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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 15 Dec 2011 03:05:42 -0500

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/2011/Dec/15/t1323936576ne2qxg3w43greqh.htm/, Retrieved Thu, 09 May 2024 00:22:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=155290, Retrieved Thu, 09 May 2024 00:22:25 +0000

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Estimated Impact

137

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-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2011-12-15 08:05:42] [51aabe75794be7f34bed5d3096a085df] [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	'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=155290&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=155290&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155290&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	0.895989	5.6667	1e-06
2	0.760851	4.812	1.1e-05
3	0.610462	3.8609	0.000202
4	0.458993	2.9029	0.002994
5	0.234991	1.4862	0.072532
6	0.052413	0.3315	0.371003
7	-0.104237	-0.6593	0.256755
8	-0.230965	-1.4607	0.075948
9	-0.38814	-2.4548	0.009271
10	-0.480893	-3.0414	0.002072
11	-0.542497	-3.4311	0.000705
12	-0.554174	-3.5049	0.000571
13	-0.565672	-3.5776	0.000463
14	-0.527539	-3.3365	0.00092
15	-0.475249	-3.0057	0.00228
16	-0.38146	-2.4126	0.010259

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.895989 & 5.6667 & 1e-06 \tabularnewline
2 & 0.760851 & 4.812 & 1.1e-05 \tabularnewline
3 & 0.610462 & 3.8609 & 0.000202 \tabularnewline
4 & 0.458993 & 2.9029 & 0.002994 \tabularnewline
5 & 0.234991 & 1.4862 & 0.072532 \tabularnewline
6 & 0.052413 & 0.3315 & 0.371003 \tabularnewline
7 & -0.104237 & -0.6593 & 0.256755 \tabularnewline
8 & -0.230965 & -1.4607 & 0.075948 \tabularnewline
9 & -0.38814 & -2.4548 & 0.009271 \tabularnewline
10 & -0.480893 & -3.0414 & 0.002072 \tabularnewline
11 & -0.542497 & -3.4311 & 0.000705 \tabularnewline
12 & -0.554174 & -3.5049 & 0.000571 \tabularnewline
13 & -0.565672 & -3.5776 & 0.000463 \tabularnewline
14 & -0.527539 & -3.3365 & 0.00092 \tabularnewline
15 & -0.475249 & -3.0057 & 0.00228 \tabularnewline
16 & -0.38146 & -2.4126 & 0.010259 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155290&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]0.895989[/C][C]5.6667[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.760851[/C][C]4.812[/C][C]1.1e-05[/C][/ROW]
[ROW][C]3[/C][C]0.610462[/C][C]3.8609[/C][C]0.000202[/C][/ROW]
[ROW][C]4[/C][C]0.458993[/C][C]2.9029[/C][C]0.002994[/C][/ROW]
[ROW][C]5[/C][C]0.234991[/C][C]1.4862[/C][C]0.072532[/C][/ROW]
[ROW][C]6[/C][C]0.052413[/C][C]0.3315[/C][C]0.371003[/C][/ROW]
[ROW][C]7[/C][C]-0.104237[/C][C]-0.6593[/C][C]0.256755[/C][/ROW]
[ROW][C]8[/C][C]-0.230965[/C][C]-1.4607[/C][C]0.075948[/C][/ROW]
[ROW][C]9[/C][C]-0.38814[/C][C]-2.4548[/C][C]0.009271[/C][/ROW]
[ROW][C]10[/C][C]-0.480893[/C][C]-3.0414[/C][C]0.002072[/C][/ROW]
[ROW][C]11[/C][C]-0.542497[/C][C]-3.4311[/C][C]0.000705[/C][/ROW]
[ROW][C]12[/C][C]-0.554174[/C][C]-3.5049[/C][C]0.000571[/C][/ROW]
[ROW][C]13[/C][C]-0.565672[/C][C]-3.5776[/C][C]0.000463[/C][/ROW]
[ROW][C]14[/C][C]-0.527539[/C][C]-3.3365[/C][C]0.00092[/C][/ROW]
[ROW][C]15[/C][C]-0.475249[/C][C]-3.0057[/C][C]0.00228[/C][/ROW]
[ROW][C]16[/C][C]-0.38146[/C][C]-2.4126[/C][C]0.010259[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155290&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155290&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	0.895989	5.6667	1e-06
2	0.760851	4.812	1.1e-05
3	0.610462	3.8609	0.000202
4	0.458993	2.9029	0.002994
5	0.234991	1.4862	0.072532
6	0.052413	0.3315	0.371003
7	-0.104237	-0.6593	0.256755
8	-0.230965	-1.4607	0.075948
9	-0.38814	-2.4548	0.009271
10	-0.480893	-3.0414	0.002072
11	-0.542497	-3.4311	0.000705
12	-0.554174	-3.5049	0.000571
13	-0.565672	-3.5776	0.000463
14	-0.527539	-3.3365	0.00092
15	-0.475249	-3.0057	0.00228
16	-0.38146	-2.4126	0.010259

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.895989	5.6667	1e-06
2	-0.212701	-1.3452	0.093062
3	-0.136365	-0.8624	0.196792
4	-0.082955	-0.5247	0.30136
5	-0.497187	-3.1445	0.001567
6	0.167444	1.059	0.147974
7	-0.076974	-0.4868	0.314518
8	-0.075938	-0.4803	0.316823
9	-0.243395	-1.5394	0.065795
10	0.038427	0.243	0.404611
11	-0.104645	-0.6618	0.255937
12	0.058524	0.3701	0.356615
13	-0.046023	-0.2911	0.38625
14	-0.108088	-0.6836	0.249082
15	-0.04439	-0.2807	0.390176
16	0.05792	0.3663	0.35803

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.895989 & 5.6667 & 1e-06 \tabularnewline
2 & -0.212701 & -1.3452 & 0.093062 \tabularnewline
3 & -0.136365 & -0.8624 & 0.196792 \tabularnewline
4 & -0.082955 & -0.5247 & 0.30136 \tabularnewline
5 & -0.497187 & -3.1445 & 0.001567 \tabularnewline
6 & 0.167444 & 1.059 & 0.147974 \tabularnewline
7 & -0.076974 & -0.4868 & 0.314518 \tabularnewline
8 & -0.075938 & -0.4803 & 0.316823 \tabularnewline
9 & -0.243395 & -1.5394 & 0.065795 \tabularnewline
10 & 0.038427 & 0.243 & 0.404611 \tabularnewline
11 & -0.104645 & -0.6618 & 0.255937 \tabularnewline
12 & 0.058524 & 0.3701 & 0.356615 \tabularnewline
13 & -0.046023 & -0.2911 & 0.38625 \tabularnewline
14 & -0.108088 & -0.6836 & 0.249082 \tabularnewline
15 & -0.04439 & -0.2807 & 0.390176 \tabularnewline
16 & 0.05792 & 0.3663 & 0.35803 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155290&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]0.895989[/C][C]5.6667[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.212701[/C][C]-1.3452[/C][C]0.093062[/C][/ROW]
[ROW][C]3[/C][C]-0.136365[/C][C]-0.8624[/C][C]0.196792[/C][/ROW]
[ROW][C]4[/C][C]-0.082955[/C][C]-0.5247[/C][C]0.30136[/C][/ROW]
[ROW][C]5[/C][C]-0.497187[/C][C]-3.1445[/C][C]0.001567[/C][/ROW]
[ROW][C]6[/C][C]0.167444[/C][C]1.059[/C][C]0.147974[/C][/ROW]
[ROW][C]7[/C][C]-0.076974[/C][C]-0.4868[/C][C]0.314518[/C][/ROW]
[ROW][C]8[/C][C]-0.075938[/C][C]-0.4803[/C][C]0.316823[/C][/ROW]
[ROW][C]9[/C][C]-0.243395[/C][C]-1.5394[/C][C]0.065795[/C][/ROW]
[ROW][C]10[/C][C]0.038427[/C][C]0.243[/C][C]0.404611[/C][/ROW]
[ROW][C]11[/C][C]-0.104645[/C][C]-0.6618[/C][C]0.255937[/C][/ROW]
[ROW][C]12[/C][C]0.058524[/C][C]0.3701[/C][C]0.356615[/C][/ROW]
[ROW][C]13[/C][C]-0.046023[/C][C]-0.2911[/C][C]0.38625[/C][/ROW]
[ROW][C]14[/C][C]-0.108088[/C][C]-0.6836[/C][C]0.249082[/C][/ROW]
[ROW][C]15[/C][C]-0.04439[/C][C]-0.2807[/C][C]0.390176[/C][/ROW]
[ROW][C]16[/C][C]0.05792[/C][C]0.3663[/C][C]0.35803[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155290&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155290&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	0.895989	5.6667	1e-06
2	-0.212701	-1.3452	0.093062
3	-0.136365	-0.8624	0.196792
4	-0.082955	-0.5247	0.30136
5	-0.497187	-3.1445	0.001567
6	0.167444	1.059	0.147974
7	-0.076974	-0.4868	0.314518
8	-0.075938	-0.4803	0.316823
9	-0.243395	-1.5394	0.065795
10	0.038427	0.243	0.404611
11	-0.104645	-0.6618	0.255937
12	0.058524	0.3701	0.356615
13	-0.046023	-0.2911	0.38625
14	-0.108088	-0.6836	0.249082
15	-0.04439	-0.2807	0.390176
16	0.05792	0.3663	0.35803

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 = 0 ; par4 = 0 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; 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')

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Input Parameters & R Code