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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 11 Dec 2008 05:56:18 -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/11/t1229000817gw4zm2acuwnmmrt.htm/, Retrieved Fri, 17 May 2024 02:02:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32210, Retrieved Fri, 17 May 2024 02:02:06 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

167

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

-       [(Partial) Autocorrelation Function] [VAC paper autocor...] [2008-12-11 12:56:18] [490fee4f334e2e025c95681783e3fd0b] [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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32210&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32210&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32210&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' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.797432	5.0434	5e-06
2	0.578424	3.6583	0.000366
3	0.459656	2.9071	0.002962
4	0.391462	2.4758	0.008812
5	0.330949	2.0931	0.021364
6	0.25353	1.6035	0.05835
7	0.193625	1.2246	0.113946
8	0.158179	1.0004	0.161563
9	0.113683	0.719	0.238162
10	0.074843	0.4733	0.319269
11	0.065837	0.4164	0.339675
12	0.037926	0.2399	0.405831
13	-0.006343	-0.0401	0.484099
14	-0.022277	-0.1409	0.444332
15	0.0023	0.0145	0.494233
16	0.009901	0.0626	0.47519

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.797432 & 5.0434 & 5e-06 \tabularnewline
2 & 0.578424 & 3.6583 & 0.000366 \tabularnewline
3 & 0.459656 & 2.9071 & 0.002962 \tabularnewline
4 & 0.391462 & 2.4758 & 0.008812 \tabularnewline
5 & 0.330949 & 2.0931 & 0.021364 \tabularnewline
6 & 0.25353 & 1.6035 & 0.05835 \tabularnewline
7 & 0.193625 & 1.2246 & 0.113946 \tabularnewline
8 & 0.158179 & 1.0004 & 0.161563 \tabularnewline
9 & 0.113683 & 0.719 & 0.238162 \tabularnewline
10 & 0.074843 & 0.4733 & 0.319269 \tabularnewline
11 & 0.065837 & 0.4164 & 0.339675 \tabularnewline
12 & 0.037926 & 0.2399 & 0.405831 \tabularnewline
13 & -0.006343 & -0.0401 & 0.484099 \tabularnewline
14 & -0.022277 & -0.1409 & 0.444332 \tabularnewline
15 & 0.0023 & 0.0145 & 0.494233 \tabularnewline
16 & 0.009901 & 0.0626 & 0.47519 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32210&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]0.797432[/C][C]5.0434[/C][C]5e-06[/C][/ROW]
[ROW][C]2[/C][C]0.578424[/C][C]3.6583[/C][C]0.000366[/C][/ROW]
[ROW][C]3[/C][C]0.459656[/C][C]2.9071[/C][C]0.002962[/C][/ROW]
[ROW][C]4[/C][C]0.391462[/C][C]2.4758[/C][C]0.008812[/C][/ROW]
[ROW][C]5[/C][C]0.330949[/C][C]2.0931[/C][C]0.021364[/C][/ROW]
[ROW][C]6[/C][C]0.25353[/C][C]1.6035[/C][C]0.05835[/C][/ROW]
[ROW][C]7[/C][C]0.193625[/C][C]1.2246[/C][C]0.113946[/C][/ROW]
[ROW][C]8[/C][C]0.158179[/C][C]1.0004[/C][C]0.161563[/C][/ROW]
[ROW][C]9[/C][C]0.113683[/C][C]0.719[/C][C]0.238162[/C][/ROW]
[ROW][C]10[/C][C]0.074843[/C][C]0.4733[/C][C]0.319269[/C][/ROW]
[ROW][C]11[/C][C]0.065837[/C][C]0.4164[/C][C]0.339675[/C][/ROW]
[ROW][C]12[/C][C]0.037926[/C][C]0.2399[/C][C]0.405831[/C][/ROW]
[ROW][C]13[/C][C]-0.006343[/C][C]-0.0401[/C][C]0.484099[/C][/ROW]
[ROW][C]14[/C][C]-0.022277[/C][C]-0.1409[/C][C]0.444332[/C][/ROW]
[ROW][C]15[/C][C]0.0023[/C][C]0.0145[/C][C]0.494233[/C][/ROW]
[ROW][C]16[/C][C]0.009901[/C][C]0.0626[/C][C]0.47519[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32210&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32210&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	0.797432	5.0434	5e-06
2	0.578424	3.6583	0.000366
3	0.459656	2.9071	0.002962
4	0.391462	2.4758	0.008812
5	0.330949	2.0931	0.021364
6	0.25353	1.6035	0.05835
7	0.193625	1.2246	0.113946
8	0.158179	1.0004	0.161563
9	0.113683	0.719	0.238162
10	0.074843	0.4733	0.319269
11	0.065837	0.4164	0.339675
12	0.037926	0.2399	0.405831
13	-0.006343	-0.0401	0.484099
14	-0.022277	-0.1409	0.444332
15	0.0023	0.0145	0.494233
16	0.009901	0.0626	0.47519

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.797432	5.0434	5e-06
2	-0.15785	-0.9983	0.16206
3	0.144968	0.9169	0.182357
4	0.027805	0.1759	0.430648
5	0.004824	0.0305	0.487907
6	-0.05605	-0.3545	0.362417
7	0.019385	0.1226	0.451519
8	0.006421	0.0406	0.483903
9	-0.052367	-0.3312	0.371111
10	0.005246	0.0332	0.486849
11	0.046071	0.2914	0.386133
12	-0.07847	-0.4963	0.311204
13	-0.038568	-0.2439	0.404268
14	0.041615	0.2632	0.396875
15	0.064186	0.4059	0.343473
16	-0.048158	-0.3046	0.381133

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.797432 & 5.0434 & 5e-06 \tabularnewline
2 & -0.15785 & -0.9983 & 0.16206 \tabularnewline
3 & 0.144968 & 0.9169 & 0.182357 \tabularnewline
4 & 0.027805 & 0.1759 & 0.430648 \tabularnewline
5 & 0.004824 & 0.0305 & 0.487907 \tabularnewline
6 & -0.05605 & -0.3545 & 0.362417 \tabularnewline
7 & 0.019385 & 0.1226 & 0.451519 \tabularnewline
8 & 0.006421 & 0.0406 & 0.483903 \tabularnewline
9 & -0.052367 & -0.3312 & 0.371111 \tabularnewline
10 & 0.005246 & 0.0332 & 0.486849 \tabularnewline
11 & 0.046071 & 0.2914 & 0.386133 \tabularnewline
12 & -0.07847 & -0.4963 & 0.311204 \tabularnewline
13 & -0.038568 & -0.2439 & 0.404268 \tabularnewline
14 & 0.041615 & 0.2632 & 0.396875 \tabularnewline
15 & 0.064186 & 0.4059 & 0.343473 \tabularnewline
16 & -0.048158 & -0.3046 & 0.381133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32210&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]0.797432[/C][C]5.0434[/C][C]5e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.15785[/C][C]-0.9983[/C][C]0.16206[/C][/ROW]
[ROW][C]3[/C][C]0.144968[/C][C]0.9169[/C][C]0.182357[/C][/ROW]
[ROW][C]4[/C][C]0.027805[/C][C]0.1759[/C][C]0.430648[/C][/ROW]
[ROW][C]5[/C][C]0.004824[/C][C]0.0305[/C][C]0.487907[/C][/ROW]
[ROW][C]6[/C][C]-0.05605[/C][C]-0.3545[/C][C]0.362417[/C][/ROW]
[ROW][C]7[/C][C]0.019385[/C][C]0.1226[/C][C]0.451519[/C][/ROW]
[ROW][C]8[/C][C]0.006421[/C][C]0.0406[/C][C]0.483903[/C][/ROW]
[ROW][C]9[/C][C]-0.052367[/C][C]-0.3312[/C][C]0.371111[/C][/ROW]
[ROW][C]10[/C][C]0.005246[/C][C]0.0332[/C][C]0.486849[/C][/ROW]
[ROW][C]11[/C][C]0.046071[/C][C]0.2914[/C][C]0.386133[/C][/ROW]
[ROW][C]12[/C][C]-0.07847[/C][C]-0.4963[/C][C]0.311204[/C][/ROW]
[ROW][C]13[/C][C]-0.038568[/C][C]-0.2439[/C][C]0.404268[/C][/ROW]
[ROW][C]14[/C][C]0.041615[/C][C]0.2632[/C][C]0.396875[/C][/ROW]
[ROW][C]15[/C][C]0.064186[/C][C]0.4059[/C][C]0.343473[/C][/ROW]
[ROW][C]16[/C][C]-0.048158[/C][C]-0.3046[/C][C]0.381133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32210&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32210&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	0.797432	5.0434	5e-06
2	-0.15785	-0.9983	0.16206
3	0.144968	0.9169	0.182357
4	0.027805	0.1759	0.430648
5	0.004824	0.0305	0.487907
6	-0.05605	-0.3545	0.362417
7	0.019385	0.1226	0.451519
8	0.006421	0.0406	0.483903
9	-0.052367	-0.3312	0.371111
10	0.005246	0.0332	0.486849
11	0.046071	0.2914	0.386133
12	-0.07847	-0.4963	0.311204
13	-0.038568	-0.2439	0.404268
14	0.041615	0.2632	0.396875
15	0.064186	0.4059	0.343473
16	-0.048158	-0.3046	0.381133

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 = 4 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ;

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code