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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 15 Jan 2012 12:02:51 -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/2012/Jan/15/t13266470226o0f2dlvycs4exe.htm/, Retrieved Fri, 03 May 2024 13:30:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161106, Retrieved Fri, 03 May 2024 13:30:21 +0000

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No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

111

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

-     [Notched Boxplots] [boxplot] [2011-10-11 16:58:56] [0f3802131247472a006387bf3e5d274d]
- RMPD    [(Partial) Autocorrelation Function] [] [2012-01-15 17:02:51] [9bda411d6223d16f0472c7feaae49b5f] [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=161106&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=161106&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161106&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	-0.337645	-2.7222	0.004158
2	-0.27137	-2.1879	0.016141
3	0.159043	1.2822	0.102155
4	0.103098	0.8312	0.204451
5	-0.148213	-1.1949	0.118228
6	0.209811	1.6916	0.047761
7	-0.242917	-1.9585	0.027235
8	0.222152	1.791	0.038971
9	0.005198	0.0419	0.483351
10	-0.3002	-2.4203	0.009156
11	-0.123473	-0.9955	0.1616
12	0.559012	4.5069	1.4e-05
13	-0.194135	-1.5652	0.0612
14	-0.185657	-1.4968	0.069641
15	-0.016487	-0.1329	0.447333
16	0.124814	1.0063	0.159006
17	-0.071017	-0.5726	0.284461
18	0.059886	0.4828	0.315423

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.337645 & -2.7222 & 0.004158 \tabularnewline
2 & -0.27137 & -2.1879 & 0.016141 \tabularnewline
3 & 0.159043 & 1.2822 & 0.102155 \tabularnewline
4 & 0.103098 & 0.8312 & 0.204451 \tabularnewline
5 & -0.148213 & -1.1949 & 0.118228 \tabularnewline
6 & 0.209811 & 1.6916 & 0.047761 \tabularnewline
7 & -0.242917 & -1.9585 & 0.027235 \tabularnewline
8 & 0.222152 & 1.791 & 0.038971 \tabularnewline
9 & 0.005198 & 0.0419 & 0.483351 \tabularnewline
10 & -0.3002 & -2.4203 & 0.009156 \tabularnewline
11 & -0.123473 & -0.9955 & 0.1616 \tabularnewline
12 & 0.559012 & 4.5069 & 1.4e-05 \tabularnewline
13 & -0.194135 & -1.5652 & 0.0612 \tabularnewline
14 & -0.185657 & -1.4968 & 0.069641 \tabularnewline
15 & -0.016487 & -0.1329 & 0.447333 \tabularnewline
16 & 0.124814 & 1.0063 & 0.159006 \tabularnewline
17 & -0.071017 & -0.5726 & 0.284461 \tabularnewline
18 & 0.059886 & 0.4828 & 0.315423 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161106&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]-0.337645[/C][C]-2.7222[/C][C]0.004158[/C][/ROW]
[ROW][C]2[/C][C]-0.27137[/C][C]-2.1879[/C][C]0.016141[/C][/ROW]
[ROW][C]3[/C][C]0.159043[/C][C]1.2822[/C][C]0.102155[/C][/ROW]
[ROW][C]4[/C][C]0.103098[/C][C]0.8312[/C][C]0.204451[/C][/ROW]
[ROW][C]5[/C][C]-0.148213[/C][C]-1.1949[/C][C]0.118228[/C][/ROW]
[ROW][C]6[/C][C]0.209811[/C][C]1.6916[/C][C]0.047761[/C][/ROW]
[ROW][C]7[/C][C]-0.242917[/C][C]-1.9585[/C][C]0.027235[/C][/ROW]
[ROW][C]8[/C][C]0.222152[/C][C]1.791[/C][C]0.038971[/C][/ROW]
[ROW][C]9[/C][C]0.005198[/C][C]0.0419[/C][C]0.483351[/C][/ROW]
[ROW][C]10[/C][C]-0.3002[/C][C]-2.4203[/C][C]0.009156[/C][/ROW]
[ROW][C]11[/C][C]-0.123473[/C][C]-0.9955[/C][C]0.1616[/C][/ROW]
[ROW][C]12[/C][C]0.559012[/C][C]4.5069[/C][C]1.4e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.194135[/C][C]-1.5652[/C][C]0.0612[/C][/ROW]
[ROW][C]14[/C][C]-0.185657[/C][C]-1.4968[/C][C]0.069641[/C][/ROW]
[ROW][C]15[/C][C]-0.016487[/C][C]-0.1329[/C][C]0.447333[/C][/ROW]
[ROW][C]16[/C][C]0.124814[/C][C]1.0063[/C][C]0.159006[/C][/ROW]
[ROW][C]17[/C][C]-0.071017[/C][C]-0.5726[/C][C]0.284461[/C][/ROW]
[ROW][C]18[/C][C]0.059886[/C][C]0.4828[/C][C]0.315423[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161106&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161106&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	-0.337645	-2.7222	0.004158
2	-0.27137	-2.1879	0.016141
3	0.159043	1.2822	0.102155
4	0.103098	0.8312	0.204451
5	-0.148213	-1.1949	0.118228
6	0.209811	1.6916	0.047761
7	-0.242917	-1.9585	0.027235
8	0.222152	1.791	0.038971
9	0.005198	0.0419	0.483351
10	-0.3002	-2.4203	0.009156
11	-0.123473	-0.9955	0.1616
12	0.559012	4.5069	1.4e-05
13	-0.194135	-1.5652	0.0612
14	-0.185657	-1.4968	0.069641
15	-0.016487	-0.1329	0.447333
16	0.124814	1.0063	0.159006
17	-0.071017	-0.5726	0.284461
18	0.059886	0.4828	0.315423

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.337645	-2.7222	0.004158
2	-0.434961	-3.5068	0.000414
3	-0.166069	-1.3389	0.092635
4	-0.006154	-0.0496	0.480292
5	-0.080602	-0.6498	0.259044
6	0.251391	2.0268	0.023395
7	-0.158081	-1.2745	0.103514
8	0.277622	2.2383	0.014318
9	0.075064	0.6052	0.273582
10	-0.251858	-2.0305	0.023198
11	-0.498701	-4.0207	7.7e-05
12	0.071975	0.5803	0.281866
13	0.198204	1.598	0.05745
14	0.135714	1.0942	0.138962
15	-0.091826	-0.7403	0.230885
16	-0.099738	-0.8041	0.212131
17	-0.083702	-0.6748	0.251089
18	-0.095847	-0.7727	0.221237

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.337645 & -2.7222 & 0.004158 \tabularnewline
2 & -0.434961 & -3.5068 & 0.000414 \tabularnewline
3 & -0.166069 & -1.3389 & 0.092635 \tabularnewline
4 & -0.006154 & -0.0496 & 0.480292 \tabularnewline
5 & -0.080602 & -0.6498 & 0.259044 \tabularnewline
6 & 0.251391 & 2.0268 & 0.023395 \tabularnewline
7 & -0.158081 & -1.2745 & 0.103514 \tabularnewline
8 & 0.277622 & 2.2383 & 0.014318 \tabularnewline
9 & 0.075064 & 0.6052 & 0.273582 \tabularnewline
10 & -0.251858 & -2.0305 & 0.023198 \tabularnewline
11 & -0.498701 & -4.0207 & 7.7e-05 \tabularnewline
12 & 0.071975 & 0.5803 & 0.281866 \tabularnewline
13 & 0.198204 & 1.598 & 0.05745 \tabularnewline
14 & 0.135714 & 1.0942 & 0.138962 \tabularnewline
15 & -0.091826 & -0.7403 & 0.230885 \tabularnewline
16 & -0.099738 & -0.8041 & 0.212131 \tabularnewline
17 & -0.083702 & -0.6748 & 0.251089 \tabularnewline
18 & -0.095847 & -0.7727 & 0.221237 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161106&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]-0.337645[/C][C]-2.7222[/C][C]0.004158[/C][/ROW]
[ROW][C]2[/C][C]-0.434961[/C][C]-3.5068[/C][C]0.000414[/C][/ROW]
[ROW][C]3[/C][C]-0.166069[/C][C]-1.3389[/C][C]0.092635[/C][/ROW]
[ROW][C]4[/C][C]-0.006154[/C][C]-0.0496[/C][C]0.480292[/C][/ROW]
[ROW][C]5[/C][C]-0.080602[/C][C]-0.6498[/C][C]0.259044[/C][/ROW]
[ROW][C]6[/C][C]0.251391[/C][C]2.0268[/C][C]0.023395[/C][/ROW]
[ROW][C]7[/C][C]-0.158081[/C][C]-1.2745[/C][C]0.103514[/C][/ROW]
[ROW][C]8[/C][C]0.277622[/C][C]2.2383[/C][C]0.014318[/C][/ROW]
[ROW][C]9[/C][C]0.075064[/C][C]0.6052[/C][C]0.273582[/C][/ROW]
[ROW][C]10[/C][C]-0.251858[/C][C]-2.0305[/C][C]0.023198[/C][/ROW]
[ROW][C]11[/C][C]-0.498701[/C][C]-4.0207[/C][C]7.7e-05[/C][/ROW]
[ROW][C]12[/C][C]0.071975[/C][C]0.5803[/C][C]0.281866[/C][/ROW]
[ROW][C]13[/C][C]0.198204[/C][C]1.598[/C][C]0.05745[/C][/ROW]
[ROW][C]14[/C][C]0.135714[/C][C]1.0942[/C][C]0.138962[/C][/ROW]
[ROW][C]15[/C][C]-0.091826[/C][C]-0.7403[/C][C]0.230885[/C][/ROW]
[ROW][C]16[/C][C]-0.099738[/C][C]-0.8041[/C][C]0.212131[/C][/ROW]
[ROW][C]17[/C][C]-0.083702[/C][C]-0.6748[/C][C]0.251089[/C][/ROW]
[ROW][C]18[/C][C]-0.095847[/C][C]-0.7727[/C][C]0.221237[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161106&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161106&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	-0.337645	-2.7222	0.004158
2	-0.434961	-3.5068	0.000414
3	-0.166069	-1.3389	0.092635
4	-0.006154	-0.0496	0.480292
5	-0.080602	-0.6498	0.259044
6	0.251391	2.0268	0.023395
7	-0.158081	-1.2745	0.103514
8	0.277622	2.2383	0.014318
9	0.075064	0.6052	0.273582
10	-0.251858	-2.0305	0.023198
11	-0.498701	-4.0207	7.7e-05
12	0.071975	0.5803	0.281866
13	0.198204	1.598	0.05745
14	0.135714	1.0942	0.138962
15	-0.091826	-0.7403	0.230885
16	-0.099738	-0.8041	0.212131
17	-0.083702	-0.6748	0.251089
18	-0.095847	-0.7727	0.221237

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):

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code