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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 11 Jan 2016 20:22:08 +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/2016/Jan/11/t14525438051nfbe3gmsw11hsw.htm/, Retrieved Tue, 07 May 2024 23:59:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=289701, Retrieved Tue, 07 May 2024 23:59:54 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-01-11 20:22:08] [d1a83db1c928d515dd26931964d56abe] [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=289701&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=289701&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289701&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	0.963295	7.4617	0
2	0.92634	7.1754	0
3	0.89305	6.9175	0
4	0.854727	6.6207	0
5	0.816356	6.3235	0
6	0.76948	5.9604	0
7	0.721459	5.5884	0
8	0.671199	5.1991	1e-06
9	0.617283	4.7815	6e-06
10	0.566673	4.3894	2.3e-05
11	0.513401	3.9768	9.5e-05
12	0.45678	3.5382	0.000392
13	0.403064	3.1221	0.001381
14	0.349309	2.7057	0.00443
15	0.291639	2.259	0.013764
16	0.235898	1.8273	0.036318
17	0.183858	1.4242	0.07979

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.963295 & 7.4617 & 0 \tabularnewline
2 & 0.92634 & 7.1754 & 0 \tabularnewline
3 & 0.89305 & 6.9175 & 0 \tabularnewline
4 & 0.854727 & 6.6207 & 0 \tabularnewline
5 & 0.816356 & 6.3235 & 0 \tabularnewline
6 & 0.76948 & 5.9604 & 0 \tabularnewline
7 & 0.721459 & 5.5884 & 0 \tabularnewline
8 & 0.671199 & 5.1991 & 1e-06 \tabularnewline
9 & 0.617283 & 4.7815 & 6e-06 \tabularnewline
10 & 0.566673 & 4.3894 & 2.3e-05 \tabularnewline
11 & 0.513401 & 3.9768 & 9.5e-05 \tabularnewline
12 & 0.45678 & 3.5382 & 0.000392 \tabularnewline
13 & 0.403064 & 3.1221 & 0.001381 \tabularnewline
14 & 0.349309 & 2.7057 & 0.00443 \tabularnewline
15 & 0.291639 & 2.259 & 0.013764 \tabularnewline
16 & 0.235898 & 1.8273 & 0.036318 \tabularnewline
17 & 0.183858 & 1.4242 & 0.07979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289701&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]0.963295[/C][C]7.4617[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.92634[/C][C]7.1754[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.89305[/C][C]6.9175[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.854727[/C][C]6.6207[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.816356[/C][C]6.3235[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.76948[/C][C]5.9604[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.721459[/C][C]5.5884[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.671199[/C][C]5.1991[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]0.617283[/C][C]4.7815[/C][C]6e-06[/C][/ROW]
[ROW][C]10[/C][C]0.566673[/C][C]4.3894[/C][C]2.3e-05[/C][/ROW]
[ROW][C]11[/C][C]0.513401[/C][C]3.9768[/C][C]9.5e-05[/C][/ROW]
[ROW][C]12[/C][C]0.45678[/C][C]3.5382[/C][C]0.000392[/C][/ROW]
[ROW][C]13[/C][C]0.403064[/C][C]3.1221[/C][C]0.001381[/C][/ROW]
[ROW][C]14[/C][C]0.349309[/C][C]2.7057[/C][C]0.00443[/C][/ROW]
[ROW][C]15[/C][C]0.291639[/C][C]2.259[/C][C]0.013764[/C][/ROW]
[ROW][C]16[/C][C]0.235898[/C][C]1.8273[/C][C]0.036318[/C][/ROW]
[ROW][C]17[/C][C]0.183858[/C][C]1.4242[/C][C]0.07979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289701&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289701&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	0.963295	7.4617	0
2	0.92634	7.1754	0
3	0.89305	6.9175	0
4	0.854727	6.6207	0
5	0.816356	6.3235	0
6	0.76948	5.9604	0
7	0.721459	5.5884	0
8	0.671199	5.1991	1e-06
9	0.617283	4.7815	6e-06
10	0.566673	4.3894	2.3e-05
11	0.513401	3.9768	9.5e-05
12	0.45678	3.5382	0.000392
13	0.403064	3.1221	0.001381
14	0.349309	2.7057	0.00443
15	0.291639	2.259	0.013764
16	0.235898	1.8273	0.036318
17	0.183858	1.4242	0.07979

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.963295	7.4617	0
2	-0.022179	-0.1718	0.432088
3	0.031724	0.2457	0.403365
4	-0.087975	-0.6815	0.249104
5	-0.01807	-0.14	0.444575
6	-0.147283	-1.1409	0.129233
7	-0.0372	-0.2882	0.387111
8	-0.074853	-0.5798	0.282108
9	-0.068379	-0.5297	0.29915
10	0.008715	0.0675	0.473203
11	-0.058197	-0.4508	0.326881
12	-0.07035	-0.5449	0.293911
13	0.000196	0.0015	0.499398
14	-0.029775	-0.2306	0.40919
15	-0.09584	-0.7424	0.230379
16	-0.01381	-0.107	0.457583
17	0.00924	0.0716	0.47159

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.963295 & 7.4617 & 0 \tabularnewline
2 & -0.022179 & -0.1718 & 0.432088 \tabularnewline
3 & 0.031724 & 0.2457 & 0.403365 \tabularnewline
4 & -0.087975 & -0.6815 & 0.249104 \tabularnewline
5 & -0.01807 & -0.14 & 0.444575 \tabularnewline
6 & -0.147283 & -1.1409 & 0.129233 \tabularnewline
7 & -0.0372 & -0.2882 & 0.387111 \tabularnewline
8 & -0.074853 & -0.5798 & 0.282108 \tabularnewline
9 & -0.068379 & -0.5297 & 0.29915 \tabularnewline
10 & 0.008715 & 0.0675 & 0.473203 \tabularnewline
11 & -0.058197 & -0.4508 & 0.326881 \tabularnewline
12 & -0.07035 & -0.5449 & 0.293911 \tabularnewline
13 & 0.000196 & 0.0015 & 0.499398 \tabularnewline
14 & -0.029775 & -0.2306 & 0.40919 \tabularnewline
15 & -0.09584 & -0.7424 & 0.230379 \tabularnewline
16 & -0.01381 & -0.107 & 0.457583 \tabularnewline
17 & 0.00924 & 0.0716 & 0.47159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289701&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]0.963295[/C][C]7.4617[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.022179[/C][C]-0.1718[/C][C]0.432088[/C][/ROW]
[ROW][C]3[/C][C]0.031724[/C][C]0.2457[/C][C]0.403365[/C][/ROW]
[ROW][C]4[/C][C]-0.087975[/C][C]-0.6815[/C][C]0.249104[/C][/ROW]
[ROW][C]5[/C][C]-0.01807[/C][C]-0.14[/C][C]0.444575[/C][/ROW]
[ROW][C]6[/C][C]-0.147283[/C][C]-1.1409[/C][C]0.129233[/C][/ROW]
[ROW][C]7[/C][C]-0.0372[/C][C]-0.2882[/C][C]0.387111[/C][/ROW]
[ROW][C]8[/C][C]-0.074853[/C][C]-0.5798[/C][C]0.282108[/C][/ROW]
[ROW][C]9[/C][C]-0.068379[/C][C]-0.5297[/C][C]0.29915[/C][/ROW]
[ROW][C]10[/C][C]0.008715[/C][C]0.0675[/C][C]0.473203[/C][/ROW]
[ROW][C]11[/C][C]-0.058197[/C][C]-0.4508[/C][C]0.326881[/C][/ROW]
[ROW][C]12[/C][C]-0.07035[/C][C]-0.5449[/C][C]0.293911[/C][/ROW]
[ROW][C]13[/C][C]0.000196[/C][C]0.0015[/C][C]0.499398[/C][/ROW]
[ROW][C]14[/C][C]-0.029775[/C][C]-0.2306[/C][C]0.40919[/C][/ROW]
[ROW][C]15[/C][C]-0.09584[/C][C]-0.7424[/C][C]0.230379[/C][/ROW]
[ROW][C]16[/C][C]-0.01381[/C][C]-0.107[/C][C]0.457583[/C][/ROW]
[ROW][C]17[/C][C]0.00924[/C][C]0.0716[/C][C]0.47159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289701&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289701&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	0.963295	7.4617	0
2	-0.022179	-0.1718	0.432088
3	0.031724	0.2457	0.403365
4	-0.087975	-0.6815	0.249104
5	-0.01807	-0.14	0.444575
6	-0.147283	-1.1409	0.129233
7	-0.0372	-0.2882	0.387111
8	-0.074853	-0.5798	0.282108
9	-0.068379	-0.5297	0.29915
10	0.008715	0.0675	0.473203
11	-0.058197	-0.4508	0.326881
12	-0.07035	-0.5449	0.293911
13	0.000196	0.0015	0.499398
14	-0.029775	-0.2306	0.40919
15	-0.09584	-0.7424	0.230379
16	-0.01381	-0.107	0.457583
17	0.00924	0.0716	0.47159

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

Parameters (R input):

par1 = Default ; 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)
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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