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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 15 Jan 2012 11:23:10 -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/2012/Jan/15/t1326644676h0wjk6hmgy4kg5g.htm/, Retrieved Fri, 03 May 2024 14:56:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161097, Retrieved Fri, 03 May 2024 14:56:39 +0000

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No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

104

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-       [(Partial) Autocorrelation Function] [] [2012-01-15 16:23:10] [618e20b48371a4632e04cdc6ff96552f] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161097&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]1 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=161097&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161097&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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.936321	7.9999	0
2	0.868112	7.4172	0
3	0.799755	6.8331	0
4	0.734923	6.2792	0
5	0.673583	5.7551	0
6	0.615515	5.259	1e-06
7	0.555893	4.7496	5e-06
8	0.493857	4.2195	3.5e-05
9	0.433848	3.7068	0.000203
10	0.382204	3.2656	0.000833
11	0.337012	2.8794	0.002612
12	0.295345	2.5234	0.006899
13	0.256615	2.1925	0.015765
14	0.220118	1.8807	0.032001
15	0.191633	1.6373	0.052934
16	0.17463	1.492	0.069999
17	0.16385	1.3999	0.082885
18	0.156348	1.3358	0.092876

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.936321 & 7.9999 & 0 \tabularnewline
2 & 0.868112 & 7.4172 & 0 \tabularnewline
3 & 0.799755 & 6.8331 & 0 \tabularnewline
4 & 0.734923 & 6.2792 & 0 \tabularnewline
5 & 0.673583 & 5.7551 & 0 \tabularnewline
6 & 0.615515 & 5.259 & 1e-06 \tabularnewline
7 & 0.555893 & 4.7496 & 5e-06 \tabularnewline
8 & 0.493857 & 4.2195 & 3.5e-05 \tabularnewline
9 & 0.433848 & 3.7068 & 0.000203 \tabularnewline
10 & 0.382204 & 3.2656 & 0.000833 \tabularnewline
11 & 0.337012 & 2.8794 & 0.002612 \tabularnewline
12 & 0.295345 & 2.5234 & 0.006899 \tabularnewline
13 & 0.256615 & 2.1925 & 0.015765 \tabularnewline
14 & 0.220118 & 1.8807 & 0.032001 \tabularnewline
15 & 0.191633 & 1.6373 & 0.052934 \tabularnewline
16 & 0.17463 & 1.492 & 0.069999 \tabularnewline
17 & 0.16385 & 1.3999 & 0.082885 \tabularnewline
18 & 0.156348 & 1.3358 & 0.092876 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161097&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]0.936321[/C][C]7.9999[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.868112[/C][C]7.4172[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.799755[/C][C]6.8331[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.734923[/C][C]6.2792[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.673583[/C][C]5.7551[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.615515[/C][C]5.259[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.555893[/C][C]4.7496[/C][C]5e-06[/C][/ROW]
[ROW][C]8[/C][C]0.493857[/C][C]4.2195[/C][C]3.5e-05[/C][/ROW]
[ROW][C]9[/C][C]0.433848[/C][C]3.7068[/C][C]0.000203[/C][/ROW]
[ROW][C]10[/C][C]0.382204[/C][C]3.2656[/C][C]0.000833[/C][/ROW]
[ROW][C]11[/C][C]0.337012[/C][C]2.8794[/C][C]0.002612[/C][/ROW]
[ROW][C]12[/C][C]0.295345[/C][C]2.5234[/C][C]0.006899[/C][/ROW]
[ROW][C]13[/C][C]0.256615[/C][C]2.1925[/C][C]0.015765[/C][/ROW]
[ROW][C]14[/C][C]0.220118[/C][C]1.8807[/C][C]0.032001[/C][/ROW]
[ROW][C]15[/C][C]0.191633[/C][C]1.6373[/C][C]0.052934[/C][/ROW]
[ROW][C]16[/C][C]0.17463[/C][C]1.492[/C][C]0.069999[/C][/ROW]
[ROW][C]17[/C][C]0.16385[/C][C]1.3999[/C][C]0.082885[/C][/ROW]
[ROW][C]18[/C][C]0.156348[/C][C]1.3358[/C][C]0.092876[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161097&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161097&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	0.936321	7.9999	0
2	0.868112	7.4172	0
3	0.799755	6.8331	0
4	0.734923	6.2792	0
5	0.673583	5.7551	0
6	0.615515	5.259	1e-06
7	0.555893	4.7496	5e-06
8	0.493857	4.2195	3.5e-05
9	0.433848	3.7068	0.000203
10	0.382204	3.2656	0.000833
11	0.337012	2.8794	0.002612
12	0.295345	2.5234	0.006899
13	0.256615	2.1925	0.015765
14	0.220118	1.8807	0.032001
15	0.191633	1.6373	0.052934
16	0.17463	1.492	0.069999
17	0.16385	1.3999	0.082885
18	0.156348	1.3358	0.092876

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.936321	7.9999	0
2	-0.06963	-0.5949	0.27687
3	-0.036495	-0.3118	0.378036
4	-0.009182	-0.0785	0.468841
5	-0.010824	-0.0925	0.463283
6	-0.012017	-0.1027	0.459252
7	-0.050025	-0.4274	0.335169
8	-0.056105	-0.4794	0.316556
9	-0.021613	-0.1847	0.427002
10	0.026336	0.225	0.411299
11	0.009221	0.0788	0.46871
12	-0.011197	-0.0957	0.462022
13	-0.009517	-0.0813	0.467708
14	-0.010557	-0.0902	0.464187
15	0.037761	0.3226	0.373948
16	0.063244	0.5404	0.295298
17	0.021754	0.1859	0.426534
18	0.008039	0.0687	0.472713

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.936321 & 7.9999 & 0 \tabularnewline
2 & -0.06963 & -0.5949 & 0.27687 \tabularnewline
3 & -0.036495 & -0.3118 & 0.378036 \tabularnewline
4 & -0.009182 & -0.0785 & 0.468841 \tabularnewline
5 & -0.010824 & -0.0925 & 0.463283 \tabularnewline
6 & -0.012017 & -0.1027 & 0.459252 \tabularnewline
7 & -0.050025 & -0.4274 & 0.335169 \tabularnewline
8 & -0.056105 & -0.4794 & 0.316556 \tabularnewline
9 & -0.021613 & -0.1847 & 0.427002 \tabularnewline
10 & 0.026336 & 0.225 & 0.411299 \tabularnewline
11 & 0.009221 & 0.0788 & 0.46871 \tabularnewline
12 & -0.011197 & -0.0957 & 0.462022 \tabularnewline
13 & -0.009517 & -0.0813 & 0.467708 \tabularnewline
14 & -0.010557 & -0.0902 & 0.464187 \tabularnewline
15 & 0.037761 & 0.3226 & 0.373948 \tabularnewline
16 & 0.063244 & 0.5404 & 0.295298 \tabularnewline
17 & 0.021754 & 0.1859 & 0.426534 \tabularnewline
18 & 0.008039 & 0.0687 & 0.472713 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161097&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]0.936321[/C][C]7.9999[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.06963[/C][C]-0.5949[/C][C]0.27687[/C][/ROW]
[ROW][C]3[/C][C]-0.036495[/C][C]-0.3118[/C][C]0.378036[/C][/ROW]
[ROW][C]4[/C][C]-0.009182[/C][C]-0.0785[/C][C]0.468841[/C][/ROW]
[ROW][C]5[/C][C]-0.010824[/C][C]-0.0925[/C][C]0.463283[/C][/ROW]
[ROW][C]6[/C][C]-0.012017[/C][C]-0.1027[/C][C]0.459252[/C][/ROW]
[ROW][C]7[/C][C]-0.050025[/C][C]-0.4274[/C][C]0.335169[/C][/ROW]
[ROW][C]8[/C][C]-0.056105[/C][C]-0.4794[/C][C]0.316556[/C][/ROW]
[ROW][C]9[/C][C]-0.021613[/C][C]-0.1847[/C][C]0.427002[/C][/ROW]
[ROW][C]10[/C][C]0.026336[/C][C]0.225[/C][C]0.411299[/C][/ROW]
[ROW][C]11[/C][C]0.009221[/C][C]0.0788[/C][C]0.46871[/C][/ROW]
[ROW][C]12[/C][C]-0.011197[/C][C]-0.0957[/C][C]0.462022[/C][/ROW]
[ROW][C]13[/C][C]-0.009517[/C][C]-0.0813[/C][C]0.467708[/C][/ROW]
[ROW][C]14[/C][C]-0.010557[/C][C]-0.0902[/C][C]0.464187[/C][/ROW]
[ROW][C]15[/C][C]0.037761[/C][C]0.3226[/C][C]0.373948[/C][/ROW]
[ROW][C]16[/C][C]0.063244[/C][C]0.5404[/C][C]0.295298[/C][/ROW]
[ROW][C]17[/C][C]0.021754[/C][C]0.1859[/C][C]0.426534[/C][/ROW]
[ROW][C]18[/C][C]0.008039[/C][C]0.0687[/C][C]0.472713[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161097&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161097&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	0.936321	7.9999	0
2	-0.06963	-0.5949	0.27687
3	-0.036495	-0.3118	0.378036
4	-0.009182	-0.0785	0.468841
5	-0.010824	-0.0925	0.463283
6	-0.012017	-0.1027	0.459252
7	-0.050025	-0.4274	0.335169
8	-0.056105	-0.4794	0.316556
9	-0.021613	-0.1847	0.427002
10	0.026336	0.225	0.411299
11	0.009221	0.0788	0.46871
12	-0.011197	-0.0957	0.462022
13	-0.009517	-0.0813	0.467708
14	-0.010557	-0.0902	0.464187
15	0.037761	0.3226	0.373948
16	0.063244	0.5404	0.295298
17	0.021754	0.1859	0.426534
18	0.008039	0.0687	0.472713

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):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

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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Input Parameters & R Code