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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Oct 2014 21:37:17 +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/2014/Oct/19/t141375108721cs1hc63lvkqzc.htm/, Retrieved Sun, 12 May 2024 05:52:15 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243784, Retrieved Sun, 12 May 2024 05:52:15 +0000

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-       [(Partial) Autocorrelation Function] [] [2014-10-19 20:37:17] [ce030e64aa9efcfbf032d2aff4cc4bf0] [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=243784&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=243784&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243784&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	0.229914	1.9373	0.028345
2	0.00933	0.0786	0.46878
3	-0.091546	-0.7714	0.22152
4	-0.172234	-1.4513	0.075554
5	-0.079288	-0.6681	0.25312
6	-0.129235	-1.089	0.139928
7	-0.20818	-1.7542	0.041859
8	-0.050075	-0.4219	0.337172
9	0.01393	0.1174	0.453446
10	0.057793	0.487	0.313889
11	0.267594	2.2548	0.013616
12	0.042266	0.3561	0.361397
13	0.06141	0.5174	0.303226
14	-0.091405	-0.7702	0.221872
15	-0.132786	-1.1189	0.133482
16	-0.057815	-0.4872	0.313824
17	-0.011554	-0.0974	0.461358
18	-0.049128	-0.414	0.340076

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.229914 & 1.9373 & 0.028345 \tabularnewline
2 & 0.00933 & 0.0786 & 0.46878 \tabularnewline
3 & -0.091546 & -0.7714 & 0.22152 \tabularnewline
4 & -0.172234 & -1.4513 & 0.075554 \tabularnewline
5 & -0.079288 & -0.6681 & 0.25312 \tabularnewline
6 & -0.129235 & -1.089 & 0.139928 \tabularnewline
7 & -0.20818 & -1.7542 & 0.041859 \tabularnewline
8 & -0.050075 & -0.4219 & 0.337172 \tabularnewline
9 & 0.01393 & 0.1174 & 0.453446 \tabularnewline
10 & 0.057793 & 0.487 & 0.313889 \tabularnewline
11 & 0.267594 & 2.2548 & 0.013616 \tabularnewline
12 & 0.042266 & 0.3561 & 0.361397 \tabularnewline
13 & 0.06141 & 0.5174 & 0.303226 \tabularnewline
14 & -0.091405 & -0.7702 & 0.221872 \tabularnewline
15 & -0.132786 & -1.1189 & 0.133482 \tabularnewline
16 & -0.057815 & -0.4872 & 0.313824 \tabularnewline
17 & -0.011554 & -0.0974 & 0.461358 \tabularnewline
18 & -0.049128 & -0.414 & 0.340076 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243784&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]0.229914[/C][C]1.9373[/C][C]0.028345[/C][/ROW]
[ROW][C]2[/C][C]0.00933[/C][C]0.0786[/C][C]0.46878[/C][/ROW]
[ROW][C]3[/C][C]-0.091546[/C][C]-0.7714[/C][C]0.22152[/C][/ROW]
[ROW][C]4[/C][C]-0.172234[/C][C]-1.4513[/C][C]0.075554[/C][/ROW]
[ROW][C]5[/C][C]-0.079288[/C][C]-0.6681[/C][C]0.25312[/C][/ROW]
[ROW][C]6[/C][C]-0.129235[/C][C]-1.089[/C][C]0.139928[/C][/ROW]
[ROW][C]7[/C][C]-0.20818[/C][C]-1.7542[/C][C]0.041859[/C][/ROW]
[ROW][C]8[/C][C]-0.050075[/C][C]-0.4219[/C][C]0.337172[/C][/ROW]
[ROW][C]9[/C][C]0.01393[/C][C]0.1174[/C][C]0.453446[/C][/ROW]
[ROW][C]10[/C][C]0.057793[/C][C]0.487[/C][C]0.313889[/C][/ROW]
[ROW][C]11[/C][C]0.267594[/C][C]2.2548[/C][C]0.013616[/C][/ROW]
[ROW][C]12[/C][C]0.042266[/C][C]0.3561[/C][C]0.361397[/C][/ROW]
[ROW][C]13[/C][C]0.06141[/C][C]0.5174[/C][C]0.303226[/C][/ROW]
[ROW][C]14[/C][C]-0.091405[/C][C]-0.7702[/C][C]0.221872[/C][/ROW]
[ROW][C]15[/C][C]-0.132786[/C][C]-1.1189[/C][C]0.133482[/C][/ROW]
[ROW][C]16[/C][C]-0.057815[/C][C]-0.4872[/C][C]0.313824[/C][/ROW]
[ROW][C]17[/C][C]-0.011554[/C][C]-0.0974[/C][C]0.461358[/C][/ROW]
[ROW][C]18[/C][C]-0.049128[/C][C]-0.414[/C][C]0.340076[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243784&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243784&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	0.229914	1.9373	0.028345
2	0.00933	0.0786	0.46878
3	-0.091546	-0.7714	0.22152
4	-0.172234	-1.4513	0.075554
5	-0.079288	-0.6681	0.25312
6	-0.129235	-1.089	0.139928
7	-0.20818	-1.7542	0.041859
8	-0.050075	-0.4219	0.337172
9	0.01393	0.1174	0.453446
10	0.057793	0.487	0.313889
11	0.267594	2.2548	0.013616
12	0.042266	0.3561	0.361397
13	0.06141	0.5174	0.303226
14	-0.091405	-0.7702	0.221872
15	-0.132786	-1.1189	0.133482
16	-0.057815	-0.4872	0.313824
17	-0.011554	-0.0974	0.461358
18	-0.049128	-0.414	0.340076

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.229914	1.9373	0.028345
2	-0.04596	-0.3873	0.349859
3	-0.088054	-0.742	0.230281
4	-0.138742	-1.1691	0.123145
5	-0.011786	-0.0993	0.460586
6	-0.127953	-1.0781	0.142309
7	-0.19635	-1.6545	0.051223
8	-0.00179	-0.0151	0.494004
9	-0.015195	-0.128	0.449242
10	-0.017108	-0.1442	0.442894
11	0.211435	1.7816	0.039547
12	-0.09298	-0.7835	0.217979
13	0.053012	0.4467	0.328232
14	-0.131798	-1.1106	0.135254
15	-0.038303	-0.3227	0.373918
16	-0.020058	-0.169	0.433133
17	0.045331	0.382	0.351814
18	-0.022015	-0.1855	0.426681

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.229914 & 1.9373 & 0.028345 \tabularnewline
2 & -0.04596 & -0.3873 & 0.349859 \tabularnewline
3 & -0.088054 & -0.742 & 0.230281 \tabularnewline
4 & -0.138742 & -1.1691 & 0.123145 \tabularnewline
5 & -0.011786 & -0.0993 & 0.460586 \tabularnewline
6 & -0.127953 & -1.0781 & 0.142309 \tabularnewline
7 & -0.19635 & -1.6545 & 0.051223 \tabularnewline
8 & -0.00179 & -0.0151 & 0.494004 \tabularnewline
9 & -0.015195 & -0.128 & 0.449242 \tabularnewline
10 & -0.017108 & -0.1442 & 0.442894 \tabularnewline
11 & 0.211435 & 1.7816 & 0.039547 \tabularnewline
12 & -0.09298 & -0.7835 & 0.217979 \tabularnewline
13 & 0.053012 & 0.4467 & 0.328232 \tabularnewline
14 & -0.131798 & -1.1106 & 0.135254 \tabularnewline
15 & -0.038303 & -0.3227 & 0.373918 \tabularnewline
16 & -0.020058 & -0.169 & 0.433133 \tabularnewline
17 & 0.045331 & 0.382 & 0.351814 \tabularnewline
18 & -0.022015 & -0.1855 & 0.426681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243784&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]0.229914[/C][C]1.9373[/C][C]0.028345[/C][/ROW]
[ROW][C]2[/C][C]-0.04596[/C][C]-0.3873[/C][C]0.349859[/C][/ROW]
[ROW][C]3[/C][C]-0.088054[/C][C]-0.742[/C][C]0.230281[/C][/ROW]
[ROW][C]4[/C][C]-0.138742[/C][C]-1.1691[/C][C]0.123145[/C][/ROW]
[ROW][C]5[/C][C]-0.011786[/C][C]-0.0993[/C][C]0.460586[/C][/ROW]
[ROW][C]6[/C][C]-0.127953[/C][C]-1.0781[/C][C]0.142309[/C][/ROW]
[ROW][C]7[/C][C]-0.19635[/C][C]-1.6545[/C][C]0.051223[/C][/ROW]
[ROW][C]8[/C][C]-0.00179[/C][C]-0.0151[/C][C]0.494004[/C][/ROW]
[ROW][C]9[/C][C]-0.015195[/C][C]-0.128[/C][C]0.449242[/C][/ROW]
[ROW][C]10[/C][C]-0.017108[/C][C]-0.1442[/C][C]0.442894[/C][/ROW]
[ROW][C]11[/C][C]0.211435[/C][C]1.7816[/C][C]0.039547[/C][/ROW]
[ROW][C]12[/C][C]-0.09298[/C][C]-0.7835[/C][C]0.217979[/C][/ROW]
[ROW][C]13[/C][C]0.053012[/C][C]0.4467[/C][C]0.328232[/C][/ROW]
[ROW][C]14[/C][C]-0.131798[/C][C]-1.1106[/C][C]0.135254[/C][/ROW]
[ROW][C]15[/C][C]-0.038303[/C][C]-0.3227[/C][C]0.373918[/C][/ROW]
[ROW][C]16[/C][C]-0.020058[/C][C]-0.169[/C][C]0.433133[/C][/ROW]
[ROW][C]17[/C][C]0.045331[/C][C]0.382[/C][C]0.351814[/C][/ROW]
[ROW][C]18[/C][C]-0.022015[/C][C]-0.1855[/C][C]0.426681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243784&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243784&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	0.229914	1.9373	0.028345
2	-0.04596	-0.3873	0.349859
3	-0.088054	-0.742	0.230281
4	-0.138742	-1.1691	0.123145
5	-0.011786	-0.0993	0.460586
6	-0.127953	-1.0781	0.142309
7	-0.19635	-1.6545	0.051223
8	-0.00179	-0.0151	0.494004
9	-0.015195	-0.128	0.449242
10	-0.017108	-0.1442	0.442894
11	0.211435	1.7816	0.039547
12	-0.09298	-0.7835	0.217979
13	0.053012	0.4467	0.328232
14	-0.131798	-1.1106	0.135254
15	-0.038303	-0.3227	0.373918
16	-0.020058	-0.169	0.433133
17	0.045331	0.382	0.351814
18	-0.022015	-0.1855	0.426681

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 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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')

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Input Parameters & R Code