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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 14 Dec 2008 12:35:36 -0700

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/2008/Dec/14/t122928337225b5e18vvwefb2c.htm/, Retrieved Wed, 29 May 2024 20:55:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33543, Retrieved Wed, 29 May 2024 20:55:35 +0000

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Estimated Impact

194

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

-     [Variance Reduction Matrix] [vrm bel20] [2008-12-10 18:40:53] [74be16979710d4c4e7c6647856088456]
- RMPD    [(Partial) Autocorrelation Function] [PACF paper Dow Jones] [2008-12-14 19:35:36] [c8dc05b1cdf5010d9a4f2d773adefb82] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33543&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33543&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33543&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.938016	10.3182	0
2	0.867671	9.5444	0
3	0.822135	9.0435	0
4	0.77645	8.541	0
5	0.726237	7.9886	0
6	0.676627	7.4429	0
7	0.64319	7.0751	0
8	0.605067	6.6557	0
9	0.55632	6.1195	0
10	0.503137	5.5345	0
11	0.446931	4.9162	1e-06
12	0.39402	4.3342	1.5e-05
13	0.341307	3.7544	0.000134
14	0.305398	3.3594	0.000523
15	0.27297	3.0027	0.001626
16	0.236011	2.5961	0.005298
17	0.206434	2.2708	0.012465
18	0.182063	2.0027	0.023723
19	0.157535	1.7329	0.042832
20	0.119383	1.3132	0.095799

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.938016 & 10.3182 & 0 \tabularnewline
2 & 0.867671 & 9.5444 & 0 \tabularnewline
3 & 0.822135 & 9.0435 & 0 \tabularnewline
4 & 0.77645 & 8.541 & 0 \tabularnewline
5 & 0.726237 & 7.9886 & 0 \tabularnewline
6 & 0.676627 & 7.4429 & 0 \tabularnewline
7 & 0.64319 & 7.0751 & 0 \tabularnewline
8 & 0.605067 & 6.6557 & 0 \tabularnewline
9 & 0.55632 & 6.1195 & 0 \tabularnewline
10 & 0.503137 & 5.5345 & 0 \tabularnewline
11 & 0.446931 & 4.9162 & 1e-06 \tabularnewline
12 & 0.39402 & 4.3342 & 1.5e-05 \tabularnewline
13 & 0.341307 & 3.7544 & 0.000134 \tabularnewline
14 & 0.305398 & 3.3594 & 0.000523 \tabularnewline
15 & 0.27297 & 3.0027 & 0.001626 \tabularnewline
16 & 0.236011 & 2.5961 & 0.005298 \tabularnewline
17 & 0.206434 & 2.2708 & 0.012465 \tabularnewline
18 & 0.182063 & 2.0027 & 0.023723 \tabularnewline
19 & 0.157535 & 1.7329 & 0.042832 \tabularnewline
20 & 0.119383 & 1.3132 & 0.095799 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33543&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]0.938016[/C][C]10.3182[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.867671[/C][C]9.5444[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.822135[/C][C]9.0435[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.77645[/C][C]8.541[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.726237[/C][C]7.9886[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.676627[/C][C]7.4429[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.64319[/C][C]7.0751[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.605067[/C][C]6.6557[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.55632[/C][C]6.1195[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.503137[/C][C]5.5345[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.446931[/C][C]4.9162[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]0.39402[/C][C]4.3342[/C][C]1.5e-05[/C][/ROW]
[ROW][C]13[/C][C]0.341307[/C][C]3.7544[/C][C]0.000134[/C][/ROW]
[ROW][C]14[/C][C]0.305398[/C][C]3.3594[/C][C]0.000523[/C][/ROW]
[ROW][C]15[/C][C]0.27297[/C][C]3.0027[/C][C]0.001626[/C][/ROW]
[ROW][C]16[/C][C]0.236011[/C][C]2.5961[/C][C]0.005298[/C][/ROW]
[ROW][C]17[/C][C]0.206434[/C][C]2.2708[/C][C]0.012465[/C][/ROW]
[ROW][C]18[/C][C]0.182063[/C][C]2.0027[/C][C]0.023723[/C][/ROW]
[ROW][C]19[/C][C]0.157535[/C][C]1.7329[/C][C]0.042832[/C][/ROW]
[ROW][C]20[/C][C]0.119383[/C][C]1.3132[/C][C]0.095799[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33543&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33543&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	0.938016	10.3182	0
2	0.867671	9.5444	0
3	0.822135	9.0435	0
4	0.77645	8.541	0
5	0.726237	7.9886	0
6	0.676627	7.4429	0
7	0.64319	7.0751	0
8	0.605067	6.6557	0
9	0.55632	6.1195	0
10	0.503137	5.5345	0
11	0.446931	4.9162	1e-06
12	0.39402	4.3342	1.5e-05
13	0.341307	3.7544	0.000134
14	0.305398	3.3594	0.000523
15	0.27297	3.0027	0.001626
16	0.236011	2.5961	0.005298
17	0.206434	2.2708	0.012465
18	0.182063	2.0027	0.023723
19	0.157535	1.7329	0.042832
20	0.119383	1.3132	0.095799

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.938016	10.3182	0
2	-0.101581	-1.1174	0.13302
3	0.175412	1.9295	0.028003
4	-0.059389	-0.6533	0.257409
5	-0.020135	-0.2215	0.412546
6	-0.027915	-0.3071	0.37966
7	0.104594	1.1505	0.126096
8	-0.086392	-0.9503	0.171924
9	-0.054051	-0.5946	0.276623
10	-0.084255	-0.9268	0.177937
11	-0.075824	-0.8341	0.202945
12	-0.019222	-0.2114	0.416447
13	-0.03577	-0.3935	0.347332
14	0.111012	1.2211	0.112205
15	-0.039628	-0.4359	0.331838
16	-0.015198	-0.1672	0.433755
17	0.031762	0.3494	0.363704
18	0.017226	0.1895	0.425016
19	-0.007207	-0.0793	0.468473
20	-0.10132	-1.1145	0.133631

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.938016 & 10.3182 & 0 \tabularnewline
2 & -0.101581 & -1.1174 & 0.13302 \tabularnewline
3 & 0.175412 & 1.9295 & 0.028003 \tabularnewline
4 & -0.059389 & -0.6533 & 0.257409 \tabularnewline
5 & -0.020135 & -0.2215 & 0.412546 \tabularnewline
6 & -0.027915 & -0.3071 & 0.37966 \tabularnewline
7 & 0.104594 & 1.1505 & 0.126096 \tabularnewline
8 & -0.086392 & -0.9503 & 0.171924 \tabularnewline
9 & -0.054051 & -0.5946 & 0.276623 \tabularnewline
10 & -0.084255 & -0.9268 & 0.177937 \tabularnewline
11 & -0.075824 & -0.8341 & 0.202945 \tabularnewline
12 & -0.019222 & -0.2114 & 0.416447 \tabularnewline
13 & -0.03577 & -0.3935 & 0.347332 \tabularnewline
14 & 0.111012 & 1.2211 & 0.112205 \tabularnewline
15 & -0.039628 & -0.4359 & 0.331838 \tabularnewline
16 & -0.015198 & -0.1672 & 0.433755 \tabularnewline
17 & 0.031762 & 0.3494 & 0.363704 \tabularnewline
18 & 0.017226 & 0.1895 & 0.425016 \tabularnewline
19 & -0.007207 & -0.0793 & 0.468473 \tabularnewline
20 & -0.10132 & -1.1145 & 0.133631 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33543&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]0.938016[/C][C]10.3182[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.101581[/C][C]-1.1174[/C][C]0.13302[/C][/ROW]
[ROW][C]3[/C][C]0.175412[/C][C]1.9295[/C][C]0.028003[/C][/ROW]
[ROW][C]4[/C][C]-0.059389[/C][C]-0.6533[/C][C]0.257409[/C][/ROW]
[ROW][C]5[/C][C]-0.020135[/C][C]-0.2215[/C][C]0.412546[/C][/ROW]
[ROW][C]6[/C][C]-0.027915[/C][C]-0.3071[/C][C]0.37966[/C][/ROW]
[ROW][C]7[/C][C]0.104594[/C][C]1.1505[/C][C]0.126096[/C][/ROW]
[ROW][C]8[/C][C]-0.086392[/C][C]-0.9503[/C][C]0.171924[/C][/ROW]
[ROW][C]9[/C][C]-0.054051[/C][C]-0.5946[/C][C]0.276623[/C][/ROW]
[ROW][C]10[/C][C]-0.084255[/C][C]-0.9268[/C][C]0.177937[/C][/ROW]
[ROW][C]11[/C][C]-0.075824[/C][C]-0.8341[/C][C]0.202945[/C][/ROW]
[ROW][C]12[/C][C]-0.019222[/C][C]-0.2114[/C][C]0.416447[/C][/ROW]
[ROW][C]13[/C][C]-0.03577[/C][C]-0.3935[/C][C]0.347332[/C][/ROW]
[ROW][C]14[/C][C]0.111012[/C][C]1.2211[/C][C]0.112205[/C][/ROW]
[ROW][C]15[/C][C]-0.039628[/C][C]-0.4359[/C][C]0.331838[/C][/ROW]
[ROW][C]16[/C][C]-0.015198[/C][C]-0.1672[/C][C]0.433755[/C][/ROW]
[ROW][C]17[/C][C]0.031762[/C][C]0.3494[/C][C]0.363704[/C][/ROW]
[ROW][C]18[/C][C]0.017226[/C][C]0.1895[/C][C]0.425016[/C][/ROW]
[ROW][C]19[/C][C]-0.007207[/C][C]-0.0793[/C][C]0.468473[/C][/ROW]
[ROW][C]20[/C][C]-0.10132[/C][C]-1.1145[/C][C]0.133631[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33543&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33543&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	0.938016	10.3182	0
2	-0.101581	-1.1174	0.13302
3	0.175412	1.9295	0.028003
4	-0.059389	-0.6533	0.257409
5	-0.020135	-0.2215	0.412546
6	-0.027915	-0.3071	0.37966
7	0.104594	1.1505	0.126096
8	-0.086392	-0.9503	0.171924
9	-0.054051	-0.5946	0.276623
10	-0.084255	-0.9268	0.177937
11	-0.075824	-0.8341	0.202945
12	-0.019222	-0.2114	0.416447
13	-0.03577	-0.3935	0.347332
14	0.111012	1.2211	0.112205
15	-0.039628	-0.4359	0.331838
16	-0.015198	-0.1672	0.433755
17	0.031762	0.3494	0.363704
18	0.017226	0.1895	0.425016
19	-0.007207	-0.0793	0.468473
20	-0.10132	-1.1145	0.133631

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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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