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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 18 Dec 2010 11:15:17 +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/18/t1292670823nkjbqp9cpsoxwfu.htm/, Retrieved Tue, 30 Apr 2024 01:07:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111846, Retrieved Tue, 30 Apr 2024 01:07:48 +0000

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Estimated Impact

117

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

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [(Partial) Autocorrelation Function] [autocorrelatie st...] [2010-12-14 18:43:32] [d6e648f00513dd750579ba7880c5fbf5]
- R  D    [(Partial) Autocorrelation Function] [] [2010-12-16 10:13:58] [58af523ef9b33032fd2497c80088399b]
-   PD      [(Partial) Autocorrelation Function] [] [2010-12-16 19:17:07] [58af523ef9b33032fd2497c80088399b]
-   PD          [(Partial) Autocorrelation Function] [] [2010-12-18 11:15:17] [7c1b7ddc8e9000e55b944088fdfb52dc] [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	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111846&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111846&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111846&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	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.263807	1.7299	0.045411
2	0.09085	0.5957	0.277234
3	-0.075858	-0.4974	0.310708
4	-0.129147	-0.8469	0.200877
5	-0.179523	-1.1772	0.122793
6	0.149177	0.9782	0.166719
7	0.181612	1.1909	0.120111
8	0.070122	0.4598	0.32398
9	-0.006008	-0.0394	0.484379
10	0.038134	0.2501	0.401866
11	-0.289609	-1.8991	0.032137
12	-0.072124	-0.4729	0.319321
13	0.063399	0.4157	0.339836
14	0.031082	0.2038	0.41973
15	-0.025134	-0.1648	0.434931
16	-0.022682	-0.1487	0.441229
17	-0.052622	-0.3451	0.365865

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.263807 & 1.7299 & 0.045411 \tabularnewline
2 & 0.09085 & 0.5957 & 0.277234 \tabularnewline
3 & -0.075858 & -0.4974 & 0.310708 \tabularnewline
4 & -0.129147 & -0.8469 & 0.200877 \tabularnewline
5 & -0.179523 & -1.1772 & 0.122793 \tabularnewline
6 & 0.149177 & 0.9782 & 0.166719 \tabularnewline
7 & 0.181612 & 1.1909 & 0.120111 \tabularnewline
8 & 0.070122 & 0.4598 & 0.32398 \tabularnewline
9 & -0.006008 & -0.0394 & 0.484379 \tabularnewline
10 & 0.038134 & 0.2501 & 0.401866 \tabularnewline
11 & -0.289609 & -1.8991 & 0.032137 \tabularnewline
12 & -0.072124 & -0.4729 & 0.319321 \tabularnewline
13 & 0.063399 & 0.4157 & 0.339836 \tabularnewline
14 & 0.031082 & 0.2038 & 0.41973 \tabularnewline
15 & -0.025134 & -0.1648 & 0.434931 \tabularnewline
16 & -0.022682 & -0.1487 & 0.441229 \tabularnewline
17 & -0.052622 & -0.3451 & 0.365865 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111846&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]0.263807[/C][C]1.7299[/C][C]0.045411[/C][/ROW]
[ROW][C]2[/C][C]0.09085[/C][C]0.5957[/C][C]0.277234[/C][/ROW]
[ROW][C]3[/C][C]-0.075858[/C][C]-0.4974[/C][C]0.310708[/C][/ROW]
[ROW][C]4[/C][C]-0.129147[/C][C]-0.8469[/C][C]0.200877[/C][/ROW]
[ROW][C]5[/C][C]-0.179523[/C][C]-1.1772[/C][C]0.122793[/C][/ROW]
[ROW][C]6[/C][C]0.149177[/C][C]0.9782[/C][C]0.166719[/C][/ROW]
[ROW][C]7[/C][C]0.181612[/C][C]1.1909[/C][C]0.120111[/C][/ROW]
[ROW][C]8[/C][C]0.070122[/C][C]0.4598[/C][C]0.32398[/C][/ROW]
[ROW][C]9[/C][C]-0.006008[/C][C]-0.0394[/C][C]0.484379[/C][/ROW]
[ROW][C]10[/C][C]0.038134[/C][C]0.2501[/C][C]0.401866[/C][/ROW]
[ROW][C]11[/C][C]-0.289609[/C][C]-1.8991[/C][C]0.032137[/C][/ROW]
[ROW][C]12[/C][C]-0.072124[/C][C]-0.4729[/C][C]0.319321[/C][/ROW]
[ROW][C]13[/C][C]0.063399[/C][C]0.4157[/C][C]0.339836[/C][/ROW]
[ROW][C]14[/C][C]0.031082[/C][C]0.2038[/C][C]0.41973[/C][/ROW]
[ROW][C]15[/C][C]-0.025134[/C][C]-0.1648[/C][C]0.434931[/C][/ROW]
[ROW][C]16[/C][C]-0.022682[/C][C]-0.1487[/C][C]0.441229[/C][/ROW]
[ROW][C]17[/C][C]-0.052622[/C][C]-0.3451[/C][C]0.365865[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111846&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111846&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	0.263807	1.7299	0.045411
2	0.09085	0.5957	0.277234
3	-0.075858	-0.4974	0.310708
4	-0.129147	-0.8469	0.200877
5	-0.179523	-1.1772	0.122793
6	0.149177	0.9782	0.166719
7	0.181612	1.1909	0.120111
8	0.070122	0.4598	0.32398
9	-0.006008	-0.0394	0.484379
10	0.038134	0.2501	0.401866
11	-0.289609	-1.8991	0.032137
12	-0.072124	-0.4729	0.319321
13	0.063399	0.4157	0.339836
14	0.031082	0.2038	0.41973
15	-0.025134	-0.1648	0.434931
16	-0.022682	-0.1487	0.441229
17	-0.052622	-0.3451	0.365865

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.263807	1.7299	0.045411
2	0.022846	0.1498	0.440806
3	-0.11324	-0.7426	0.230891
4	-0.091776	-0.6018	0.275228
5	-0.121505	-0.7968	0.214983
6	0.255752	1.6771	0.050392
7	0.105067	0.689	0.24727
8	-0.080881	-0.5304	0.299291
9	-0.050457	-0.3309	0.371176
10	0.095629	0.6271	0.266961
11	-0.260996	-1.7115	0.0471
12	0.077905	0.5109	0.306031
13	0.087175	0.5716	0.285269
14	-0.080274	-0.5264	0.300661
15	-0.055796	-0.3659	0.358124
16	-0.111855	-0.7335	0.233622
17	0.090644	0.5944	0.277682

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.263807 & 1.7299 & 0.045411 \tabularnewline
2 & 0.022846 & 0.1498 & 0.440806 \tabularnewline
3 & -0.11324 & -0.7426 & 0.230891 \tabularnewline
4 & -0.091776 & -0.6018 & 0.275228 \tabularnewline
5 & -0.121505 & -0.7968 & 0.214983 \tabularnewline
6 & 0.255752 & 1.6771 & 0.050392 \tabularnewline
7 & 0.105067 & 0.689 & 0.24727 \tabularnewline
8 & -0.080881 & -0.5304 & 0.299291 \tabularnewline
9 & -0.050457 & -0.3309 & 0.371176 \tabularnewline
10 & 0.095629 & 0.6271 & 0.266961 \tabularnewline
11 & -0.260996 & -1.7115 & 0.0471 \tabularnewline
12 & 0.077905 & 0.5109 & 0.306031 \tabularnewline
13 & 0.087175 & 0.5716 & 0.285269 \tabularnewline
14 & -0.080274 & -0.5264 & 0.300661 \tabularnewline
15 & -0.055796 & -0.3659 & 0.358124 \tabularnewline
16 & -0.111855 & -0.7335 & 0.233622 \tabularnewline
17 & 0.090644 & 0.5944 & 0.277682 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111846&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]0.263807[/C][C]1.7299[/C][C]0.045411[/C][/ROW]
[ROW][C]2[/C][C]0.022846[/C][C]0.1498[/C][C]0.440806[/C][/ROW]
[ROW][C]3[/C][C]-0.11324[/C][C]-0.7426[/C][C]0.230891[/C][/ROW]
[ROW][C]4[/C][C]-0.091776[/C][C]-0.6018[/C][C]0.275228[/C][/ROW]
[ROW][C]5[/C][C]-0.121505[/C][C]-0.7968[/C][C]0.214983[/C][/ROW]
[ROW][C]6[/C][C]0.255752[/C][C]1.6771[/C][C]0.050392[/C][/ROW]
[ROW][C]7[/C][C]0.105067[/C][C]0.689[/C][C]0.24727[/C][/ROW]
[ROW][C]8[/C][C]-0.080881[/C][C]-0.5304[/C][C]0.299291[/C][/ROW]
[ROW][C]9[/C][C]-0.050457[/C][C]-0.3309[/C][C]0.371176[/C][/ROW]
[ROW][C]10[/C][C]0.095629[/C][C]0.6271[/C][C]0.266961[/C][/ROW]
[ROW][C]11[/C][C]-0.260996[/C][C]-1.7115[/C][C]0.0471[/C][/ROW]
[ROW][C]12[/C][C]0.077905[/C][C]0.5109[/C][C]0.306031[/C][/ROW]
[ROW][C]13[/C][C]0.087175[/C][C]0.5716[/C][C]0.285269[/C][/ROW]
[ROW][C]14[/C][C]-0.080274[/C][C]-0.5264[/C][C]0.300661[/C][/ROW]
[ROW][C]15[/C][C]-0.055796[/C][C]-0.3659[/C][C]0.358124[/C][/ROW]
[ROW][C]16[/C][C]-0.111855[/C][C]-0.7335[/C][C]0.233622[/C][/ROW]
[ROW][C]17[/C][C]0.090644[/C][C]0.5944[/C][C]0.277682[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111846&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111846&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	0.263807	1.7299	0.045411
2	0.022846	0.1498	0.440806
3	-0.11324	-0.7426	0.230891
4	-0.091776	-0.6018	0.275228
5	-0.121505	-0.7968	0.214983
6	0.255752	1.6771	0.050392
7	0.105067	0.689	0.24727
8	-0.080881	-0.5304	0.299291
9	-0.050457	-0.3309	0.371176
10	0.095629	0.6271	0.266961
11	-0.260996	-1.7115	0.0471
12	0.077905	0.5109	0.306031
13	0.087175	0.5716	0.285269
14	-0.080274	-0.5264	0.300661
15	-0.055796	-0.3659	0.358124
16	-0.111855	-0.7335	0.233622
17	0.090644	0.5944	0.277682

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code