057289
12	0.193931	1.0798	0.144288
13	-0.026203	-0.1459	0.442476
14	-0.249693	-1.3902	0.08718
15	-0.215473	-1.1997	0.119672

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.362259	2.017	0.026215
2	-0.365661	-2.0359	0.025191
3	-0.019746	-0.1099	0.456582
4	-0.15905	-0.8856	0.191338
5	-0.274563	-1.5287	0.06824
6	-0.059393	-0.3307	0.371553
7	-0.397485	-2.2131	0.017192
8	-0.101386	-0.5645	0.28824
9	-0.174204	-0.9699	0.169795
10	0.068273	0.3801	0.353221
11	0.004096	0.0228	0.490976
12	0.076657	0.4268	0.336234
13	-0.047782	-0.266	0.395985
14	-0.212755	-1.1846	0.122596
15	0.067557	0.3761	0.354687

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.362259 & 2.017 & 0.026215 \tabularnewline
2 & -0.365661 & -2.0359 & 0.025191 \tabularnewline
3 & -0.019746 & -0.1099 & 0.456582 \tabularnewline
4 & -0.15905 & -0.8856 & 0.191338 \tabularnewline
5 & -0.274563 & -1.5287 & 0.06824 \tabularnewline
6 & -0.059393 & -0.3307 & 0.371553 \tabularnewline
7 & -0.397485 & -2.2131 & 0.017192 \tabularnewline
8 & -0.101386 & -0.5645 & 0.28824 \tabularnewline
9 & -0.174204 & -0.9699 & 0.169795 \tabularnewline
10 & 0.068273 & 0.3801 & 0.353221 \tabularnewline
11 & 0.004096 & 0.0228 & 0.490976 \tabularnewline
12 & 0.076657 & 0.4268 & 0.336234 \tabularnewline
13 & -0.047782 & -0.266 & 0.395985 \tabularnewline
14 & -0.212755 & -1.1846 & 0.122596 \tabularnewline
15 & 0.067557 & 0.3761 & 0.354687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286421&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]0.362259[/C][C]2.017[/C][C]0.026215[/C][/ROW]
[ROW][C]2[/C][C]-0.365661[/C][C]-2.0359[/C][C]0.025191[/C][/ROW]
[ROW][C]3[/C][C]-0.019746[/C][C]-0.1099[/C][C]0.456582[/C][/ROW]
[ROW][C]4[/C][C]-0.15905[/C][C]-0.8856[/C][C]0.191338[/C][/ROW]
[ROW][C]5[/C][C]-0.274563[/C][C]-1.5287[/C][C]0.06824[/C][/ROW]
[ROW][C]6[/C][C]-0.059393[/C][C]-0.3307[/C][C]0.371553[/C][/ROW]
[ROW][C]7[/C][C]-0.397485[/C][C]-2.2131[/C][C]0.017192[/C][/ROW]
[ROW][C]8[/C][C]-0.101386[/C][C]-0.5645[/C][C]0.28824[/C][/ROW]
[ROW][C]9[/C][C]-0.174204[/C][C]-0.9699[/C][C]0.169795[/C][/ROW]
[ROW][C]10[/C][C]0.068273[/C][C]0.3801[/C][C]0.353221[/C][/ROW]
[ROW][C]11[/C][C]0.004096[/C][C]0.0228[/C][C]0.490976[/C][/ROW]
[ROW][C]12[/C][C]0.076657[/C][C]0.4268[/C][C]0.336234[/C][/ROW]
[ROW][C]13[/C][C]-0.047782[/C][C]-0.266[/C][C]0.395985[/C][/ROW]
[ROW][C]14[/C][C]-0.212755[/C][C]-1.1846[/C][C]0.122596[/C][/ROW]
[ROW][C]15[/C][C]0.067557[/C][C]0.3761[/C][C]0.354687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286421&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286421&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	0.362259	2.017	0.026215
2	-0.365661	-2.0359	0.025191
3	-0.019746	-0.1099	0.456582
4	-0.15905	-0.8856	0.191338
5	-0.274563	-1.5287	0.06824
6	-0.059393	-0.3307	0.371553
7	-0.397485	-2.2131	0.017192
8	-0.101386	-0.5645	0.28824
9	-0.174204	-0.9699	0.169795
10	0.068273	0.3801	0.353221
11	0.004096	0.0228	0.490976
12	0.076657	0.4268	0.336234
13	-0.047782	-0.266	0.395985
14	-0.212755	-1.1846	0.122596
15	0.067557	0.3761	0.354687

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):

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 1 ; 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,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')

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Input Parameters & R Code