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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Nov 2012 16:08:42 -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/Nov/18/t1353272957uu6fq48fwbmv4nd.htm/, Retrieved Mon, 29 Apr 2024 17:37:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=190361, Retrieved Mon, 29 Apr 2024 17:37:16 +0000

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-     [(Partial) Autocorrelation Function] [Autocorrelatie co...] [2012-11-18 17:55:43] [414c2ec381eb4adb801f9ac6823317d8]
- R PD    [(Partial) Autocorrelation Function] [Gedifferenci�erde...] [2012-11-18 21:08:42] [a5163a6b16cb463ddc5e8265592a0086] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190361&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]2 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=190361&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190361&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	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.952187	7.3756	0
2	0.898849	6.9625	0
3	0.83895	6.4985	0
4	0.773596	5.9922	0
5	0.694995	5.3834	1e-06
6	0.627184	4.8581	4e-06
7	0.554505	4.2952	3.2e-05
8	0.473575	3.6683	0.00026
9	0.397276	3.0773	0.001573
10	0.333713	2.5849	0.006094
11	0.273045	2.115	0.019296
12	0.208591	1.6157	0.055698
13	0.160363	1.2422	0.109505
14	0.119841	0.9283	0.178489
15	0.080326	0.6222	0.268083
16	0.041193	0.3191	0.375386
17	0.006446	0.0499	0.480171
18	-0.038448	-0.2978	0.383435

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.952187 & 7.3756 & 0 \tabularnewline
2 & 0.898849 & 6.9625 & 0 \tabularnewline
3 & 0.83895 & 6.4985 & 0 \tabularnewline
4 & 0.773596 & 5.9922 & 0 \tabularnewline
5 & 0.694995 & 5.3834 & 1e-06 \tabularnewline
6 & 0.627184 & 4.8581 & 4e-06 \tabularnewline
7 & 0.554505 & 4.2952 & 3.2e-05 \tabularnewline
8 & 0.473575 & 3.6683 & 0.00026 \tabularnewline
9 & 0.397276 & 3.0773 & 0.001573 \tabularnewline
10 & 0.333713 & 2.5849 & 0.006094 \tabularnewline
11 & 0.273045 & 2.115 & 0.019296 \tabularnewline
12 & 0.208591 & 1.6157 & 0.055698 \tabularnewline
13 & 0.160363 & 1.2422 & 0.109505 \tabularnewline
14 & 0.119841 & 0.9283 & 0.178489 \tabularnewline
15 & 0.080326 & 0.6222 & 0.268083 \tabularnewline
16 & 0.041193 & 0.3191 & 0.375386 \tabularnewline
17 & 0.006446 & 0.0499 & 0.480171 \tabularnewline
18 & -0.038448 & -0.2978 & 0.383435 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190361&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]0.952187[/C][C]7.3756[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.898849[/C][C]6.9625[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.83895[/C][C]6.4985[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.773596[/C][C]5.9922[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.694995[/C][C]5.3834[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.627184[/C][C]4.8581[/C][C]4e-06[/C][/ROW]
[ROW][C]7[/C][C]0.554505[/C][C]4.2952[/C][C]3.2e-05[/C][/ROW]
[ROW][C]8[/C][C]0.473575[/C][C]3.6683[/C][C]0.00026[/C][/ROW]
[ROW][C]9[/C][C]0.397276[/C][C]3.0773[/C][C]0.001573[/C][/ROW]
[ROW][C]10[/C][C]0.333713[/C][C]2.5849[/C][C]0.006094[/C][/ROW]
[ROW][C]11[/C][C]0.273045[/C][C]2.115[/C][C]0.019296[/C][/ROW]
[ROW][C]12[/C][C]0.208591[/C][C]1.6157[/C][C]0.055698[/C][/ROW]
[ROW][C]13[/C][C]0.160363[/C][C]1.2422[/C][C]0.109505[/C][/ROW]
[ROW][C]14[/C][C]0.119841[/C][C]0.9283[/C][C]0.178489[/C][/ROW]
[ROW][C]15[/C][C]0.080326[/C][C]0.6222[/C][C]0.268083[/C][/ROW]
[ROW][C]16[/C][C]0.041193[/C][C]0.3191[/C][C]0.375386[/C][/ROW]
[ROW][C]17[/C][C]0.006446[/C][C]0.0499[/C][C]0.480171[/C][/ROW]
[ROW][C]18[/C][C]-0.038448[/C][C]-0.2978[/C][C]0.383435[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190361&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190361&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	0.952187	7.3756	0
2	0.898849	6.9625	0
3	0.83895	6.4985	0
4	0.773596	5.9922	0
5	0.694995	5.3834	1e-06
6	0.627184	4.8581	4e-06
7	0.554505	4.2952	3.2e-05
8	0.473575	3.6683	0.00026
9	0.397276	3.0773	0.001573
10	0.333713	2.5849	0.006094
11	0.273045	2.115	0.019296
12	0.208591	1.6157	0.055698
13	0.160363	1.2422	0.109505
14	0.119841	0.9283	0.178489
15	0.080326	0.6222	0.268083
16	0.041193	0.3191	0.375386
17	0.006446	0.0499	0.480171
18	-0.038448	-0.2978	0.383435

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.952187	7.3756	0
2	-0.083681	-0.6482	0.259667
3	-0.095611	-0.7406	0.230912
4	-0.084915	-0.6578	0.256607
5	-0.172927	-1.3395	0.092732
6	0.091105	0.7057	0.241555
7	-0.090566	-0.7015	0.242845
8	-0.137112	-1.0621	0.14623
9	0.019198	0.1487	0.441141
10	0.064936	0.503	0.308404
11	0.002622	0.0203	0.491933
12	-0.10537	-0.8162	0.20881
13	0.090295	0.6994	0.243494
14	0.025613	0.1984	0.421703
15	-0.031553	-0.2444	0.403875
16	-0.062022	-0.4804	0.316338
17	-0.075073	-0.5815	0.281536
18	-0.131611	-1.0195	0.156041

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.952187 & 7.3756 & 0 \tabularnewline
2 & -0.083681 & -0.6482 & 0.259667 \tabularnewline
3 & -0.095611 & -0.7406 & 0.230912 \tabularnewline
4 & -0.084915 & -0.6578 & 0.256607 \tabularnewline
5 & -0.172927 & -1.3395 & 0.092732 \tabularnewline
6 & 0.091105 & 0.7057 & 0.241555 \tabularnewline
7 & -0.090566 & -0.7015 & 0.242845 \tabularnewline
8 & -0.137112 & -1.0621 & 0.14623 \tabularnewline
9 & 0.019198 & 0.1487 & 0.441141 \tabularnewline
10 & 0.064936 & 0.503 & 0.308404 \tabularnewline
11 & 0.002622 & 0.0203 & 0.491933 \tabularnewline
12 & -0.10537 & -0.8162 & 0.20881 \tabularnewline
13 & 0.090295 & 0.6994 & 0.243494 \tabularnewline
14 & 0.025613 & 0.1984 & 0.421703 \tabularnewline
15 & -0.031553 & -0.2444 & 0.403875 \tabularnewline
16 & -0.062022 & -0.4804 & 0.316338 \tabularnewline
17 & -0.075073 & -0.5815 & 0.281536 \tabularnewline
18 & -0.131611 & -1.0195 & 0.156041 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190361&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]0.952187[/C][C]7.3756[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.083681[/C][C]-0.6482[/C][C]0.259667[/C][/ROW]
[ROW][C]3[/C][C]-0.095611[/C][C]-0.7406[/C][C]0.230912[/C][/ROW]
[ROW][C]4[/C][C]-0.084915[/C][C]-0.6578[/C][C]0.256607[/C][/ROW]
[ROW][C]5[/C][C]-0.172927[/C][C]-1.3395[/C][C]0.092732[/C][/ROW]
[ROW][C]6[/C][C]0.091105[/C][C]0.7057[/C][C]0.241555[/C][/ROW]
[ROW][C]7[/C][C]-0.090566[/C][C]-0.7015[/C][C]0.242845[/C][/ROW]
[ROW][C]8[/C][C]-0.137112[/C][C]-1.0621[/C][C]0.14623[/C][/ROW]
[ROW][C]9[/C][C]0.019198[/C][C]0.1487[/C][C]0.441141[/C][/ROW]
[ROW][C]10[/C][C]0.064936[/C][C]0.503[/C][C]0.308404[/C][/ROW]
[ROW][C]11[/C][C]0.002622[/C][C]0.0203[/C][C]0.491933[/C][/ROW]
[ROW][C]12[/C][C]-0.10537[/C][C]-0.8162[/C][C]0.20881[/C][/ROW]
[ROW][C]13[/C][C]0.090295[/C][C]0.6994[/C][C]0.243494[/C][/ROW]
[ROW][C]14[/C][C]0.025613[/C][C]0.1984[/C][C]0.421703[/C][/ROW]
[ROW][C]15[/C][C]-0.031553[/C][C]-0.2444[/C][C]0.403875[/C][/ROW]
[ROW][C]16[/C][C]-0.062022[/C][C]-0.4804[/C][C]0.316338[/C][/ROW]
[ROW][C]17[/C][C]-0.075073[/C][C]-0.5815[/C][C]0.281536[/C][/ROW]
[ROW][C]18[/C][C]-0.131611[/C][C]-1.0195[/C][C]0.156041[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190361&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190361&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	0.952187	7.3756	0
2	-0.083681	-0.6482	0.259667
3	-0.095611	-0.7406	0.230912
4	-0.084915	-0.6578	0.256607
5	-0.172927	-1.3395	0.092732
6	0.091105	0.7057	0.241555
7	-0.090566	-0.7015	0.242845
8	-0.137112	-1.0621	0.14623
9	0.019198	0.1487	0.441141
10	0.064936	0.503	0.308404
11	0.002622	0.0203	0.491933
12	-0.10537	-0.8162	0.20881
13	0.090295	0.6994	0.243494
14	0.025613	0.1984	0.421703
15	-0.031553	-0.2444	0.403875
16	-0.062022	-0.4804	0.316338
17	-0.075073	-0.5815	0.281536
18	-0.131611	-1.0195	0.156041

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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Input Parameters & R Code