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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 16 Dec 2007 08:23:46 -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/2007/Dec/16/t1197817643qnv6tqcbgtuvz5v.htm/, Retrieved Thu, 02 May 2024 10:11:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4205, Retrieved Thu, 02 May 2024 10:11:56 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

d=0 D=0 industriele productie

Estimated Impact

198

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2007-12-16 15:23:46] [0eafefa7b02d47065fceb6c46f54fbf9] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4205&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4205&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4205&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.6023	0
1	0.900855	7.7494	0
2	0.773645	6.6551	0
3	0.637575	5.4846	0
4	0.516287	4.4413	1.5e-05
5	0.435207	3.7438	0.000178
6	0.396916	3.4144	0.00052
7	0.387431	3.3328	0.000672
8	0.394478	3.3934	0.000556
9	0.397357	3.4182	0.000514
10	0.382204	3.2878	0.000773
11	0.350289	3.0133	0.001768
12	0.303285	2.609	0.005492
13	0.243435	2.0941	0.019838
14	0.184568	1.5877	0.058308
15	0.136614	1.1752	0.121841
16	0.109203	0.9394	0.175292
17	0.097596	0.8395	0.201933

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.6023 & 0 \tabularnewline
1 & 0.900855 & 7.7494 & 0 \tabularnewline
2 & 0.773645 & 6.6551 & 0 \tabularnewline
3 & 0.637575 & 5.4846 & 0 \tabularnewline
4 & 0.516287 & 4.4413 & 1.5e-05 \tabularnewline
5 & 0.435207 & 3.7438 & 0.000178 \tabularnewline
6 & 0.396916 & 3.4144 & 0.00052 \tabularnewline
7 & 0.387431 & 3.3328 & 0.000672 \tabularnewline
8 & 0.394478 & 3.3934 & 0.000556 \tabularnewline
9 & 0.397357 & 3.4182 & 0.000514 \tabularnewline
10 & 0.382204 & 3.2878 & 0.000773 \tabularnewline
11 & 0.350289 & 3.0133 & 0.001768 \tabularnewline
12 & 0.303285 & 2.609 & 0.005492 \tabularnewline
13 & 0.243435 & 2.0941 & 0.019838 \tabularnewline
14 & 0.184568 & 1.5877 & 0.058308 \tabularnewline
15 & 0.136614 & 1.1752 & 0.121841 \tabularnewline
16 & 0.109203 & 0.9394 & 0.175292 \tabularnewline
17 & 0.097596 & 0.8395 & 0.201933 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4205&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]0[/C][C]1[/C][C]8.6023[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.900855[/C][C]7.7494[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.773645[/C][C]6.6551[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.637575[/C][C]5.4846[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.516287[/C][C]4.4413[/C][C]1.5e-05[/C][/ROW]
[ROW][C]5[/C][C]0.435207[/C][C]3.7438[/C][C]0.000178[/C][/ROW]
[ROW][C]6[/C][C]0.396916[/C][C]3.4144[/C][C]0.00052[/C][/ROW]
[ROW][C]7[/C][C]0.387431[/C][C]3.3328[/C][C]0.000672[/C][/ROW]
[ROW][C]8[/C][C]0.394478[/C][C]3.3934[/C][C]0.000556[/C][/ROW]
[ROW][C]9[/C][C]0.397357[/C][C]3.4182[/C][C]0.000514[/C][/ROW]
[ROW][C]10[/C][C]0.382204[/C][C]3.2878[/C][C]0.000773[/C][/ROW]
[ROW][C]11[/C][C]0.350289[/C][C]3.0133[/C][C]0.001768[/C][/ROW]
[ROW][C]12[/C][C]0.303285[/C][C]2.609[/C][C]0.005492[/C][/ROW]
[ROW][C]13[/C][C]0.243435[/C][C]2.0941[/C][C]0.019838[/C][/ROW]
[ROW][C]14[/C][C]0.184568[/C][C]1.5877[/C][C]0.058308[/C][/ROW]
[ROW][C]15[/C][C]0.136614[/C][C]1.1752[/C][C]0.121841[/C][/ROW]
[ROW][C]16[/C][C]0.109203[/C][C]0.9394[/C][C]0.175292[/C][/ROW]
[ROW][C]17[/C][C]0.097596[/C][C]0.8395[/C][C]0.201933[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4205&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4205&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
0	1	8.6023	0
1	0.900855	7.7494	0
2	0.773645	6.6551	0
3	0.637575	5.4846	0
4	0.516287	4.4413	1.5e-05
5	0.435207	3.7438	0.000178
6	0.396916	3.4144	0.00052
7	0.387431	3.3328	0.000672
8	0.394478	3.3934	0.000556
9	0.397357	3.4182	0.000514
10	0.382204	3.2878	0.000773
11	0.350289	3.0133	0.001768
12	0.303285	2.609	0.005492
13	0.243435	2.0941	0.019838
14	0.184568	1.5877	0.058308
15	0.136614	1.1752	0.121841
16	0.109203	0.9394	0.175292
17	0.097596	0.8395	0.201933

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.900855	7.7494	0
1	-0.20107	-1.7297	0.95607
2	-0.101561	-0.8737	0.807435
3	0.008336	0.0717	0.471514
4	0.124357	1.0698	0.144103
5	0.122327	1.0523	0.148045
6	0.062757	0.5399	0.295459
7	0.046721	0.4019	0.344455
8	-0.00985	-0.0847	0.533649
9	-0.041066	-0.3533	0.637553
10	-0.018928	-0.1628	0.564449
11	-0.029517	-0.2539	0.599869
12	-0.059624	-0.5129	0.695227
13	-0.026335	-0.2265	0.589299
14	-0.004434	-0.0381	0.515161
15	0.031419	0.2703	0.393851
16	4.4e-05	4e-04	0.499849
17	-0.068175	-0.5865	0.720326

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.900855 & 7.7494 & 0 \tabularnewline
1 & -0.20107 & -1.7297 & 0.95607 \tabularnewline
2 & -0.101561 & -0.8737 & 0.807435 \tabularnewline
3 & 0.008336 & 0.0717 & 0.471514 \tabularnewline
4 & 0.124357 & 1.0698 & 0.144103 \tabularnewline
5 & 0.122327 & 1.0523 & 0.148045 \tabularnewline
6 & 0.062757 & 0.5399 & 0.295459 \tabularnewline
7 & 0.046721 & 0.4019 & 0.344455 \tabularnewline
8 & -0.00985 & -0.0847 & 0.533649 \tabularnewline
9 & -0.041066 & -0.3533 & 0.637553 \tabularnewline
10 & -0.018928 & -0.1628 & 0.564449 \tabularnewline
11 & -0.029517 & -0.2539 & 0.599869 \tabularnewline
12 & -0.059624 & -0.5129 & 0.695227 \tabularnewline
13 & -0.026335 & -0.2265 & 0.589299 \tabularnewline
14 & -0.004434 & -0.0381 & 0.515161 \tabularnewline
15 & 0.031419 & 0.2703 & 0.393851 \tabularnewline
16 & 4.4e-05 & 4e-04 & 0.499849 \tabularnewline
17 & -0.068175 & -0.5865 & 0.720326 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4205&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]0[/C][C]0.900855[/C][C]7.7494[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.20107[/C][C]-1.7297[/C][C]0.95607[/C][/ROW]
[ROW][C]2[/C][C]-0.101561[/C][C]-0.8737[/C][C]0.807435[/C][/ROW]
[ROW][C]3[/C][C]0.008336[/C][C]0.0717[/C][C]0.471514[/C][/ROW]
[ROW][C]4[/C][C]0.124357[/C][C]1.0698[/C][C]0.144103[/C][/ROW]
[ROW][C]5[/C][C]0.122327[/C][C]1.0523[/C][C]0.148045[/C][/ROW]
[ROW][C]6[/C][C]0.062757[/C][C]0.5399[/C][C]0.295459[/C][/ROW]
[ROW][C]7[/C][C]0.046721[/C][C]0.4019[/C][C]0.344455[/C][/ROW]
[ROW][C]8[/C][C]-0.00985[/C][C]-0.0847[/C][C]0.533649[/C][/ROW]
[ROW][C]9[/C][C]-0.041066[/C][C]-0.3533[/C][C]0.637553[/C][/ROW]
[ROW][C]10[/C][C]-0.018928[/C][C]-0.1628[/C][C]0.564449[/C][/ROW]
[ROW][C]11[/C][C]-0.029517[/C][C]-0.2539[/C][C]0.599869[/C][/ROW]
[ROW][C]12[/C][C]-0.059624[/C][C]-0.5129[/C][C]0.695227[/C][/ROW]
[ROW][C]13[/C][C]-0.026335[/C][C]-0.2265[/C][C]0.589299[/C][/ROW]
[ROW][C]14[/C][C]-0.004434[/C][C]-0.0381[/C][C]0.515161[/C][/ROW]
[ROW][C]15[/C][C]0.031419[/C][C]0.2703[/C][C]0.393851[/C][/ROW]
[ROW][C]16[/C][C]4.4e-05[/C][C]4e-04[/C][C]0.499849[/C][/ROW]
[ROW][C]17[/C][C]-0.068175[/C][C]-0.5865[/C][C]0.720326[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4205&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4205&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
0	0.900855	7.7494	0
1	-0.20107	-1.7297	0.95607
2	-0.101561	-0.8737	0.807435
3	0.008336	0.0717	0.471514
4	0.124357	1.0698	0.144103
5	0.122327	1.0523	0.148045
6	0.062757	0.5399	0.295459
7	0.046721	0.4019	0.344455
8	-0.00985	-0.0847	0.533649
9	-0.041066	-0.3533	0.637553
10	-0.018928	-0.1628	0.564449
11	-0.029517	-0.2539	0.599869
12	-0.059624	-0.5129	0.695227
13	-0.026335	-0.2265	0.589299
14	-0.004434	-0.0381	0.515161
15	0.031419	0.2703	0.393851
16	4.4e-05	4e-04	0.499849
17	-0.068175	-0.5865	0.720326

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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