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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Oct 2014 20:28:50 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/19/t1413746956trvanh88xxqvtsv.htm/, Retrieved Sun, 12 May 2024 08:05:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243751, Retrieved Sun, 12 May 2024 08:05:26 +0000

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-       [(Partial) Autocorrelation Function] [] [2014-10-19 19:28:50] [062c419fa600f620f2df94d64c8876ba] [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=243751&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=243751&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243751&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	0.455223	4.4603	1.1e-05
2	0.446074	4.3706	1.6e-05
3	0.464204	4.5483	8e-06
4	0.438998	4.3013	2e-05
5	0.277908	2.7229	0.003843
6	0.365435	3.5805	0.00027
7	0.250759	2.4569	0.007904
8	0.189794	1.8596	0.033003
9	0.231291	2.2662	0.012843
10	0.155874	1.5272	0.064994
11	0.110268	1.0804	0.141336
12	0.172609	1.6912	0.04702
13	-0.037767	-0.37	0.356085
14	0.036238	0.3551	0.361661
15	-0.019052	-0.1867	0.426157
16	-7e-05	-7e-04	0.499727
17	-0.087383	-0.8562	0.197017
18	0.00412	0.0404	0.483944
19	-0.111232	-1.0898	0.139254

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.455223 & 4.4603 & 1.1e-05 \tabularnewline
2 & 0.446074 & 4.3706 & 1.6e-05 \tabularnewline
3 & 0.464204 & 4.5483 & 8e-06 \tabularnewline
4 & 0.438998 & 4.3013 & 2e-05 \tabularnewline
5 & 0.277908 & 2.7229 & 0.003843 \tabularnewline
6 & 0.365435 & 3.5805 & 0.00027 \tabularnewline
7 & 0.250759 & 2.4569 & 0.007904 \tabularnewline
8 & 0.189794 & 1.8596 & 0.033003 \tabularnewline
9 & 0.231291 & 2.2662 & 0.012843 \tabularnewline
10 & 0.155874 & 1.5272 & 0.064994 \tabularnewline
11 & 0.110268 & 1.0804 & 0.141336 \tabularnewline
12 & 0.172609 & 1.6912 & 0.04702 \tabularnewline
13 & -0.037767 & -0.37 & 0.356085 \tabularnewline
14 & 0.036238 & 0.3551 & 0.361661 \tabularnewline
15 & -0.019052 & -0.1867 & 0.426157 \tabularnewline
16 & -7e-05 & -7e-04 & 0.499727 \tabularnewline
17 & -0.087383 & -0.8562 & 0.197017 \tabularnewline
18 & 0.00412 & 0.0404 & 0.483944 \tabularnewline
19 & -0.111232 & -1.0898 & 0.139254 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243751&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]0.455223[/C][C]4.4603[/C][C]1.1e-05[/C][/ROW]
[ROW][C]2[/C][C]0.446074[/C][C]4.3706[/C][C]1.6e-05[/C][/ROW]
[ROW][C]3[/C][C]0.464204[/C][C]4.5483[/C][C]8e-06[/C][/ROW]
[ROW][C]4[/C][C]0.438998[/C][C]4.3013[/C][C]2e-05[/C][/ROW]
[ROW][C]5[/C][C]0.277908[/C][C]2.7229[/C][C]0.003843[/C][/ROW]
[ROW][C]6[/C][C]0.365435[/C][C]3.5805[/C][C]0.00027[/C][/ROW]
[ROW][C]7[/C][C]0.250759[/C][C]2.4569[/C][C]0.007904[/C][/ROW]
[ROW][C]8[/C][C]0.189794[/C][C]1.8596[/C][C]0.033003[/C][/ROW]
[ROW][C]9[/C][C]0.231291[/C][C]2.2662[/C][C]0.012843[/C][/ROW]
[ROW][C]10[/C][C]0.155874[/C][C]1.5272[/C][C]0.064994[/C][/ROW]
[ROW][C]11[/C][C]0.110268[/C][C]1.0804[/C][C]0.141336[/C][/ROW]
[ROW][C]12[/C][C]0.172609[/C][C]1.6912[/C][C]0.04702[/C][/ROW]
[ROW][C]13[/C][C]-0.037767[/C][C]-0.37[/C][C]0.356085[/C][/ROW]
[ROW][C]14[/C][C]0.036238[/C][C]0.3551[/C][C]0.361661[/C][/ROW]
[ROW][C]15[/C][C]-0.019052[/C][C]-0.1867[/C][C]0.426157[/C][/ROW]
[ROW][C]16[/C][C]-7e-05[/C][C]-7e-04[/C][C]0.499727[/C][/ROW]
[ROW][C]17[/C][C]-0.087383[/C][C]-0.8562[/C][C]0.197017[/C][/ROW]
[ROW][C]18[/C][C]0.00412[/C][C]0.0404[/C][C]0.483944[/C][/ROW]
[ROW][C]19[/C][C]-0.111232[/C][C]-1.0898[/C][C]0.139254[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243751&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243751&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	0.455223	4.4603	1.1e-05
2	0.446074	4.3706	1.6e-05
3	0.464204	4.5483	8e-06
4	0.438998	4.3013	2e-05
5	0.277908	2.7229	0.003843
6	0.365435	3.5805	0.00027
7	0.250759	2.4569	0.007904
8	0.189794	1.8596	0.033003
9	0.231291	2.2662	0.012843
10	0.155874	1.5272	0.064994
11	0.110268	1.0804	0.141336
12	0.172609	1.6912	0.04702
13	-0.037767	-0.37	0.356085
14	0.036238	0.3551	0.361661
15	-0.019052	-0.1867	0.426157
16	-7e-05	-7e-04	0.499727
17	-0.087383	-0.8562	0.197017
18	0.00412	0.0404	0.483944
19	-0.111232	-1.0898	0.139254

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.455223	4.4603	1.1e-05
2	0.301279	2.9519	0.001985
3	0.256891	2.517	0.006746
4	0.166935	1.6356	0.052596
5	-0.101601	-0.9955	0.161003
6	0.107118	1.0495	0.148283
7	-0.070471	-0.6905	0.245783
8	-0.070051	-0.6864	0.247073
9	0.07153	0.7009	0.242546
10	-0.068001	-0.6663	0.253417
11	-0.005946	-0.0583	0.476834
12	0.080737	0.7911	0.215429
13	-0.26833	-2.6291	0.004985
14	0.067578	0.6621	0.254739
15	-0.100244	-0.9822	0.164239
16	0.048103	0.4713	0.319242
17	0.006184	0.0606	0.475905
18	0.004342	0.0425	0.483075
19	-0.026803	-0.2626	0.396706

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.455223 & 4.4603 & 1.1e-05 \tabularnewline
2 & 0.301279 & 2.9519 & 0.001985 \tabularnewline
3 & 0.256891 & 2.517 & 0.006746 \tabularnewline
4 & 0.166935 & 1.6356 & 0.052596 \tabularnewline
5 & -0.101601 & -0.9955 & 0.161003 \tabularnewline
6 & 0.107118 & 1.0495 & 0.148283 \tabularnewline
7 & -0.070471 & -0.6905 & 0.245783 \tabularnewline
8 & -0.070051 & -0.6864 & 0.247073 \tabularnewline
9 & 0.07153 & 0.7009 & 0.242546 \tabularnewline
10 & -0.068001 & -0.6663 & 0.253417 \tabularnewline
11 & -0.005946 & -0.0583 & 0.476834 \tabularnewline
12 & 0.080737 & 0.7911 & 0.215429 \tabularnewline
13 & -0.26833 & -2.6291 & 0.004985 \tabularnewline
14 & 0.067578 & 0.6621 & 0.254739 \tabularnewline
15 & -0.100244 & -0.9822 & 0.164239 \tabularnewline
16 & 0.048103 & 0.4713 & 0.319242 \tabularnewline
17 & 0.006184 & 0.0606 & 0.475905 \tabularnewline
18 & 0.004342 & 0.0425 & 0.483075 \tabularnewline
19 & -0.026803 & -0.2626 & 0.396706 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243751&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]0.455223[/C][C]4.4603[/C][C]1.1e-05[/C][/ROW]
[ROW][C]2[/C][C]0.301279[/C][C]2.9519[/C][C]0.001985[/C][/ROW]
[ROW][C]3[/C][C]0.256891[/C][C]2.517[/C][C]0.006746[/C][/ROW]
[ROW][C]4[/C][C]0.166935[/C][C]1.6356[/C][C]0.052596[/C][/ROW]
[ROW][C]5[/C][C]-0.101601[/C][C]-0.9955[/C][C]0.161003[/C][/ROW]
[ROW][C]6[/C][C]0.107118[/C][C]1.0495[/C][C]0.148283[/C][/ROW]
[ROW][C]7[/C][C]-0.070471[/C][C]-0.6905[/C][C]0.245783[/C][/ROW]
[ROW][C]8[/C][C]-0.070051[/C][C]-0.6864[/C][C]0.247073[/C][/ROW]
[ROW][C]9[/C][C]0.07153[/C][C]0.7009[/C][C]0.242546[/C][/ROW]
[ROW][C]10[/C][C]-0.068001[/C][C]-0.6663[/C][C]0.253417[/C][/ROW]
[ROW][C]11[/C][C]-0.005946[/C][C]-0.0583[/C][C]0.476834[/C][/ROW]
[ROW][C]12[/C][C]0.080737[/C][C]0.7911[/C][C]0.215429[/C][/ROW]
[ROW][C]13[/C][C]-0.26833[/C][C]-2.6291[/C][C]0.004985[/C][/ROW]
[ROW][C]14[/C][C]0.067578[/C][C]0.6621[/C][C]0.254739[/C][/ROW]
[ROW][C]15[/C][C]-0.100244[/C][C]-0.9822[/C][C]0.164239[/C][/ROW]
[ROW][C]16[/C][C]0.048103[/C][C]0.4713[/C][C]0.319242[/C][/ROW]
[ROW][C]17[/C][C]0.006184[/C][C]0.0606[/C][C]0.475905[/C][/ROW]
[ROW][C]18[/C][C]0.004342[/C][C]0.0425[/C][C]0.483075[/C][/ROW]
[ROW][C]19[/C][C]-0.026803[/C][C]-0.2626[/C][C]0.396706[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243751&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243751&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	0.455223	4.4603	1.1e-05
2	0.301279	2.9519	0.001985
3	0.256891	2.517	0.006746
4	0.166935	1.6356	0.052596
5	-0.101601	-0.9955	0.161003
6	0.107118	1.0495	0.148283
7	-0.070471	-0.6905	0.245783
8	-0.070051	-0.6864	0.247073
9	0.07153	0.7009	0.242546
10	-0.068001	-0.6663	0.253417
11	-0.005946	-0.0583	0.476834
12	0.080737	0.7911	0.215429
13	-0.26833	-2.6291	0.004985
14	0.067578	0.6621	0.254739
15	-0.100244	-0.9822	0.164239
16	0.048103	0.4713	0.319242
17	0.006184	0.0606	0.475905
18	0.004342	0.0425	0.483075
19	-0.026803	-0.2626	0.396706

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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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code