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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 15 Dec 2010 18:12:16 +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/2010/Dec/15/t1292436633ucshez6f8g0cali.htm/, Retrieved Fri, 03 May 2024 14:03:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110634, Retrieved Fri, 03 May 2024 14:03:48 +0000

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Estimated Impact

107

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- RMPD      [(Partial) Autocorrelation Function] [ACF] [2010-12-15 18:12:16] [fd751bc40fbbb4c72222c10190589d42] [Current]

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Histogram

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2
1
-8
-1
1
-1
2
2
1
-1
-2
-2
-1
-8
-4
-6
-3
-3
-7
-9
-11
-13
-11
-9
-17
-22
-25
-20
-24
-24
-22
-19
-18
-17
-11
-11
-12
-10
-15
-15
-15
-13
-8
-13
-9
-7
-4
-4
-2
0

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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110634&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110634&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110634&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' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.15196	-1.0637	0.146336
2	-0.015244	-0.1067	0.457729
3	0.049787	0.3485	0.364475
4	0.027016	0.1891	0.425394
5	0.078744	0.5512	0.291998
6	-0.09419	-0.6593	0.256386
7	0.059629	0.4174	0.339102
8	0.061069	0.4275	0.335449
9	-0.164827	-1.1538	0.127091
10	-0.100958	-0.7067	0.241549
11	0.252537	1.7678	0.041664
12	-0.042053	-0.2944	0.384859
13	0.091073	0.6375	0.263379
14	-0.066059	-0.4624	0.322915
15	0.113414	0.7939	0.215541
16	-0.073455	-0.5142	0.304716

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.15196 & -1.0637 & 0.146336 \tabularnewline
2 & -0.015244 & -0.1067 & 0.457729 \tabularnewline
3 & 0.049787 & 0.3485 & 0.364475 \tabularnewline
4 & 0.027016 & 0.1891 & 0.425394 \tabularnewline
5 & 0.078744 & 0.5512 & 0.291998 \tabularnewline
6 & -0.09419 & -0.6593 & 0.256386 \tabularnewline
7 & 0.059629 & 0.4174 & 0.339102 \tabularnewline
8 & 0.061069 & 0.4275 & 0.335449 \tabularnewline
9 & -0.164827 & -1.1538 & 0.127091 \tabularnewline
10 & -0.100958 & -0.7067 & 0.241549 \tabularnewline
11 & 0.252537 & 1.7678 & 0.041664 \tabularnewline
12 & -0.042053 & -0.2944 & 0.384859 \tabularnewline
13 & 0.091073 & 0.6375 & 0.263379 \tabularnewline
14 & -0.066059 & -0.4624 & 0.322915 \tabularnewline
15 & 0.113414 & 0.7939 & 0.215541 \tabularnewline
16 & -0.073455 & -0.5142 & 0.304716 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110634&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]-0.15196[/C][C]-1.0637[/C][C]0.146336[/C][/ROW]
[ROW][C]2[/C][C]-0.015244[/C][C]-0.1067[/C][C]0.457729[/C][/ROW]
[ROW][C]3[/C][C]0.049787[/C][C]0.3485[/C][C]0.364475[/C][/ROW]
[ROW][C]4[/C][C]0.027016[/C][C]0.1891[/C][C]0.425394[/C][/ROW]
[ROW][C]5[/C][C]0.078744[/C][C]0.5512[/C][C]0.291998[/C][/ROW]
[ROW][C]6[/C][C]-0.09419[/C][C]-0.6593[/C][C]0.256386[/C][/ROW]
[ROW][C]7[/C][C]0.059629[/C][C]0.4174[/C][C]0.339102[/C][/ROW]
[ROW][C]8[/C][C]0.061069[/C][C]0.4275[/C][C]0.335449[/C][/ROW]
[ROW][C]9[/C][C]-0.164827[/C][C]-1.1538[/C][C]0.127091[/C][/ROW]
[ROW][C]10[/C][C]-0.100958[/C][C]-0.7067[/C][C]0.241549[/C][/ROW]
[ROW][C]11[/C][C]0.252537[/C][C]1.7678[/C][C]0.041664[/C][/ROW]
[ROW][C]12[/C][C]-0.042053[/C][C]-0.2944[/C][C]0.384859[/C][/ROW]
[ROW][C]13[/C][C]0.091073[/C][C]0.6375[/C][C]0.263379[/C][/ROW]
[ROW][C]14[/C][C]-0.066059[/C][C]-0.4624[/C][C]0.322915[/C][/ROW]
[ROW][C]15[/C][C]0.113414[/C][C]0.7939[/C][C]0.215541[/C][/ROW]
[ROW][C]16[/C][C]-0.073455[/C][C]-0.5142[/C][C]0.304716[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110634&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110634&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	-0.15196	-1.0637	0.146336
2	-0.015244	-0.1067	0.457729
3	0.049787	0.3485	0.364475
4	0.027016	0.1891	0.425394
5	0.078744	0.5512	0.291998
6	-0.09419	-0.6593	0.256386
7	0.059629	0.4174	0.339102
8	0.061069	0.4275	0.335449
9	-0.164827	-1.1538	0.127091
10	-0.100958	-0.7067	0.241549
11	0.252537	1.7678	0.041664
12	-0.042053	-0.2944	0.384859
13	0.091073	0.6375	0.263379
14	-0.066059	-0.4624	0.322915
15	0.113414	0.7939	0.215541
16	-0.073455	-0.5142	0.304716

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.15196	-1.0637	0.146336
2	-0.039241	-0.2747	0.392354
3	0.042461	0.2972	0.383774
4	0.041855	0.293	0.385386
5	0.094319	0.6602	0.256097
6	-0.070441	-0.4931	0.312076
7	0.035325	0.2473	0.402865
8	0.064208	0.4495	0.327543
9	-0.148363	-1.0385	0.152057
10	-0.160281	-1.122	0.133672
11	0.230973	1.6168	0.05617
12	0.025683	0.1798	0.429034
13	0.123253	0.8628	0.196234
14	-0.018175	-0.1272	0.449641
15	0.085393	0.5978	0.276379
16	-0.126109	-0.8828	0.190837

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.15196 & -1.0637 & 0.146336 \tabularnewline
2 & -0.039241 & -0.2747 & 0.392354 \tabularnewline
3 & 0.042461 & 0.2972 & 0.383774 \tabularnewline
4 & 0.041855 & 0.293 & 0.385386 \tabularnewline
5 & 0.094319 & 0.6602 & 0.256097 \tabularnewline
6 & -0.070441 & -0.4931 & 0.312076 \tabularnewline
7 & 0.035325 & 0.2473 & 0.402865 \tabularnewline
8 & 0.064208 & 0.4495 & 0.327543 \tabularnewline
9 & -0.148363 & -1.0385 & 0.152057 \tabularnewline
10 & -0.160281 & -1.122 & 0.133672 \tabularnewline
11 & 0.230973 & 1.6168 & 0.05617 \tabularnewline
12 & 0.025683 & 0.1798 & 0.429034 \tabularnewline
13 & 0.123253 & 0.8628 & 0.196234 \tabularnewline
14 & -0.018175 & -0.1272 & 0.449641 \tabularnewline
15 & 0.085393 & 0.5978 & 0.276379 \tabularnewline
16 & -0.126109 & -0.8828 & 0.190837 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110634&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]-0.15196[/C][C]-1.0637[/C][C]0.146336[/C][/ROW]
[ROW][C]2[/C][C]-0.039241[/C][C]-0.2747[/C][C]0.392354[/C][/ROW]
[ROW][C]3[/C][C]0.042461[/C][C]0.2972[/C][C]0.383774[/C][/ROW]
[ROW][C]4[/C][C]0.041855[/C][C]0.293[/C][C]0.385386[/C][/ROW]
[ROW][C]5[/C][C]0.094319[/C][C]0.6602[/C][C]0.256097[/C][/ROW]
[ROW][C]6[/C][C]-0.070441[/C][C]-0.4931[/C][C]0.312076[/C][/ROW]
[ROW][C]7[/C][C]0.035325[/C][C]0.2473[/C][C]0.402865[/C][/ROW]
[ROW][C]8[/C][C]0.064208[/C][C]0.4495[/C][C]0.327543[/C][/ROW]
[ROW][C]9[/C][C]-0.148363[/C][C]-1.0385[/C][C]0.152057[/C][/ROW]
[ROW][C]10[/C][C]-0.160281[/C][C]-1.122[/C][C]0.133672[/C][/ROW]
[ROW][C]11[/C][C]0.230973[/C][C]1.6168[/C][C]0.05617[/C][/ROW]
[ROW][C]12[/C][C]0.025683[/C][C]0.1798[/C][C]0.429034[/C][/ROW]
[ROW][C]13[/C][C]0.123253[/C][C]0.8628[/C][C]0.196234[/C][/ROW]
[ROW][C]14[/C][C]-0.018175[/C][C]-0.1272[/C][C]0.449641[/C][/ROW]
[ROW][C]15[/C][C]0.085393[/C][C]0.5978[/C][C]0.276379[/C][/ROW]
[ROW][C]16[/C][C]-0.126109[/C][C]-0.8828[/C][C]0.190837[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110634&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110634&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	-0.15196	-1.0637	0.146336
2	-0.039241	-0.2747	0.392354
3	0.042461	0.2972	0.383774
4	0.041855	0.293	0.385386
5	0.094319	0.6602	0.256097
6	-0.070441	-0.4931	0.312076
7	0.035325	0.2473	0.402865
8	0.064208	0.4495	0.327543
9	-0.148363	-1.0385	0.152057
10	-0.160281	-1.122	0.133672
11	0.230973	1.6168	0.05617
12	0.025683	0.1798	0.429034
13	0.123253	0.8628	0.196234
14	-0.018175	-0.1272	0.449641
15	0.085393	0.5978	0.276379
16	-0.126109	-0.8828	0.190837

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 = 1 ; par2 = 2 ; par3 = 0 ; par4 = 12 ;

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