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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 13 Nov 2013 04:02:45 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Nov/13/t1384333457zveam40ac0kn2l0.htm/, Retrieved Mon, 29 Apr 2024 00:16:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=224641, Retrieved Mon, 29 Apr 2024 00:16:50 +0000

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-       [(Partial) Autocorrelation Function] [] [2013-11-13 09:02:45] [3050d341fa02a6066b7b273abfa2c28b] [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	'Gwilym Jenkins' @ jenkins.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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224641&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224641&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224641&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.247657	2.2563	0.013342
2	-0.328247	-2.9905	0.001833
3	-0.354678	-3.2313	0.000884
4	-0.164047	-1.4945	0.069413
5	0.02849	0.2596	0.397924
6	0.17134	1.561	0.061166
7	0.057033	0.5196	0.302365
8	-0.13292	-1.211	0.114673
9	-0.306525	-2.7926	0.003245
10	-0.306145	-2.7891	0.003276
11	0.203207	1.8513	0.033841
12	0.80262	7.3122	0
13	0.240939	2.1951	0.015476
14	-0.306103	-2.7887	0.00328
15	-0.285064	-2.5971	0.00556
16	-0.149514	-1.3621	0.08842
17	0.035501	0.3234	0.373591
18	0.130713	1.1909	0.118553
19	0.052215	0.4757	0.317769

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.247657 & 2.2563 & 0.013342 \tabularnewline
2 & -0.328247 & -2.9905 & 0.001833 \tabularnewline
3 & -0.354678 & -3.2313 & 0.000884 \tabularnewline
4 & -0.164047 & -1.4945 & 0.069413 \tabularnewline
5 & 0.02849 & 0.2596 & 0.397924 \tabularnewline
6 & 0.17134 & 1.561 & 0.061166 \tabularnewline
7 & 0.057033 & 0.5196 & 0.302365 \tabularnewline
8 & -0.13292 & -1.211 & 0.114673 \tabularnewline
9 & -0.306525 & -2.7926 & 0.003245 \tabularnewline
10 & -0.306145 & -2.7891 & 0.003276 \tabularnewline
11 & 0.203207 & 1.8513 & 0.033841 \tabularnewline
12 & 0.80262 & 7.3122 & 0 \tabularnewline
13 & 0.240939 & 2.1951 & 0.015476 \tabularnewline
14 & -0.306103 & -2.7887 & 0.00328 \tabularnewline
15 & -0.285064 & -2.5971 & 0.00556 \tabularnewline
16 & -0.149514 & -1.3621 & 0.08842 \tabularnewline
17 & 0.035501 & 0.3234 & 0.373591 \tabularnewline
18 & 0.130713 & 1.1909 & 0.118553 \tabularnewline
19 & 0.052215 & 0.4757 & 0.317769 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224641&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]0.247657[/C][C]2.2563[/C][C]0.013342[/C][/ROW]
[ROW][C]2[/C][C]-0.328247[/C][C]-2.9905[/C][C]0.001833[/C][/ROW]
[ROW][C]3[/C][C]-0.354678[/C][C]-3.2313[/C][C]0.000884[/C][/ROW]
[ROW][C]4[/C][C]-0.164047[/C][C]-1.4945[/C][C]0.069413[/C][/ROW]
[ROW][C]5[/C][C]0.02849[/C][C]0.2596[/C][C]0.397924[/C][/ROW]
[ROW][C]6[/C][C]0.17134[/C][C]1.561[/C][C]0.061166[/C][/ROW]
[ROW][C]7[/C][C]0.057033[/C][C]0.5196[/C][C]0.302365[/C][/ROW]
[ROW][C]8[/C][C]-0.13292[/C][C]-1.211[/C][C]0.114673[/C][/ROW]
[ROW][C]9[/C][C]-0.306525[/C][C]-2.7926[/C][C]0.003245[/C][/ROW]
[ROW][C]10[/C][C]-0.306145[/C][C]-2.7891[/C][C]0.003276[/C][/ROW]
[ROW][C]11[/C][C]0.203207[/C][C]1.8513[/C][C]0.033841[/C][/ROW]
[ROW][C]12[/C][C]0.80262[/C][C]7.3122[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.240939[/C][C]2.1951[/C][C]0.015476[/C][/ROW]
[ROW][C]14[/C][C]-0.306103[/C][C]-2.7887[/C][C]0.00328[/C][/ROW]
[ROW][C]15[/C][C]-0.285064[/C][C]-2.5971[/C][C]0.00556[/C][/ROW]
[ROW][C]16[/C][C]-0.149514[/C][C]-1.3621[/C][C]0.08842[/C][/ROW]
[ROW][C]17[/C][C]0.035501[/C][C]0.3234[/C][C]0.373591[/C][/ROW]
[ROW][C]18[/C][C]0.130713[/C][C]1.1909[/C][C]0.118553[/C][/ROW]
[ROW][C]19[/C][C]0.052215[/C][C]0.4757[/C][C]0.317769[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224641&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224641&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	0.247657	2.2563	0.013342
2	-0.328247	-2.9905	0.001833
3	-0.354678	-3.2313	0.000884
4	-0.164047	-1.4945	0.069413
5	0.02849	0.2596	0.397924
6	0.17134	1.561	0.061166
7	0.057033	0.5196	0.302365
8	-0.13292	-1.211	0.114673
9	-0.306525	-2.7926	0.003245
10	-0.306145	-2.7891	0.003276
11	0.203207	1.8513	0.033841
12	0.80262	7.3122	0
13	0.240939	2.1951	0.015476
14	-0.306103	-2.7887	0.00328
15	-0.285064	-2.5971	0.00556
16	-0.149514	-1.3621	0.08842
17	0.035501	0.3234	0.373591
18	0.130713	1.1909	0.118553
19	0.052215	0.4757	0.317769

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.247657	2.2563	0.013342
2	-0.415037	-3.7812	0.000147
3	-0.176143	-1.6047	0.056174
4	-0.183341	-1.6703	0.049312
5	-0.103523	-0.9431	0.174173
6	0.011364	0.1035	0.458895
7	-0.12359	-1.126	0.131714
8	-0.149935	-1.366	0.087819
9	-0.352967	-3.2157	0.000928
10	-0.486657	-4.4337	1.4e-05
11	-0.099479	-0.9063	0.183701
12	0.581597	5.2986	0
13	-0.137519	-1.2529	0.106888
14	-0.036188	-0.3297	0.371233
15	0.188745	1.7196	0.04462
16	-0.024728	-0.2253	0.411157
17	0.081005	0.738	0.231302
18	-0.086655	-0.7895	0.216046
19	-0.033381	-0.3041	0.3809

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.247657 & 2.2563 & 0.013342 \tabularnewline
2 & -0.415037 & -3.7812 & 0.000147 \tabularnewline
3 & -0.176143 & -1.6047 & 0.056174 \tabularnewline
4 & -0.183341 & -1.6703 & 0.049312 \tabularnewline
5 & -0.103523 & -0.9431 & 0.174173 \tabularnewline
6 & 0.011364 & 0.1035 & 0.458895 \tabularnewline
7 & -0.12359 & -1.126 & 0.131714 \tabularnewline
8 & -0.149935 & -1.366 & 0.087819 \tabularnewline
9 & -0.352967 & -3.2157 & 0.000928 \tabularnewline
10 & -0.486657 & -4.4337 & 1.4e-05 \tabularnewline
11 & -0.099479 & -0.9063 & 0.183701 \tabularnewline
12 & 0.581597 & 5.2986 & 0 \tabularnewline
13 & -0.137519 & -1.2529 & 0.106888 \tabularnewline
14 & -0.036188 & -0.3297 & 0.371233 \tabularnewline
15 & 0.188745 & 1.7196 & 0.04462 \tabularnewline
16 & -0.024728 & -0.2253 & 0.411157 \tabularnewline
17 & 0.081005 & 0.738 & 0.231302 \tabularnewline
18 & -0.086655 & -0.7895 & 0.216046 \tabularnewline
19 & -0.033381 & -0.3041 & 0.3809 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224641&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]0.247657[/C][C]2.2563[/C][C]0.013342[/C][/ROW]
[ROW][C]2[/C][C]-0.415037[/C][C]-3.7812[/C][C]0.000147[/C][/ROW]
[ROW][C]3[/C][C]-0.176143[/C][C]-1.6047[/C][C]0.056174[/C][/ROW]
[ROW][C]4[/C][C]-0.183341[/C][C]-1.6703[/C][C]0.049312[/C][/ROW]
[ROW][C]5[/C][C]-0.103523[/C][C]-0.9431[/C][C]0.174173[/C][/ROW]
[ROW][C]6[/C][C]0.011364[/C][C]0.1035[/C][C]0.458895[/C][/ROW]
[ROW][C]7[/C][C]-0.12359[/C][C]-1.126[/C][C]0.131714[/C][/ROW]
[ROW][C]8[/C][C]-0.149935[/C][C]-1.366[/C][C]0.087819[/C][/ROW]
[ROW][C]9[/C][C]-0.352967[/C][C]-3.2157[/C][C]0.000928[/C][/ROW]
[ROW][C]10[/C][C]-0.486657[/C][C]-4.4337[/C][C]1.4e-05[/C][/ROW]
[ROW][C]11[/C][C]-0.099479[/C][C]-0.9063[/C][C]0.183701[/C][/ROW]
[ROW][C]12[/C][C]0.581597[/C][C]5.2986[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.137519[/C][C]-1.2529[/C][C]0.106888[/C][/ROW]
[ROW][C]14[/C][C]-0.036188[/C][C]-0.3297[/C][C]0.371233[/C][/ROW]
[ROW][C]15[/C][C]0.188745[/C][C]1.7196[/C][C]0.04462[/C][/ROW]
[ROW][C]16[/C][C]-0.024728[/C][C]-0.2253[/C][C]0.411157[/C][/ROW]
[ROW][C]17[/C][C]0.081005[/C][C]0.738[/C][C]0.231302[/C][/ROW]
[ROW][C]18[/C][C]-0.086655[/C][C]-0.7895[/C][C]0.216046[/C][/ROW]
[ROW][C]19[/C][C]-0.033381[/C][C]-0.3041[/C][C]0.3809[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224641&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224641&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	0.247657	2.2563	0.013342
2	-0.415037	-3.7812	0.000147
3	-0.176143	-1.6047	0.056174
4	-0.183341	-1.6703	0.049312
5	-0.103523	-0.9431	0.174173
6	0.011364	0.1035	0.458895
7	-0.12359	-1.126	0.131714
8	-0.149935	-1.366	0.087819
9	-0.352967	-3.2157	0.000928
10	-0.486657	-4.4337	1.4e-05
11	-0.099479	-0.9063	0.183701
12	0.581597	5.2986	0
13	-0.137519	-1.2529	0.106888
14	-0.036188	-0.3297	0.371233
15	0.188745	1.7196	0.04462
16	-0.024728	-0.2253	0.411157
17	0.081005	0.738	0.231302
18	-0.086655	-0.7895	0.216046
19	-0.033381	-0.3041	0.3809

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code