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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

Wed, 28 Mar 2012 15:59:49 -0400

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/Mar/28/t1332964984vb9yarrmcsxd2ub.htm/, Retrieved Sun, 05 May 2024 10:45:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164175, Retrieved Sun, 05 May 2024 10:45:35 +0000

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Original text written by user:

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No (this computation is public)

User-defined keywords

Estimated Impact

191

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

-       [(Partial) Autocorrelation Function] [] [2012-03-28 19:59:49] [26fc2906931796130cbcdf91b421d42d] [Current]

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1.44
1.45
1.45
1.47
1.49
1.5
1.5
1.5
1.5
1.5
1.5
1.51
1.52
1.51
1.51
1.51
1.52
1.52
1.52
1.52
1.52
1.53
1.53
1.53
1.53
1.54
1.54
1.55
1.56
1.55
1.56
1.56
1.56
1.56
1.57
1.56
1.57
1.58
1.58
1.58
1.6
1.61
1.61
1.61
1.6
1.59
1.56
1.57
1.55
1.59
1.62
1.63
1.62
1.56
1.56
1.54
1.54
1.52
1.56
1.59

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=164175&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=164175&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164175&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	0.13222	1.0156	0.156984
2	0.095425	0.733	0.233238
3	-0.254935	-1.9582	0.027471
4	-0.193385	-1.4854	0.071379
5	-0.246734	-1.8952	0.031484
6	-0.290942	-2.2348	0.014616
7	0.12754	0.9796	0.16563
8	0.045032	0.3459	0.365324
9	0.374435	2.8761	0.002797
10	0.058792	0.4516	0.326609
11	0.067587	0.5191	0.3028
12	-0.116971	-0.8985	0.186293
13	-0.066417	-0.5102	0.305923
14	-0.101605	-0.7804	0.219125
15	-0.038325	-0.2944	0.38475
16	-0.053375	-0.41	0.341652
17	-0.031978	-0.2456	0.403411

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.13222 & 1.0156 & 0.156984 \tabularnewline
2 & 0.095425 & 0.733 & 0.233238 \tabularnewline
3 & -0.254935 & -1.9582 & 0.027471 \tabularnewline
4 & -0.193385 & -1.4854 & 0.071379 \tabularnewline
5 & -0.246734 & -1.8952 & 0.031484 \tabularnewline
6 & -0.290942 & -2.2348 & 0.014616 \tabularnewline
7 & 0.12754 & 0.9796 & 0.16563 \tabularnewline
8 & 0.045032 & 0.3459 & 0.365324 \tabularnewline
9 & 0.374435 & 2.8761 & 0.002797 \tabularnewline
10 & 0.058792 & 0.4516 & 0.326609 \tabularnewline
11 & 0.067587 & 0.5191 & 0.3028 \tabularnewline
12 & -0.116971 & -0.8985 & 0.186293 \tabularnewline
13 & -0.066417 & -0.5102 & 0.305923 \tabularnewline
14 & -0.101605 & -0.7804 & 0.219125 \tabularnewline
15 & -0.038325 & -0.2944 & 0.38475 \tabularnewline
16 & -0.053375 & -0.41 & 0.341652 \tabularnewline
17 & -0.031978 & -0.2456 & 0.403411 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164175&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]0.13222[/C][C]1.0156[/C][C]0.156984[/C][/ROW]
[ROW][C]2[/C][C]0.095425[/C][C]0.733[/C][C]0.233238[/C][/ROW]
[ROW][C]3[/C][C]-0.254935[/C][C]-1.9582[/C][C]0.027471[/C][/ROW]
[ROW][C]4[/C][C]-0.193385[/C][C]-1.4854[/C][C]0.071379[/C][/ROW]
[ROW][C]5[/C][C]-0.246734[/C][C]-1.8952[/C][C]0.031484[/C][/ROW]
[ROW][C]6[/C][C]-0.290942[/C][C]-2.2348[/C][C]0.014616[/C][/ROW]
[ROW][C]7[/C][C]0.12754[/C][C]0.9796[/C][C]0.16563[/C][/ROW]
[ROW][C]8[/C][C]0.045032[/C][C]0.3459[/C][C]0.365324[/C][/ROW]
[ROW][C]9[/C][C]0.374435[/C][C]2.8761[/C][C]0.002797[/C][/ROW]
[ROW][C]10[/C][C]0.058792[/C][C]0.4516[/C][C]0.326609[/C][/ROW]
[ROW][C]11[/C][C]0.067587[/C][C]0.5191[/C][C]0.3028[/C][/ROW]
[ROW][C]12[/C][C]-0.116971[/C][C]-0.8985[/C][C]0.186293[/C][/ROW]
[ROW][C]13[/C][C]-0.066417[/C][C]-0.5102[/C][C]0.305923[/C][/ROW]
[ROW][C]14[/C][C]-0.101605[/C][C]-0.7804[/C][C]0.219125[/C][/ROW]
[ROW][C]15[/C][C]-0.038325[/C][C]-0.2944[/C][C]0.38475[/C][/ROW]
[ROW][C]16[/C][C]-0.053375[/C][C]-0.41[/C][C]0.341652[/C][/ROW]
[ROW][C]17[/C][C]-0.031978[/C][C]-0.2456[/C][C]0.403411[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164175&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164175&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	0.13222	1.0156	0.156984
2	0.095425	0.733	0.233238
3	-0.254935	-1.9582	0.027471
4	-0.193385	-1.4854	0.071379
5	-0.246734	-1.8952	0.031484
6	-0.290942	-2.2348	0.014616
7	0.12754	0.9796	0.16563
8	0.045032	0.3459	0.365324
9	0.374435	2.8761	0.002797
10	0.058792	0.4516	0.326609
11	0.067587	0.5191	0.3028
12	-0.116971	-0.8985	0.186293
13	-0.066417	-0.5102	0.305923
14	-0.101605	-0.7804	0.219125
15	-0.038325	-0.2944	0.38475
16	-0.053375	-0.41	0.341652
17	-0.031978	-0.2456	0.403411

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.13222	1.0156	0.156984
2	0.07933	0.6093	0.272317
3	-0.283755	-2.1796	0.016647
4	-0.144767	-1.112	0.135329
5	-0.169899	-1.305	0.098476
6	-0.330094	-2.5355	0.006949
7	0.151339	1.1625	0.124865
8	-0.076435	-0.5871	0.279685
9	0.186463	1.4323	0.078674
10	-0.031646	-0.2431	0.404395
11	-0.073084	-0.5614	0.288337
12	-0.01761	-0.1353	0.446432
13	0.089519	0.6876	0.247196
14	-0.031998	-0.2458	0.403352
15	0.144593	1.1106	0.135614
16	-0.188823	-1.4504	0.076125
17	-0.055317	-0.4249	0.336229

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.13222 & 1.0156 & 0.156984 \tabularnewline
2 & 0.07933 & 0.6093 & 0.272317 \tabularnewline
3 & -0.283755 & -2.1796 & 0.016647 \tabularnewline
4 & -0.144767 & -1.112 & 0.135329 \tabularnewline
5 & -0.169899 & -1.305 & 0.098476 \tabularnewline
6 & -0.330094 & -2.5355 & 0.006949 \tabularnewline
7 & 0.151339 & 1.1625 & 0.124865 \tabularnewline
8 & -0.076435 & -0.5871 & 0.279685 \tabularnewline
9 & 0.186463 & 1.4323 & 0.078674 \tabularnewline
10 & -0.031646 & -0.2431 & 0.404395 \tabularnewline
11 & -0.073084 & -0.5614 & 0.288337 \tabularnewline
12 & -0.01761 & -0.1353 & 0.446432 \tabularnewline
13 & 0.089519 & 0.6876 & 0.247196 \tabularnewline
14 & -0.031998 & -0.2458 & 0.403352 \tabularnewline
15 & 0.144593 & 1.1106 & 0.135614 \tabularnewline
16 & -0.188823 & -1.4504 & 0.076125 \tabularnewline
17 & -0.055317 & -0.4249 & 0.336229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164175&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]0.13222[/C][C]1.0156[/C][C]0.156984[/C][/ROW]
[ROW][C]2[/C][C]0.07933[/C][C]0.6093[/C][C]0.272317[/C][/ROW]
[ROW][C]3[/C][C]-0.283755[/C][C]-2.1796[/C][C]0.016647[/C][/ROW]
[ROW][C]4[/C][C]-0.144767[/C][C]-1.112[/C][C]0.135329[/C][/ROW]
[ROW][C]5[/C][C]-0.169899[/C][C]-1.305[/C][C]0.098476[/C][/ROW]
[ROW][C]6[/C][C]-0.330094[/C][C]-2.5355[/C][C]0.006949[/C][/ROW]
[ROW][C]7[/C][C]0.151339[/C][C]1.1625[/C][C]0.124865[/C][/ROW]
[ROW][C]8[/C][C]-0.076435[/C][C]-0.5871[/C][C]0.279685[/C][/ROW]
[ROW][C]9[/C][C]0.186463[/C][C]1.4323[/C][C]0.078674[/C][/ROW]
[ROW][C]10[/C][C]-0.031646[/C][C]-0.2431[/C][C]0.404395[/C][/ROW]
[ROW][C]11[/C][C]-0.073084[/C][C]-0.5614[/C][C]0.288337[/C][/ROW]
[ROW][C]12[/C][C]-0.01761[/C][C]-0.1353[/C][C]0.446432[/C][/ROW]
[ROW][C]13[/C][C]0.089519[/C][C]0.6876[/C][C]0.247196[/C][/ROW]
[ROW][C]14[/C][C]-0.031998[/C][C]-0.2458[/C][C]0.403352[/C][/ROW]
[ROW][C]15[/C][C]0.144593[/C][C]1.1106[/C][C]0.135614[/C][/ROW]
[ROW][C]16[/C][C]-0.188823[/C][C]-1.4504[/C][C]0.076125[/C][/ROW]
[ROW][C]17[/C][C]-0.055317[/C][C]-0.4249[/C][C]0.336229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164175&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164175&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	0.13222	1.0156	0.156984
2	0.07933	0.6093	0.272317
3	-0.283755	-2.1796	0.016647
4	-0.144767	-1.112	0.135329
5	-0.169899	-1.305	0.098476
6	-0.330094	-2.5355	0.006949
7	0.151339	1.1625	0.124865
8	-0.076435	-0.5871	0.279685
9	0.186463	1.4323	0.078674
10	-0.031646	-0.2431	0.404395
11	-0.073084	-0.5614	0.288337
12	-0.01761	-0.1353	0.446432
13	0.089519	0.6876	0.247196
14	-0.031998	-0.2458	0.403352
15	0.144593	1.1106	0.135614
16	-0.188823	-1.4504	0.076125
17	-0.055317	-0.4249	0.336229

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

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code