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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 22 Nov 2011 10:16:48 -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/2011/Nov/22/t1321975039lrktnnhp4hjxi9g.htm/, Retrieved Wed, 24 Apr 2024 12:14:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=146276, Retrieved Wed, 24 Apr 2024 12:14:07 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

133

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

-     [Univariate Explorative Data Analysis] [Univariate EDA] [2008-12-04 14:40:57] [bc937651ef42bf891200cf0e0edc7238]
- RMPD  [Univariate Data Series] [] [2010-12-14 17:58:22] [9b13650c94c5192ca5135ec8a1fa39f7]
-   PD    [Univariate Data Series] [] [2010-12-15 15:41:03] [9b13650c94c5192ca5135ec8a1fa39f7]
- RMPD        [(Partial) Autocorrelation Function] [] [2011-11-22 15:16:48] [5fd8c857995b7937a45335fd5ccccdde] [Current]
- R P           [(Partial) Autocorrelation Function] [] [2011-11-22 15:41:01] [9b13650c94c5192ca5135ec8a1fa39f7] 

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-14
-7
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1
-1
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1
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0
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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	'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146276&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=146276&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146276&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.897378	6.9511	0
2	0.826687	6.4035	0
3	0.750085	5.8101	0
4	0.653187	5.0596	2e-06
5	0.560313	4.3402	2.8e-05
6	0.443986	3.4391	0.000534
7	0.359035	2.7811	0.003614
8	0.267406	2.0713	0.021319
9	0.154859	1.1995	0.117519
10	0.100756	0.7805	0.219097
11	0.047944	0.3714	0.355835
12	-0.029664	-0.2298	0.409522
13	-0.092121	-0.7136	0.239131
14	-0.171523	-1.3286	0.094503
15	-0.236733	-1.8337	0.035828
16	-0.329322	-2.5509	0.006656
17	-0.383741	-2.9724	0.002124

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.897378 & 6.9511 & 0 \tabularnewline
2 & 0.826687 & 6.4035 & 0 \tabularnewline
3 & 0.750085 & 5.8101 & 0 \tabularnewline
4 & 0.653187 & 5.0596 & 2e-06 \tabularnewline
5 & 0.560313 & 4.3402 & 2.8e-05 \tabularnewline
6 & 0.443986 & 3.4391 & 0.000534 \tabularnewline
7 & 0.359035 & 2.7811 & 0.003614 \tabularnewline
8 & 0.267406 & 2.0713 & 0.021319 \tabularnewline
9 & 0.154859 & 1.1995 & 0.117519 \tabularnewline
10 & 0.100756 & 0.7805 & 0.219097 \tabularnewline
11 & 0.047944 & 0.3714 & 0.355835 \tabularnewline
12 & -0.029664 & -0.2298 & 0.409522 \tabularnewline
13 & -0.092121 & -0.7136 & 0.239131 \tabularnewline
14 & -0.171523 & -1.3286 & 0.094503 \tabularnewline
15 & -0.236733 & -1.8337 & 0.035828 \tabularnewline
16 & -0.329322 & -2.5509 & 0.006656 \tabularnewline
17 & -0.383741 & -2.9724 & 0.002124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146276&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]0.897378[/C][C]6.9511[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.826687[/C][C]6.4035[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.750085[/C][C]5.8101[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.653187[/C][C]5.0596[/C][C]2e-06[/C][/ROW]
[ROW][C]5[/C][C]0.560313[/C][C]4.3402[/C][C]2.8e-05[/C][/ROW]
[ROW][C]6[/C][C]0.443986[/C][C]3.4391[/C][C]0.000534[/C][/ROW]
[ROW][C]7[/C][C]0.359035[/C][C]2.7811[/C][C]0.003614[/C][/ROW]
[ROW][C]8[/C][C]0.267406[/C][C]2.0713[/C][C]0.021319[/C][/ROW]
[ROW][C]9[/C][C]0.154859[/C][C]1.1995[/C][C]0.117519[/C][/ROW]
[ROW][C]10[/C][C]0.100756[/C][C]0.7805[/C][C]0.219097[/C][/ROW]
[ROW][C]11[/C][C]0.047944[/C][C]0.3714[/C][C]0.355835[/C][/ROW]
[ROW][C]12[/C][C]-0.029664[/C][C]-0.2298[/C][C]0.409522[/C][/ROW]
[ROW][C]13[/C][C]-0.092121[/C][C]-0.7136[/C][C]0.239131[/C][/ROW]
[ROW][C]14[/C][C]-0.171523[/C][C]-1.3286[/C][C]0.094503[/C][/ROW]
[ROW][C]15[/C][C]-0.236733[/C][C]-1.8337[/C][C]0.035828[/C][/ROW]
[ROW][C]16[/C][C]-0.329322[/C][C]-2.5509[/C][C]0.006656[/C][/ROW]
[ROW][C]17[/C][C]-0.383741[/C][C]-2.9724[/C][C]0.002124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=146276&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146276&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	0.897378	6.9511	0
2	0.826687	6.4035	0
3	0.750085	5.8101	0
4	0.653187	5.0596	2e-06
5	0.560313	4.3402	2.8e-05
6	0.443986	3.4391	0.000534
7	0.359035	2.7811	0.003614
8	0.267406	2.0713	0.021319
9	0.154859	1.1995	0.117519
10	0.100756	0.7805	0.219097
11	0.047944	0.3714	0.355835
12	-0.029664	-0.2298	0.409522
13	-0.092121	-0.7136	0.239131
14	-0.171523	-1.3286	0.094503
15	-0.236733	-1.8337	0.035828
16	-0.329322	-2.5509	0.006656
17	-0.383741	-2.9724	0.002124

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.897378	6.9511	0
2	0.109905	0.8513	0.198987
3	-0.046054	-0.3567	0.361271
4	-0.154622	-1.1977	0.117872
5	-0.069593	-0.5391	0.295918
6	-0.180484	-1.398	0.083627
7	0.062588	0.4848	0.314791
8	-0.050943	-0.3946	0.347267
9	-0.171574	-1.329	0.094439
10	0.174768	1.3537	0.090448
11	0.050408	0.3905	0.348789
12	-0.21228	-1.6443	0.052671
13	-0.060575	-0.4692	0.32031
14	-0.155322	-1.2031	0.116829
15	-0.115523	-0.8948	0.187224
16	-0.184998	-1.433	0.078525
17	0.129981	1.0068	0.15903

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.897378 & 6.9511 & 0 \tabularnewline
2 & 0.109905 & 0.8513 & 0.198987 \tabularnewline
3 & -0.046054 & -0.3567 & 0.361271 \tabularnewline
4 & -0.154622 & -1.1977 & 0.117872 \tabularnewline
5 & -0.069593 & -0.5391 & 0.295918 \tabularnewline
6 & -0.180484 & -1.398 & 0.083627 \tabularnewline
7 & 0.062588 & 0.4848 & 0.314791 \tabularnewline
8 & -0.050943 & -0.3946 & 0.347267 \tabularnewline
9 & -0.171574 & -1.329 & 0.094439 \tabularnewline
10 & 0.174768 & 1.3537 & 0.090448 \tabularnewline
11 & 0.050408 & 0.3905 & 0.348789 \tabularnewline
12 & -0.21228 & -1.6443 & 0.052671 \tabularnewline
13 & -0.060575 & -0.4692 & 0.32031 \tabularnewline
14 & -0.155322 & -1.2031 & 0.116829 \tabularnewline
15 & -0.115523 & -0.8948 & 0.187224 \tabularnewline
16 & -0.184998 & -1.433 & 0.078525 \tabularnewline
17 & 0.129981 & 1.0068 & 0.15903 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=146276&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]0.897378[/C][C]6.9511[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.109905[/C][C]0.8513[/C][C]0.198987[/C][/ROW]
[ROW][C]3[/C][C]-0.046054[/C][C]-0.3567[/C][C]0.361271[/C][/ROW]
[ROW][C]4[/C][C]-0.154622[/C][C]-1.1977[/C][C]0.117872[/C][/ROW]
[ROW][C]5[/C][C]-0.069593[/C][C]-0.5391[/C][C]0.295918[/C][/ROW]
[ROW][C]6[/C][C]-0.180484[/C][C]-1.398[/C][C]0.083627[/C][/ROW]
[ROW][C]7[/C][C]0.062588[/C][C]0.4848[/C][C]0.314791[/C][/ROW]
[ROW][C]8[/C][C]-0.050943[/C][C]-0.3946[/C][C]0.347267[/C][/ROW]
[ROW][C]9[/C][C]-0.171574[/C][C]-1.329[/C][C]0.094439[/C][/ROW]
[ROW][C]10[/C][C]0.174768[/C][C]1.3537[/C][C]0.090448[/C][/ROW]
[ROW][C]11[/C][C]0.050408[/C][C]0.3905[/C][C]0.348789[/C][/ROW]
[ROW][C]12[/C][C]-0.21228[/C][C]-1.6443[/C][C]0.052671[/C][/ROW]
[ROW][C]13[/C][C]-0.060575[/C][C]-0.4692[/C][C]0.32031[/C][/ROW]
[ROW][C]14[/C][C]-0.155322[/C][C]-1.2031[/C][C]0.116829[/C][/ROW]
[ROW][C]15[/C][C]-0.115523[/C][C]-0.8948[/C][C]0.187224[/C][/ROW]
[ROW][C]16[/C][C]-0.184998[/C][C]-1.433[/C][C]0.078525[/C][/ROW]
[ROW][C]17[/C][C]0.129981[/C][C]1.0068[/C][C]0.15903[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=146276&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=146276&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	0.897378	6.9511	0
2	0.109905	0.8513	0.198987
3	-0.046054	-0.3567	0.361271
4	-0.154622	-1.1977	0.117872
5	-0.069593	-0.5391	0.295918
6	-0.180484	-1.398	0.083627
7	0.062588	0.4848	0.314791
8	-0.050943	-0.3946	0.347267
9	-0.171574	-1.329	0.094439
10	0.174768	1.3537	0.090448
11	0.050408	0.3905	0.348789
12	-0.21228	-1.6443	0.052671
13	-0.060575	-0.4692	0.32031
14	-0.155322	-1.2031	0.116829
15	-0.115523	-0.8948	0.187224
16	-0.184998	-1.433	0.078525
17	0.129981	1.0068	0.15903

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')

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Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code