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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

Thu, 06 Jan 2011 14:07:24 +0000

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/Jan/06/t129432291127nvidkplugx5zd.htm/, Retrieved Mon, 27 May 2024 18:15:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117287, Retrieved Mon, 27 May 2024 18:15:01 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

230

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

-       [(Partial) Autocorrelation Function] [6bis: nieuw] [2011-01-06 14:07:24] [ac6548ae9fe194312a6a7ae1d0184c66] [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	'Gwilym Jenkins' @ www.wessa.org

\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 & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117287&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]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117287&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117287&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	'Gwilym Jenkins' @ www.wessa.org

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.932661	7.9139	0
2	0.899455	7.6321	0
3	0.861649	7.3113	0
4	0.825565	7.0052	0
5	0.784001	6.6525	0
6	0.774666	6.5733	0
7	0.707769	6.0056	0
8	0.671656	5.6992	0
9	0.631172	5.3557	0
10	0.595117	5.0497	2e-06
11	0.552289	4.6863	6e-06
12	0.536825	4.5551	1e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.932661 & 7.9139 & 0 \tabularnewline
2 & 0.899455 & 7.6321 & 0 \tabularnewline
3 & 0.861649 & 7.3113 & 0 \tabularnewline
4 & 0.825565 & 7.0052 & 0 \tabularnewline
5 & 0.784001 & 6.6525 & 0 \tabularnewline
6 & 0.774666 & 6.5733 & 0 \tabularnewline
7 & 0.707769 & 6.0056 & 0 \tabularnewline
8 & 0.671656 & 5.6992 & 0 \tabularnewline
9 & 0.631172 & 5.3557 & 0 \tabularnewline
10 & 0.595117 & 5.0497 & 2e-06 \tabularnewline
11 & 0.552289 & 4.6863 & 6e-06 \tabularnewline
12 & 0.536825 & 4.5551 & 1e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117287&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]0.932661[/C][C]7.9139[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.899455[/C][C]7.6321[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.861649[/C][C]7.3113[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.825565[/C][C]7.0052[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.784001[/C][C]6.6525[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.774666[/C][C]6.5733[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.707769[/C][C]6.0056[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.671656[/C][C]5.6992[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.631172[/C][C]5.3557[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.595117[/C][C]5.0497[/C][C]2e-06[/C][/ROW]
[ROW][C]11[/C][C]0.552289[/C][C]4.6863[/C][C]6e-06[/C][/ROW]
[ROW][C]12[/C][C]0.536825[/C][C]4.5551[/C][C]1e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117287&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117287&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	0.932661	7.9139	0
2	0.899455	7.6321	0
3	0.861649	7.3113	0
4	0.825565	7.0052	0
5	0.784001	6.6525	0
6	0.774666	6.5733	0
7	0.707769	6.0056	0
8	0.671656	5.6992	0
9	0.631172	5.3557	0
10	0.595117	5.0497	2e-06
11	0.552289	4.6863	6e-06
12	0.536825	4.5551	1e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.932661	7.9139	0
2	0.227428	1.9298	0.028786
3	0.011631	0.0987	0.460829
4	-0.007182	-0.0609	0.475788
5	-0.05869	-0.498	0.310001
6	0.218105	1.8507	0.034159
7	-0.369816	-3.138	0.001233
8	0.060831	0.5162	0.30366
9	0.000586	0.005	0.498022
10	0.010019	0.085	0.466242
11	-0.018472	-0.1567	0.437943
12	0.046959	0.3985	0.345734

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.932661 & 7.9139 & 0 \tabularnewline
2 & 0.227428 & 1.9298 & 0.028786 \tabularnewline
3 & 0.011631 & 0.0987 & 0.460829 \tabularnewline
4 & -0.007182 & -0.0609 & 0.475788 \tabularnewline
5 & -0.05869 & -0.498 & 0.310001 \tabularnewline
6 & 0.218105 & 1.8507 & 0.034159 \tabularnewline
7 & -0.369816 & -3.138 & 0.001233 \tabularnewline
8 & 0.060831 & 0.5162 & 0.30366 \tabularnewline
9 & 0.000586 & 0.005 & 0.498022 \tabularnewline
10 & 0.010019 & 0.085 & 0.466242 \tabularnewline
11 & -0.018472 & -0.1567 & 0.437943 \tabularnewline
12 & 0.046959 & 0.3985 & 0.345734 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117287&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]0.932661[/C][C]7.9139[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.227428[/C][C]1.9298[/C][C]0.028786[/C][/ROW]
[ROW][C]3[/C][C]0.011631[/C][C]0.0987[/C][C]0.460829[/C][/ROW]
[ROW][C]4[/C][C]-0.007182[/C][C]-0.0609[/C][C]0.475788[/C][/ROW]
[ROW][C]5[/C][C]-0.05869[/C][C]-0.498[/C][C]0.310001[/C][/ROW]
[ROW][C]6[/C][C]0.218105[/C][C]1.8507[/C][C]0.034159[/C][/ROW]
[ROW][C]7[/C][C]-0.369816[/C][C]-3.138[/C][C]0.001233[/C][/ROW]
[ROW][C]8[/C][C]0.060831[/C][C]0.5162[/C][C]0.30366[/C][/ROW]
[ROW][C]9[/C][C]0.000586[/C][C]0.005[/C][C]0.498022[/C][/ROW]
[ROW][C]10[/C][C]0.010019[/C][C]0.085[/C][C]0.466242[/C][/ROW]
[ROW][C]11[/C][C]-0.018472[/C][C]-0.1567[/C][C]0.437943[/C][/ROW]
[ROW][C]12[/C][C]0.046959[/C][C]0.3985[/C][C]0.345734[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117287&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117287&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	0.932661	7.9139	0
2	0.227428	1.9298	0.028786
3	0.011631	0.0987	0.460829
4	-0.007182	-0.0609	0.475788
5	-0.05869	-0.498	0.310001
6	0.218105	1.8507	0.034159
7	-0.369816	-3.138	0.001233
8	0.060831	0.5162	0.30366
9	0.000586	0.005	0.498022
10	0.010019	0.085	0.466242
11	-0.018472	-0.1567	0.437943
12	0.046959	0.3985	0.345734

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

Parameters (R input):

par1 = 12 ; 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')

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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code