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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Dec 2011 17:43:17 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/22/t1324593848gledka7hqvrtkg0.htm/, Retrieved Fri, 03 May 2024 12:41:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160047, Retrieved Fri, 03 May 2024 12:41:48 +0000

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

-       [(Partial) Autocorrelation Function] [] [2011-12-22 22:43:17] [3bdb54d050744f47368418ea7c7e8e96] [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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160047&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160047&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160047&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.522771	4.7913	4e-06
2	0.002693	0.0247	0.490184
3	-0.126967	-1.1637	0.123926
4	-0.083584	-0.7661	0.222894
5	-0.071741	-0.6575	0.256324
6	-0.132327	-1.2128	0.114303
7	-0.158826	-1.4557	0.074606
8	-0.174378	-1.5982	0.056877
9	-0.109137	-1.0003	0.16003
10	0.083741	0.7675	0.222469
11	0.387576	3.5522	0.000315
12	0.577295	5.291	0
13	0.305667	2.8015	0.003156
14	-0.074023	-0.6784	0.249682
15	-0.144008	-1.3199	0.095235
16	-0.098735	-0.9049	0.184048
17	-0.052586	-0.482	0.315543
18	-0.095255	-0.873	0.192569
19	-0.130905	-1.1998	0.116803

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.522771 & 4.7913 & 4e-06 \tabularnewline
2 & 0.002693 & 0.0247 & 0.490184 \tabularnewline
3 & -0.126967 & -1.1637 & 0.123926 \tabularnewline
4 & -0.083584 & -0.7661 & 0.222894 \tabularnewline
5 & -0.071741 & -0.6575 & 0.256324 \tabularnewline
6 & -0.132327 & -1.2128 & 0.114303 \tabularnewline
7 & -0.158826 & -1.4557 & 0.074606 \tabularnewline
8 & -0.174378 & -1.5982 & 0.056877 \tabularnewline
9 & -0.109137 & -1.0003 & 0.16003 \tabularnewline
10 & 0.083741 & 0.7675 & 0.222469 \tabularnewline
11 & 0.387576 & 3.5522 & 0.000315 \tabularnewline
12 & 0.577295 & 5.291 & 0 \tabularnewline
13 & 0.305667 & 2.8015 & 0.003156 \tabularnewline
14 & -0.074023 & -0.6784 & 0.249682 \tabularnewline
15 & -0.144008 & -1.3199 & 0.095235 \tabularnewline
16 & -0.098735 & -0.9049 & 0.184048 \tabularnewline
17 & -0.052586 & -0.482 & 0.315543 \tabularnewline
18 & -0.095255 & -0.873 & 0.192569 \tabularnewline
19 & -0.130905 & -1.1998 & 0.116803 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160047&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]0.522771[/C][C]4.7913[/C][C]4e-06[/C][/ROW]
[ROW][C]2[/C][C]0.002693[/C][C]0.0247[/C][C]0.490184[/C][/ROW]
[ROW][C]3[/C][C]-0.126967[/C][C]-1.1637[/C][C]0.123926[/C][/ROW]
[ROW][C]4[/C][C]-0.083584[/C][C]-0.7661[/C][C]0.222894[/C][/ROW]
[ROW][C]5[/C][C]-0.071741[/C][C]-0.6575[/C][C]0.256324[/C][/ROW]
[ROW][C]6[/C][C]-0.132327[/C][C]-1.2128[/C][C]0.114303[/C][/ROW]
[ROW][C]7[/C][C]-0.158826[/C][C]-1.4557[/C][C]0.074606[/C][/ROW]
[ROW][C]8[/C][C]-0.174378[/C][C]-1.5982[/C][C]0.056877[/C][/ROW]
[ROW][C]9[/C][C]-0.109137[/C][C]-1.0003[/C][C]0.16003[/C][/ROW]
[ROW][C]10[/C][C]0.083741[/C][C]0.7675[/C][C]0.222469[/C][/ROW]
[ROW][C]11[/C][C]0.387576[/C][C]3.5522[/C][C]0.000315[/C][/ROW]
[ROW][C]12[/C][C]0.577295[/C][C]5.291[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.305667[/C][C]2.8015[/C][C]0.003156[/C][/ROW]
[ROW][C]14[/C][C]-0.074023[/C][C]-0.6784[/C][C]0.249682[/C][/ROW]
[ROW][C]15[/C][C]-0.144008[/C][C]-1.3199[/C][C]0.095235[/C][/ROW]
[ROW][C]16[/C][C]-0.098735[/C][C]-0.9049[/C][C]0.184048[/C][/ROW]
[ROW][C]17[/C][C]-0.052586[/C][C]-0.482[/C][C]0.315543[/C][/ROW]
[ROW][C]18[/C][C]-0.095255[/C][C]-0.873[/C][C]0.192569[/C][/ROW]
[ROW][C]19[/C][C]-0.130905[/C][C]-1.1998[/C][C]0.116803[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160047&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160047&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	0.522771	4.7913	4e-06
2	0.002693	0.0247	0.490184
3	-0.126967	-1.1637	0.123926
4	-0.083584	-0.7661	0.222894
5	-0.071741	-0.6575	0.256324
6	-0.132327	-1.2128	0.114303
7	-0.158826	-1.4557	0.074606
8	-0.174378	-1.5982	0.056877
9	-0.109137	-1.0003	0.16003
10	0.083741	0.7675	0.222469
11	0.387576	3.5522	0.000315
12	0.577295	5.291	0
13	0.305667	2.8015	0.003156
14	-0.074023	-0.6784	0.249682
15	-0.144008	-1.3199	0.095235
16	-0.098735	-0.9049	0.184048
17	-0.052586	-0.482	0.315543
18	-0.095255	-0.873	0.192569
19	-0.130905	-1.1998	0.116803

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.522771	4.7913	4e-06
2	-0.372357	-3.4127	0.000496
3	0.105054	0.9628	0.169197
4	-0.06662	-0.6106	0.271561
5	-0.055405	-0.5078	0.306465
6	-0.11654	-1.0681	0.144266
7	-0.049714	-0.4556	0.324912
8	-0.142858	-1.3093	0.096998
9	0.025	0.2291	0.409662
10	0.133045	1.2194	0.113056
11	0.352744	3.233	0.000876
12	0.318514	2.9192	0.002251
13	-0.140832	-1.2907	0.100167
14	-0.081814	-0.7498	0.227724
15	0.015162	0.139	0.444907
16	-0.131276	-1.2032	0.116147
17	0.104778	0.9603	0.169829
18	-0.005307	-0.0486	0.480659
19	0.076489	0.701	0.242609

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.522771 & 4.7913 & 4e-06 \tabularnewline
2 & -0.372357 & -3.4127 & 0.000496 \tabularnewline
3 & 0.105054 & 0.9628 & 0.169197 \tabularnewline
4 & -0.06662 & -0.6106 & 0.271561 \tabularnewline
5 & -0.055405 & -0.5078 & 0.306465 \tabularnewline
6 & -0.11654 & -1.0681 & 0.144266 \tabularnewline
7 & -0.049714 & -0.4556 & 0.324912 \tabularnewline
8 & -0.142858 & -1.3093 & 0.096998 \tabularnewline
9 & 0.025 & 0.2291 & 0.409662 \tabularnewline
10 & 0.133045 & 1.2194 & 0.113056 \tabularnewline
11 & 0.352744 & 3.233 & 0.000876 \tabularnewline
12 & 0.318514 & 2.9192 & 0.002251 \tabularnewline
13 & -0.140832 & -1.2907 & 0.100167 \tabularnewline
14 & -0.081814 & -0.7498 & 0.227724 \tabularnewline
15 & 0.015162 & 0.139 & 0.444907 \tabularnewline
16 & -0.131276 & -1.2032 & 0.116147 \tabularnewline
17 & 0.104778 & 0.9603 & 0.169829 \tabularnewline
18 & -0.005307 & -0.0486 & 0.480659 \tabularnewline
19 & 0.076489 & 0.701 & 0.242609 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160047&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]0.522771[/C][C]4.7913[/C][C]4e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.372357[/C][C]-3.4127[/C][C]0.000496[/C][/ROW]
[ROW][C]3[/C][C]0.105054[/C][C]0.9628[/C][C]0.169197[/C][/ROW]
[ROW][C]4[/C][C]-0.06662[/C][C]-0.6106[/C][C]0.271561[/C][/ROW]
[ROW][C]5[/C][C]-0.055405[/C][C]-0.5078[/C][C]0.306465[/C][/ROW]
[ROW][C]6[/C][C]-0.11654[/C][C]-1.0681[/C][C]0.144266[/C][/ROW]
[ROW][C]7[/C][C]-0.049714[/C][C]-0.4556[/C][C]0.324912[/C][/ROW]
[ROW][C]8[/C][C]-0.142858[/C][C]-1.3093[/C][C]0.096998[/C][/ROW]
[ROW][C]9[/C][C]0.025[/C][C]0.2291[/C][C]0.409662[/C][/ROW]
[ROW][C]10[/C][C]0.133045[/C][C]1.2194[/C][C]0.113056[/C][/ROW]
[ROW][C]11[/C][C]0.352744[/C][C]3.233[/C][C]0.000876[/C][/ROW]
[ROW][C]12[/C][C]0.318514[/C][C]2.9192[/C][C]0.002251[/C][/ROW]
[ROW][C]13[/C][C]-0.140832[/C][C]-1.2907[/C][C]0.100167[/C][/ROW]
[ROW][C]14[/C][C]-0.081814[/C][C]-0.7498[/C][C]0.227724[/C][/ROW]
[ROW][C]15[/C][C]0.015162[/C][C]0.139[/C][C]0.444907[/C][/ROW]
[ROW][C]16[/C][C]-0.131276[/C][C]-1.2032[/C][C]0.116147[/C][/ROW]
[ROW][C]17[/C][C]0.104778[/C][C]0.9603[/C][C]0.169829[/C][/ROW]
[ROW][C]18[/C][C]-0.005307[/C][C]-0.0486[/C][C]0.480659[/C][/ROW]
[ROW][C]19[/C][C]0.076489[/C][C]0.701[/C][C]0.242609[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160047&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160047&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	0.522771	4.7913	4e-06
2	-0.372357	-3.4127	0.000496
3	0.105054	0.9628	0.169197
4	-0.06662	-0.6106	0.271561
5	-0.055405	-0.5078	0.306465
6	-0.11654	-1.0681	0.144266
7	-0.049714	-0.4556	0.324912
8	-0.142858	-1.3093	0.096998
9	0.025	0.2291	0.409662
10	0.133045	1.2194	0.113056
11	0.352744	3.233	0.000876
12	0.318514	2.9192	0.002251
13	-0.140832	-1.2907	0.100167
14	-0.081814	-0.7498	0.227724
15	0.015162	0.139	0.444907
16	-0.131276	-1.2032	0.116147
17	0.104778	0.9603	0.169829
18	-0.005307	-0.0486	0.480659
19	0.076489	0.701	0.242609

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)
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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code