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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 03 Jan 2015 09:24:15 +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/2015/Jan/03/t1420277184fhlw0tj4wpwq92g.htm/, Retrieved Tue, 14 May 2024 16:48:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271879, Retrieved Tue, 14 May 2024 16:48:54 +0000

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IsPrivate?

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User-defined keywords

Estimated Impact

119

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

-       [(Partial) Autocorrelation Function] [] [2015-01-03 09:24:15] [5cf6a598f846f655ef95f65053f7ffc6] [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	'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271879&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271879&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271879&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	'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.02602	0.2208	0.412942
2	0.028235	0.2396	0.405668
3	-0.204217	-1.7328	0.043703
4	0.000164	0.0014	0.499447
5	0.042831	0.3634	0.358673
6	0.034181	0.29	0.386311
7	0.029257	0.2483	0.402322
8	-0.120783	-1.0249	0.154426
9	-0.094368	-0.8007	0.212959
10	-0.073679	-0.6252	0.266912
11	0.084052	0.7132	0.239013
12	0.050177	0.4258	0.335774
13	0.066248	0.5621	0.287885
14	-0.089482	-0.7593	0.225081
15	-0.043475	-0.3689	0.356643
16	-0.169128	-1.4351	0.077794
17	-0.017484	-0.1484	0.441238
18	0.047426	0.4024	0.344282
19	0.013219	0.1122	0.455501
20	0.024082	0.2043	0.41933
21	-0.054527	-0.4627	0.322497
22	-0.011239	-0.0954	0.462144
23	-0.02166	-0.1838	0.427346
24	0.044395	0.3767	0.35375

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.02602 & 0.2208 & 0.412942 \tabularnewline
2 & 0.028235 & 0.2396 & 0.405668 \tabularnewline
3 & -0.204217 & -1.7328 & 0.043703 \tabularnewline
4 & 0.000164 & 0.0014 & 0.499447 \tabularnewline
5 & 0.042831 & 0.3634 & 0.358673 \tabularnewline
6 & 0.034181 & 0.29 & 0.386311 \tabularnewline
7 & 0.029257 & 0.2483 & 0.402322 \tabularnewline
8 & -0.120783 & -1.0249 & 0.154426 \tabularnewline
9 & -0.094368 & -0.8007 & 0.212959 \tabularnewline
10 & -0.073679 & -0.6252 & 0.266912 \tabularnewline
11 & 0.084052 & 0.7132 & 0.239013 \tabularnewline
12 & 0.050177 & 0.4258 & 0.335774 \tabularnewline
13 & 0.066248 & 0.5621 & 0.287885 \tabularnewline
14 & -0.089482 & -0.7593 & 0.225081 \tabularnewline
15 & -0.043475 & -0.3689 & 0.356643 \tabularnewline
16 & -0.169128 & -1.4351 & 0.077794 \tabularnewline
17 & -0.017484 & -0.1484 & 0.441238 \tabularnewline
18 & 0.047426 & 0.4024 & 0.344282 \tabularnewline
19 & 0.013219 & 0.1122 & 0.455501 \tabularnewline
20 & 0.024082 & 0.2043 & 0.41933 \tabularnewline
21 & -0.054527 & -0.4627 & 0.322497 \tabularnewline
22 & -0.011239 & -0.0954 & 0.462144 \tabularnewline
23 & -0.02166 & -0.1838 & 0.427346 \tabularnewline
24 & 0.044395 & 0.3767 & 0.35375 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271879&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]0.02602[/C][C]0.2208[/C][C]0.412942[/C][/ROW]
[ROW][C]2[/C][C]0.028235[/C][C]0.2396[/C][C]0.405668[/C][/ROW]
[ROW][C]3[/C][C]-0.204217[/C][C]-1.7328[/C][C]0.043703[/C][/ROW]
[ROW][C]4[/C][C]0.000164[/C][C]0.0014[/C][C]0.499447[/C][/ROW]
[ROW][C]5[/C][C]0.042831[/C][C]0.3634[/C][C]0.358673[/C][/ROW]
[ROW][C]6[/C][C]0.034181[/C][C]0.29[/C][C]0.386311[/C][/ROW]
[ROW][C]7[/C][C]0.029257[/C][C]0.2483[/C][C]0.402322[/C][/ROW]
[ROW][C]8[/C][C]-0.120783[/C][C]-1.0249[/C][C]0.154426[/C][/ROW]
[ROW][C]9[/C][C]-0.094368[/C][C]-0.8007[/C][C]0.212959[/C][/ROW]
[ROW][C]10[/C][C]-0.073679[/C][C]-0.6252[/C][C]0.266912[/C][/ROW]
[ROW][C]11[/C][C]0.084052[/C][C]0.7132[/C][C]0.239013[/C][/ROW]
[ROW][C]12[/C][C]0.050177[/C][C]0.4258[/C][C]0.335774[/C][/ROW]
[ROW][C]13[/C][C]0.066248[/C][C]0.5621[/C][C]0.287885[/C][/ROW]
[ROW][C]14[/C][C]-0.089482[/C][C]-0.7593[/C][C]0.225081[/C][/ROW]
[ROW][C]15[/C][C]-0.043475[/C][C]-0.3689[/C][C]0.356643[/C][/ROW]
[ROW][C]16[/C][C]-0.169128[/C][C]-1.4351[/C][C]0.077794[/C][/ROW]
[ROW][C]17[/C][C]-0.017484[/C][C]-0.1484[/C][C]0.441238[/C][/ROW]
[ROW][C]18[/C][C]0.047426[/C][C]0.4024[/C][C]0.344282[/C][/ROW]
[ROW][C]19[/C][C]0.013219[/C][C]0.1122[/C][C]0.455501[/C][/ROW]
[ROW][C]20[/C][C]0.024082[/C][C]0.2043[/C][C]0.41933[/C][/ROW]
[ROW][C]21[/C][C]-0.054527[/C][C]-0.4627[/C][C]0.322497[/C][/ROW]
[ROW][C]22[/C][C]-0.011239[/C][C]-0.0954[/C][C]0.462144[/C][/ROW]
[ROW][C]23[/C][C]-0.02166[/C][C]-0.1838[/C][C]0.427346[/C][/ROW]
[ROW][C]24[/C][C]0.044395[/C][C]0.3767[/C][C]0.35375[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271879&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271879&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	0.02602	0.2208	0.412942
2	0.028235	0.2396	0.405668
3	-0.204217	-1.7328	0.043703
4	0.000164	0.0014	0.499447
5	0.042831	0.3634	0.358673
6	0.034181	0.29	0.386311
7	0.029257	0.2483	0.402322
8	-0.120783	-1.0249	0.154426
9	-0.094368	-0.8007	0.212959
10	-0.073679	-0.6252	0.266912
11	0.084052	0.7132	0.239013
12	0.050177	0.4258	0.335774
13	0.066248	0.5621	0.287885
14	-0.089482	-0.7593	0.225081
15	-0.043475	-0.3689	0.356643
16	-0.169128	-1.4351	0.077794
17	-0.017484	-0.1484	0.441238
18	0.047426	0.4024	0.344282
19	0.013219	0.1122	0.455501
20	0.024082	0.2043	0.41933
21	-0.054527	-0.4627	0.322497
22	-0.011239	-0.0954	0.462144
23	-0.02166	-0.1838	0.427346
24	0.044395	0.3767	0.35375

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.02602	0.2208	0.412942
2	0.027577	0.234	0.407827
3	-0.205945	-1.7475	0.042407
4	0.011424	0.0969	0.461522
5	0.057497	0.4879	0.313559
6	-0.012069	-0.1024	0.459359
7	0.028317	0.2403	0.405399
8	-0.108192	-0.918	0.180832
9	-0.090022	-0.7639	0.223722
10	-0.052936	-0.4492	0.327326
11	0.050432	0.4279	0.334991
12	0.016424	0.1394	0.444778
13	0.047673	0.4045	0.343515
14	-0.064806	-0.5499	0.292045
15	-0.02374	-0.2014	0.42046
16	-0.165413	-1.4036	0.082372
17	-0.062603	-0.5312	0.298455
18	0.025755	0.2185	0.413815
19	-0.042471	-0.3604	0.359808
20	0.029761	0.2525	0.400675
21	-0.001795	-0.0152	0.493946
22	-0.029439	-0.2498	0.401729
23	-0.028062	-0.2381	0.406234
24	-0.023395	-0.1985	0.421603

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.02602 & 0.2208 & 0.412942 \tabularnewline
2 & 0.027577 & 0.234 & 0.407827 \tabularnewline
3 & -0.205945 & -1.7475 & 0.042407 \tabularnewline
4 & 0.011424 & 0.0969 & 0.461522 \tabularnewline
5 & 0.057497 & 0.4879 & 0.313559 \tabularnewline
6 & -0.012069 & -0.1024 & 0.459359 \tabularnewline
7 & 0.028317 & 0.2403 & 0.405399 \tabularnewline
8 & -0.108192 & -0.918 & 0.180832 \tabularnewline
9 & -0.090022 & -0.7639 & 0.223722 \tabularnewline
10 & -0.052936 & -0.4492 & 0.327326 \tabularnewline
11 & 0.050432 & 0.4279 & 0.334991 \tabularnewline
12 & 0.016424 & 0.1394 & 0.444778 \tabularnewline
13 & 0.047673 & 0.4045 & 0.343515 \tabularnewline
14 & -0.064806 & -0.5499 & 0.292045 \tabularnewline
15 & -0.02374 & -0.2014 & 0.42046 \tabularnewline
16 & -0.165413 & -1.4036 & 0.082372 \tabularnewline
17 & -0.062603 & -0.5312 & 0.298455 \tabularnewline
18 & 0.025755 & 0.2185 & 0.413815 \tabularnewline
19 & -0.042471 & -0.3604 & 0.359808 \tabularnewline
20 & 0.029761 & 0.2525 & 0.400675 \tabularnewline
21 & -0.001795 & -0.0152 & 0.493946 \tabularnewline
22 & -0.029439 & -0.2498 & 0.401729 \tabularnewline
23 & -0.028062 & -0.2381 & 0.406234 \tabularnewline
24 & -0.023395 & -0.1985 & 0.421603 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271879&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]0.02602[/C][C]0.2208[/C][C]0.412942[/C][/ROW]
[ROW][C]2[/C][C]0.027577[/C][C]0.234[/C][C]0.407827[/C][/ROW]
[ROW][C]3[/C][C]-0.205945[/C][C]-1.7475[/C][C]0.042407[/C][/ROW]
[ROW][C]4[/C][C]0.011424[/C][C]0.0969[/C][C]0.461522[/C][/ROW]
[ROW][C]5[/C][C]0.057497[/C][C]0.4879[/C][C]0.313559[/C][/ROW]
[ROW][C]6[/C][C]-0.012069[/C][C]-0.1024[/C][C]0.459359[/C][/ROW]
[ROW][C]7[/C][C]0.028317[/C][C]0.2403[/C][C]0.405399[/C][/ROW]
[ROW][C]8[/C][C]-0.108192[/C][C]-0.918[/C][C]0.180832[/C][/ROW]
[ROW][C]9[/C][C]-0.090022[/C][C]-0.7639[/C][C]0.223722[/C][/ROW]
[ROW][C]10[/C][C]-0.052936[/C][C]-0.4492[/C][C]0.327326[/C][/ROW]
[ROW][C]11[/C][C]0.050432[/C][C]0.4279[/C][C]0.334991[/C][/ROW]
[ROW][C]12[/C][C]0.016424[/C][C]0.1394[/C][C]0.444778[/C][/ROW]
[ROW][C]13[/C][C]0.047673[/C][C]0.4045[/C][C]0.343515[/C][/ROW]
[ROW][C]14[/C][C]-0.064806[/C][C]-0.5499[/C][C]0.292045[/C][/ROW]
[ROW][C]15[/C][C]-0.02374[/C][C]-0.2014[/C][C]0.42046[/C][/ROW]
[ROW][C]16[/C][C]-0.165413[/C][C]-1.4036[/C][C]0.082372[/C][/ROW]
[ROW][C]17[/C][C]-0.062603[/C][C]-0.5312[/C][C]0.298455[/C][/ROW]
[ROW][C]18[/C][C]0.025755[/C][C]0.2185[/C][C]0.413815[/C][/ROW]
[ROW][C]19[/C][C]-0.042471[/C][C]-0.3604[/C][C]0.359808[/C][/ROW]
[ROW][C]20[/C][C]0.029761[/C][C]0.2525[/C][C]0.400675[/C][/ROW]
[ROW][C]21[/C][C]-0.001795[/C][C]-0.0152[/C][C]0.493946[/C][/ROW]
[ROW][C]22[/C][C]-0.029439[/C][C]-0.2498[/C][C]0.401729[/C][/ROW]
[ROW][C]23[/C][C]-0.028062[/C][C]-0.2381[/C][C]0.406234[/C][/ROW]
[ROW][C]24[/C][C]-0.023395[/C][C]-0.1985[/C][C]0.421603[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271879&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271879&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	0.02602	0.2208	0.412942
2	0.027577	0.234	0.407827
3	-0.205945	-1.7475	0.042407
4	0.011424	0.0969	0.461522
5	0.057497	0.4879	0.313559
6	-0.012069	-0.1024	0.459359
7	0.028317	0.2403	0.405399
8	-0.108192	-0.918	0.180832
9	-0.090022	-0.7639	0.223722
10	-0.052936	-0.4492	0.327326
11	0.050432	0.4279	0.334991
12	0.016424	0.1394	0.444778
13	0.047673	0.4045	0.343515
14	-0.064806	-0.5499	0.292045
15	-0.02374	-0.2014	0.42046
16	-0.165413	-1.4036	0.082372
17	-0.062603	-0.5312	0.298455
18	0.025755	0.2185	0.413815
19	-0.042471	-0.3604	0.359808
20	0.029761	0.2525	0.400675
21	-0.001795	-0.0152	0.493946
22	-0.029439	-0.2498	0.401729
23	-0.028062	-0.2381	0.406234
24	-0.023395	-0.1985	0.421603

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 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 24 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code