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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 29 Dec 2010 09:44:31 +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/29/t1293615737wlc7w8wxd68ukpj.htm/, Retrieved Fri, 03 May 2024 08:56:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116650, Retrieved Fri, 03 May 2024 08:56:51 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

128

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 ru...] [2010-12-14 18:37:20] [d6e648f00513dd750579ba7880c5fbf5]
- R  D    [(Partial) Autocorrelation Function] [] [2010-12-16 10:15:17] [b10d6b9682dfaaa479f495240bcd67cf]
-   PD      [(Partial) Autocorrelation Function] [] [2010-12-19 15:38:05] [b10d6b9682dfaaa479f495240bcd67cf]
-    D        [(Partial) Autocorrelation Function] [] [2010-12-28 20:57:12] [58af523ef9b33032fd2497c80088399b]
-    D            [(Partial) Autocorrelation Function] [] [2010-12-29 09:44:31] [a3cd012a7211edfe9ed4466e21aef6a6] [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	'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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116650&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116650&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116650&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.290067	2.1512	0.017935
2	0.087162	0.6464	0.26035
3	-0.232281	-1.7226	0.045286
4	-0.372489	-2.7624	0.003893
5	-0.036806	-0.273	0.392953
6	-0.12116	-0.8985	0.186405
7	0.022519	0.167	0.433988
8	-0.233221	-1.7296	0.044654
9	-0.167551	-1.2426	0.109645
10	0.128251	0.9511	0.172849
11	0.107391	0.7964	0.214603
12	0.523948	3.8857	0.000138
13	0.205107	1.5211	0.06698
14	0.03855	0.2859	0.388018
15	-0.144326	-1.0704	0.144568
16	-0.279112	-2.0699	0.021583
17	-0.013541	-0.1004	0.460188

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.290067 & 2.1512 & 0.017935 \tabularnewline
2 & 0.087162 & 0.6464 & 0.26035 \tabularnewline
3 & -0.232281 & -1.7226 & 0.045286 \tabularnewline
4 & -0.372489 & -2.7624 & 0.003893 \tabularnewline
5 & -0.036806 & -0.273 & 0.392953 \tabularnewline
6 & -0.12116 & -0.8985 & 0.186405 \tabularnewline
7 & 0.022519 & 0.167 & 0.433988 \tabularnewline
8 & -0.233221 & -1.7296 & 0.044654 \tabularnewline
9 & -0.167551 & -1.2426 & 0.109645 \tabularnewline
10 & 0.128251 & 0.9511 & 0.172849 \tabularnewline
11 & 0.107391 & 0.7964 & 0.214603 \tabularnewline
12 & 0.523948 & 3.8857 & 0.000138 \tabularnewline
13 & 0.205107 & 1.5211 & 0.06698 \tabularnewline
14 & 0.03855 & 0.2859 & 0.388018 \tabularnewline
15 & -0.144326 & -1.0704 & 0.144568 \tabularnewline
16 & -0.279112 & -2.0699 & 0.021583 \tabularnewline
17 & -0.013541 & -0.1004 & 0.460188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116650&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]0.290067[/C][C]2.1512[/C][C]0.017935[/C][/ROW]
[ROW][C]2[/C][C]0.087162[/C][C]0.6464[/C][C]0.26035[/C][/ROW]
[ROW][C]3[/C][C]-0.232281[/C][C]-1.7226[/C][C]0.045286[/C][/ROW]
[ROW][C]4[/C][C]-0.372489[/C][C]-2.7624[/C][C]0.003893[/C][/ROW]
[ROW][C]5[/C][C]-0.036806[/C][C]-0.273[/C][C]0.392953[/C][/ROW]
[ROW][C]6[/C][C]-0.12116[/C][C]-0.8985[/C][C]0.186405[/C][/ROW]
[ROW][C]7[/C][C]0.022519[/C][C]0.167[/C][C]0.433988[/C][/ROW]
[ROW][C]8[/C][C]-0.233221[/C][C]-1.7296[/C][C]0.044654[/C][/ROW]
[ROW][C]9[/C][C]-0.167551[/C][C]-1.2426[/C][C]0.109645[/C][/ROW]
[ROW][C]10[/C][C]0.128251[/C][C]0.9511[/C][C]0.172849[/C][/ROW]
[ROW][C]11[/C][C]0.107391[/C][C]0.7964[/C][C]0.214603[/C][/ROW]
[ROW][C]12[/C][C]0.523948[/C][C]3.8857[/C][C]0.000138[/C][/ROW]
[ROW][C]13[/C][C]0.205107[/C][C]1.5211[/C][C]0.06698[/C][/ROW]
[ROW][C]14[/C][C]0.03855[/C][C]0.2859[/C][C]0.388018[/C][/ROW]
[ROW][C]15[/C][C]-0.144326[/C][C]-1.0704[/C][C]0.144568[/C][/ROW]
[ROW][C]16[/C][C]-0.279112[/C][C]-2.0699[/C][C]0.021583[/C][/ROW]
[ROW][C]17[/C][C]-0.013541[/C][C]-0.1004[/C][C]0.460188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116650&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116650&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	0.290067	2.1512	0.017935
2	0.087162	0.6464	0.26035
3	-0.232281	-1.7226	0.045286
4	-0.372489	-2.7624	0.003893
5	-0.036806	-0.273	0.392953
6	-0.12116	-0.8985	0.186405
7	0.022519	0.167	0.433988
8	-0.233221	-1.7296	0.044654
9	-0.167551	-1.2426	0.109645
10	0.128251	0.9511	0.172849
11	0.107391	0.7964	0.214603
12	0.523948	3.8857	0.000138
13	0.205107	1.5211	0.06698
14	0.03855	0.2859	0.388018
15	-0.144326	-1.0704	0.144568
16	-0.279112	-2.0699	0.021583
17	-0.013541	-0.1004	0.460188

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.290067	2.1512	0.017935
2	0.003301	0.0245	0.490279
3	-0.282184	-2.0927	0.0205
4	-0.273647	-2.0294	0.023633
5	0.211122	1.5657	0.061574
6	-0.189068	-1.4022	0.083242
7	-0.100012	-0.7417	0.230709
8	-0.349793	-2.5941	0.006065
9	-0.020712	-0.1536	0.439242
10	0.216487	1.6055	0.057054
11	-0.082417	-0.6112	0.271786
12	0.323619	2.4	0.009903
13	0.021513	0.1595	0.436913
14	-0.006181	-0.0458	0.481803
15	-0.042929	-0.3184	0.375705
16	0.042723	0.3168	0.376282
17	0.064384	0.4775	0.317454

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.290067 & 2.1512 & 0.017935 \tabularnewline
2 & 0.003301 & 0.0245 & 0.490279 \tabularnewline
3 & -0.282184 & -2.0927 & 0.0205 \tabularnewline
4 & -0.273647 & -2.0294 & 0.023633 \tabularnewline
5 & 0.211122 & 1.5657 & 0.061574 \tabularnewline
6 & -0.189068 & -1.4022 & 0.083242 \tabularnewline
7 & -0.100012 & -0.7417 & 0.230709 \tabularnewline
8 & -0.349793 & -2.5941 & 0.006065 \tabularnewline
9 & -0.020712 & -0.1536 & 0.439242 \tabularnewline
10 & 0.216487 & 1.6055 & 0.057054 \tabularnewline
11 & -0.082417 & -0.6112 & 0.271786 \tabularnewline
12 & 0.323619 & 2.4 & 0.009903 \tabularnewline
13 & 0.021513 & 0.1595 & 0.436913 \tabularnewline
14 & -0.006181 & -0.0458 & 0.481803 \tabularnewline
15 & -0.042929 & -0.3184 & 0.375705 \tabularnewline
16 & 0.042723 & 0.3168 & 0.376282 \tabularnewline
17 & 0.064384 & 0.4775 & 0.317454 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116650&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]0.290067[/C][C]2.1512[/C][C]0.017935[/C][/ROW]
[ROW][C]2[/C][C]0.003301[/C][C]0.0245[/C][C]0.490279[/C][/ROW]
[ROW][C]3[/C][C]-0.282184[/C][C]-2.0927[/C][C]0.0205[/C][/ROW]
[ROW][C]4[/C][C]-0.273647[/C][C]-2.0294[/C][C]0.023633[/C][/ROW]
[ROW][C]5[/C][C]0.211122[/C][C]1.5657[/C][C]0.061574[/C][/ROW]
[ROW][C]6[/C][C]-0.189068[/C][C]-1.4022[/C][C]0.083242[/C][/ROW]
[ROW][C]7[/C][C]-0.100012[/C][C]-0.7417[/C][C]0.230709[/C][/ROW]
[ROW][C]8[/C][C]-0.349793[/C][C]-2.5941[/C][C]0.006065[/C][/ROW]
[ROW][C]9[/C][C]-0.020712[/C][C]-0.1536[/C][C]0.439242[/C][/ROW]
[ROW][C]10[/C][C]0.216487[/C][C]1.6055[/C][C]0.057054[/C][/ROW]
[ROW][C]11[/C][C]-0.082417[/C][C]-0.6112[/C][C]0.271786[/C][/ROW]
[ROW][C]12[/C][C]0.323619[/C][C]2.4[/C][C]0.009903[/C][/ROW]
[ROW][C]13[/C][C]0.021513[/C][C]0.1595[/C][C]0.436913[/C][/ROW]
[ROW][C]14[/C][C]-0.006181[/C][C]-0.0458[/C][C]0.481803[/C][/ROW]
[ROW][C]15[/C][C]-0.042929[/C][C]-0.3184[/C][C]0.375705[/C][/ROW]
[ROW][C]16[/C][C]0.042723[/C][C]0.3168[/C][C]0.376282[/C][/ROW]
[ROW][C]17[/C][C]0.064384[/C][C]0.4775[/C][C]0.317454[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116650&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116650&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	0.290067	2.1512	0.017935
2	0.003301	0.0245	0.490279
3	-0.282184	-2.0927	0.0205
4	-0.273647	-2.0294	0.023633
5	0.211122	1.5657	0.061574
6	-0.189068	-1.4022	0.083242
7	-0.100012	-0.7417	0.230709
8	-0.349793	-2.5941	0.006065
9	-0.020712	-0.1536	0.439242
10	0.216487	1.6055	0.057054
11	-0.082417	-0.6112	0.271786
12	0.323619	2.4	0.009903
13	0.021513	0.1595	0.436913
14	-0.006181	-0.0458	0.481803
15	-0.042929	-0.3184	0.375705
16	0.042723	0.3168	0.376282
17	0.064384	0.4775	0.317454

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code