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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 14 Dec 2007 03:32:50 -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/14/t119762809870hrozboito33jc.htm/, Retrieved Thu, 02 May 2024 21:21:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3827, Retrieved Thu, 02 May 2024 21:21:32 +0000

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No (this computation is public)

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Estimated Impact

175

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-       [(Partial) Autocorrelation Function] [oliezaden] [2007-12-14 10:32:50] [a98121933c09d0d44a9f89053acd1df1] [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=3827&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=3827&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3827&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	9.6437	0
1	0.910752	8.783	0
2	0.803237	7.7461	0
3	0.68268	6.5835	0
4	0.562466	5.4242	0
5	0.454413	4.3822	1.5e-05
6	0.367352	3.5426	0.000311
7	0.28131	2.7129	0.003974
8	0.211073	2.0355	0.022322
9	0.164889	1.5901	0.057599
10	0.14567	1.4048	0.081708
11	0.139993	1.35	0.09014
12	0.149801	1.4446	0.075962
13	0.157006	1.5141	0.066694
14	0.15431	1.4881	0.070053
15	0.13433	1.2954	0.099189
16	0.110124	1.062	0.145493
17	0.084416	0.8141	0.20884
18	0.067179	0.6479	0.259339

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.6437 & 0 \tabularnewline
1 & 0.910752 & 8.783 & 0 \tabularnewline
2 & 0.803237 & 7.7461 & 0 \tabularnewline
3 & 0.68268 & 6.5835 & 0 \tabularnewline
4 & 0.562466 & 5.4242 & 0 \tabularnewline
5 & 0.454413 & 4.3822 & 1.5e-05 \tabularnewline
6 & 0.367352 & 3.5426 & 0.000311 \tabularnewline
7 & 0.28131 & 2.7129 & 0.003974 \tabularnewline
8 & 0.211073 & 2.0355 & 0.022322 \tabularnewline
9 & 0.164889 & 1.5901 & 0.057599 \tabularnewline
10 & 0.14567 & 1.4048 & 0.081708 \tabularnewline
11 & 0.139993 & 1.35 & 0.09014 \tabularnewline
12 & 0.149801 & 1.4446 & 0.075962 \tabularnewline
13 & 0.157006 & 1.5141 & 0.066694 \tabularnewline
14 & 0.15431 & 1.4881 & 0.070053 \tabularnewline
15 & 0.13433 & 1.2954 & 0.099189 \tabularnewline
16 & 0.110124 & 1.062 & 0.145493 \tabularnewline
17 & 0.084416 & 0.8141 & 0.20884 \tabularnewline
18 & 0.067179 & 0.6479 & 0.259339 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3827&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]9.6437[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.910752[/C][C]8.783[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.803237[/C][C]7.7461[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.68268[/C][C]6.5835[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.562466[/C][C]5.4242[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.454413[/C][C]4.3822[/C][C]1.5e-05[/C][/ROW]
[ROW][C]6[/C][C]0.367352[/C][C]3.5426[/C][C]0.000311[/C][/ROW]
[ROW][C]7[/C][C]0.28131[/C][C]2.7129[/C][C]0.003974[/C][/ROW]
[ROW][C]8[/C][C]0.211073[/C][C]2.0355[/C][C]0.022322[/C][/ROW]
[ROW][C]9[/C][C]0.164889[/C][C]1.5901[/C][C]0.057599[/C][/ROW]
[ROW][C]10[/C][C]0.14567[/C][C]1.4048[/C][C]0.081708[/C][/ROW]
[ROW][C]11[/C][C]0.139993[/C][C]1.35[/C][C]0.09014[/C][/ROW]
[ROW][C]12[/C][C]0.149801[/C][C]1.4446[/C][C]0.075962[/C][/ROW]
[ROW][C]13[/C][C]0.157006[/C][C]1.5141[/C][C]0.066694[/C][/ROW]
[ROW][C]14[/C][C]0.15431[/C][C]1.4881[/C][C]0.070053[/C][/ROW]
[ROW][C]15[/C][C]0.13433[/C][C]1.2954[/C][C]0.099189[/C][/ROW]
[ROW][C]16[/C][C]0.110124[/C][C]1.062[/C][C]0.145493[/C][/ROW]
[ROW][C]17[/C][C]0.084416[/C][C]0.8141[/C][C]0.20884[/C][/ROW]
[ROW][C]18[/C][C]0.067179[/C][C]0.6479[/C][C]0.259339[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3827&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3827&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	9.6437	0
1	0.910752	8.783	0
2	0.803237	7.7461	0
3	0.68268	6.5835	0
4	0.562466	5.4242	0
5	0.454413	4.3822	1.5e-05
6	0.367352	3.5426	0.000311
7	0.28131	2.7129	0.003974
8	0.211073	2.0355	0.022322
9	0.164889	1.5901	0.057599
10	0.14567	1.4048	0.081708
11	0.139993	1.35	0.09014
12	0.149801	1.4446	0.075962
13	0.157006	1.5141	0.066694
14	0.15431	1.4881	0.070053
15	0.13433	1.2954	0.099189
16	0.110124	1.062	0.145493
17	0.084416	0.8141	0.20884
18	0.067179	0.6479	0.259339

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.910752	8.783	0
1	-0.15382	-1.4834	0.929324
2	-0.127956	-1.234	0.889837
3	-0.057409	-0.5536	0.709421
4	0.00025	0.0024	0.499043
5	0.040687	0.3924	0.347841
6	-0.088762	-0.856	0.802898
7	0.012984	0.1252	0.450314
8	0.075704	0.7301	0.233593
9	0.094808	0.9143	0.181462
10	0.013546	0.1306	0.448173
11	0.040919	0.3946	0.347018
12	-0.024301	-0.2344	0.592388
13	-0.047547	-0.4585	0.676177
14	-0.086436	-0.8336	0.796668
15	-0.007891	-0.0761	0.530246
16	0.015565	0.1501	0.440504
17	0.050543	0.4874	0.313555
18	0.00922	0.0889	0.46467

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.910752 & 8.783 & 0 \tabularnewline
1 & -0.15382 & -1.4834 & 0.929324 \tabularnewline
2 & -0.127956 & -1.234 & 0.889837 \tabularnewline
3 & -0.057409 & -0.5536 & 0.709421 \tabularnewline
4 & 0.00025 & 0.0024 & 0.499043 \tabularnewline
5 & 0.040687 & 0.3924 & 0.347841 \tabularnewline
6 & -0.088762 & -0.856 & 0.802898 \tabularnewline
7 & 0.012984 & 0.1252 & 0.450314 \tabularnewline
8 & 0.075704 & 0.7301 & 0.233593 \tabularnewline
9 & 0.094808 & 0.9143 & 0.181462 \tabularnewline
10 & 0.013546 & 0.1306 & 0.448173 \tabularnewline
11 & 0.040919 & 0.3946 & 0.347018 \tabularnewline
12 & -0.024301 & -0.2344 & 0.592388 \tabularnewline
13 & -0.047547 & -0.4585 & 0.676177 \tabularnewline
14 & -0.086436 & -0.8336 & 0.796668 \tabularnewline
15 & -0.007891 & -0.0761 & 0.530246 \tabularnewline
16 & 0.015565 & 0.1501 & 0.440504 \tabularnewline
17 & 0.050543 & 0.4874 & 0.313555 \tabularnewline
18 & 0.00922 & 0.0889 & 0.46467 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3827&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]0.910752[/C][C]8.783[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.15382[/C][C]-1.4834[/C][C]0.929324[/C][/ROW]
[ROW][C]2[/C][C]-0.127956[/C][C]-1.234[/C][C]0.889837[/C][/ROW]
[ROW][C]3[/C][C]-0.057409[/C][C]-0.5536[/C][C]0.709421[/C][/ROW]
[ROW][C]4[/C][C]0.00025[/C][C]0.0024[/C][C]0.499043[/C][/ROW]
[ROW][C]5[/C][C]0.040687[/C][C]0.3924[/C][C]0.347841[/C][/ROW]
[ROW][C]6[/C][C]-0.088762[/C][C]-0.856[/C][C]0.802898[/C][/ROW]
[ROW][C]7[/C][C]0.012984[/C][C]0.1252[/C][C]0.450314[/C][/ROW]
[ROW][C]8[/C][C]0.075704[/C][C]0.7301[/C][C]0.233593[/C][/ROW]
[ROW][C]9[/C][C]0.094808[/C][C]0.9143[/C][C]0.181462[/C][/ROW]
[ROW][C]10[/C][C]0.013546[/C][C]0.1306[/C][C]0.448173[/C][/ROW]
[ROW][C]11[/C][C]0.040919[/C][C]0.3946[/C][C]0.347018[/C][/ROW]
[ROW][C]12[/C][C]-0.024301[/C][C]-0.2344[/C][C]0.592388[/C][/ROW]
[ROW][C]13[/C][C]-0.047547[/C][C]-0.4585[/C][C]0.676177[/C][/ROW]
[ROW][C]14[/C][C]-0.086436[/C][C]-0.8336[/C][C]0.796668[/C][/ROW]
[ROW][C]15[/C][C]-0.007891[/C][C]-0.0761[/C][C]0.530246[/C][/ROW]
[ROW][C]16[/C][C]0.015565[/C][C]0.1501[/C][C]0.440504[/C][/ROW]
[ROW][C]17[/C][C]0.050543[/C][C]0.4874[/C][C]0.313555[/C][/ROW]
[ROW][C]18[/C][C]0.00922[/C][C]0.0889[/C][C]0.46467[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3827&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3827&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	0.910752	8.783	0
1	-0.15382	-1.4834	0.929324
2	-0.127956	-1.234	0.889837
3	-0.057409	-0.5536	0.709421
4	0.00025	0.0024	0.499043
5	0.040687	0.3924	0.347841
6	-0.088762	-0.856	0.802898
7	0.012984	0.1252	0.450314
8	0.075704	0.7301	0.233593
9	0.094808	0.9143	0.181462
10	0.013546	0.1306	0.448173
11	0.040919	0.3946	0.347018
12	-0.024301	-0.2344	0.592388
13	-0.047547	-0.4585	0.676177
14	-0.086436	-0.8336	0.796668
15	-0.007891	-0.0761	0.530246
16	0.015565	0.1501	0.440504
17	0.050543	0.4874	0.313555
18	0.00922	0.0889	0.46467

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 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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