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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 26 Nov 2009 04:28:53 -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/2009/Nov/26/t1259235008uvnj5qraw5n4zb9.htm/, Retrieved Mon, 29 Apr 2024 04:14:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59837, Retrieved Mon, 29 Apr 2024 04:14:11 +0000

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Estimated Impact

125

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-   PD          [(Partial) Autocorrelation Function] [Methode 1 lambda=...] [2009-11-26 11:28:53] [b1ac221d009d6e5c29a4ef1869874933] [Current]
-   P             [(Partial) Autocorrelation Function] [ACF] [2009-12-17 14:46:05] [863a41223bd4bb97f4e5094488ffff34] 

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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=59837&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=59837&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59837&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	-0.609906	-4.7243	7e-06
2	0.139593	1.0813	0.141949
3	-0.030083	-0.233	0.40827
4	0.003422	0.0265	0.489472
5	-0.064338	-0.4984	0.310026
6	0.212721	1.6477	0.052318
7	-0.273488	-2.1184	0.019144
8	0.137844	1.0677	0.144958
9	0.084414	0.6539	0.257847
10	-0.20143	-1.5603	0.061978
11	0.241586	1.8713	0.03309
12	-0.21183	-1.6408	0.053032
13	0.079148	0.6131	0.271071
14	-0.074623	-0.578	0.282704
15	0.168672	1.3065	0.098179
16	-0.229038	-1.7741	0.040558
17	0.253424	1.963	0.027143
18	-0.190459	-1.4753	0.072681

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.609906 & -4.7243 & 7e-06 \tabularnewline
2 & 0.139593 & 1.0813 & 0.141949 \tabularnewline
3 & -0.030083 & -0.233 & 0.40827 \tabularnewline
4 & 0.003422 & 0.0265 & 0.489472 \tabularnewline
5 & -0.064338 & -0.4984 & 0.310026 \tabularnewline
6 & 0.212721 & 1.6477 & 0.052318 \tabularnewline
7 & -0.273488 & -2.1184 & 0.019144 \tabularnewline
8 & 0.137844 & 1.0677 & 0.144958 \tabularnewline
9 & 0.084414 & 0.6539 & 0.257847 \tabularnewline
10 & -0.20143 & -1.5603 & 0.061978 \tabularnewline
11 & 0.241586 & 1.8713 & 0.03309 \tabularnewline
12 & -0.21183 & -1.6408 & 0.053032 \tabularnewline
13 & 0.079148 & 0.6131 & 0.271071 \tabularnewline
14 & -0.074623 & -0.578 & 0.282704 \tabularnewline
15 & 0.168672 & 1.3065 & 0.098179 \tabularnewline
16 & -0.229038 & -1.7741 & 0.040558 \tabularnewline
17 & 0.253424 & 1.963 & 0.027143 \tabularnewline
18 & -0.190459 & -1.4753 & 0.072681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59837&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]-0.609906[/C][C]-4.7243[/C][C]7e-06[/C][/ROW]
[ROW][C]2[/C][C]0.139593[/C][C]1.0813[/C][C]0.141949[/C][/ROW]
[ROW][C]3[/C][C]-0.030083[/C][C]-0.233[/C][C]0.40827[/C][/ROW]
[ROW][C]4[/C][C]0.003422[/C][C]0.0265[/C][C]0.489472[/C][/ROW]
[ROW][C]5[/C][C]-0.064338[/C][C]-0.4984[/C][C]0.310026[/C][/ROW]
[ROW][C]6[/C][C]0.212721[/C][C]1.6477[/C][C]0.052318[/C][/ROW]
[ROW][C]7[/C][C]-0.273488[/C][C]-2.1184[/C][C]0.019144[/C][/ROW]
[ROW][C]8[/C][C]0.137844[/C][C]1.0677[/C][C]0.144958[/C][/ROW]
[ROW][C]9[/C][C]0.084414[/C][C]0.6539[/C][C]0.257847[/C][/ROW]
[ROW][C]10[/C][C]-0.20143[/C][C]-1.5603[/C][C]0.061978[/C][/ROW]
[ROW][C]11[/C][C]0.241586[/C][C]1.8713[/C][C]0.03309[/C][/ROW]
[ROW][C]12[/C][C]-0.21183[/C][C]-1.6408[/C][C]0.053032[/C][/ROW]
[ROW][C]13[/C][C]0.079148[/C][C]0.6131[/C][C]0.271071[/C][/ROW]
[ROW][C]14[/C][C]-0.074623[/C][C]-0.578[/C][C]0.282704[/C][/ROW]
[ROW][C]15[/C][C]0.168672[/C][C]1.3065[/C][C]0.098179[/C][/ROW]
[ROW][C]16[/C][C]-0.229038[/C][C]-1.7741[/C][C]0.040558[/C][/ROW]
[ROW][C]17[/C][C]0.253424[/C][C]1.963[/C][C]0.027143[/C][/ROW]
[ROW][C]18[/C][C]-0.190459[/C][C]-1.4753[/C][C]0.072681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59837&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59837&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	-0.609906	-4.7243	7e-06
2	0.139593	1.0813	0.141949
3	-0.030083	-0.233	0.40827
4	0.003422	0.0265	0.489472
5	-0.064338	-0.4984	0.310026
6	0.212721	1.6477	0.052318
7	-0.273488	-2.1184	0.019144
8	0.137844	1.0677	0.144958
9	0.084414	0.6539	0.257847
10	-0.20143	-1.5603	0.061978
11	0.241586	1.8713	0.03309
12	-0.21183	-1.6408	0.053032
13	0.079148	0.6131	0.271071
14	-0.074623	-0.578	0.282704
15	0.168672	1.3065	0.098179
16	-0.229038	-1.7741	0.040558
17	0.253424	1.963	0.027143
18	-0.190459	-1.4753	0.072681

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.609906	-4.7243	7e-06
2	-0.370042	-2.8663	0.00286
3	-0.256687	-1.9883	0.025674
4	-0.196583	-1.5227	0.066541
5	-0.288759	-2.2367	0.014517
6	0.045607	0.3533	0.362563
7	-0.127969	-0.9912	0.162774
8	-0.184519	-1.4293	0.079056
9	0.08845	0.6851	0.247949
10	-0.095056	-0.7363	0.232208
11	0.160796	1.2455	0.108891
12	-0.010273	-0.0796	0.468421
13	0.005609	0.0434	0.482744
14	-0.208631	-1.6161	0.055665
15	-0.057152	-0.4427	0.32979
16	-0.168451	-1.3048	0.098469
17	-0.082963	-0.6426	0.261457
18	-0.009601	-0.0744	0.470481

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.609906 & -4.7243 & 7e-06 \tabularnewline
2 & -0.370042 & -2.8663 & 0.00286 \tabularnewline
3 & -0.256687 & -1.9883 & 0.025674 \tabularnewline
4 & -0.196583 & -1.5227 & 0.066541 \tabularnewline
5 & -0.288759 & -2.2367 & 0.014517 \tabularnewline
6 & 0.045607 & 0.3533 & 0.362563 \tabularnewline
7 & -0.127969 & -0.9912 & 0.162774 \tabularnewline
8 & -0.184519 & -1.4293 & 0.079056 \tabularnewline
9 & 0.08845 & 0.6851 & 0.247949 \tabularnewline
10 & -0.095056 & -0.7363 & 0.232208 \tabularnewline
11 & 0.160796 & 1.2455 & 0.108891 \tabularnewline
12 & -0.010273 & -0.0796 & 0.468421 \tabularnewline
13 & 0.005609 & 0.0434 & 0.482744 \tabularnewline
14 & -0.208631 & -1.6161 & 0.055665 \tabularnewline
15 & -0.057152 & -0.4427 & 0.32979 \tabularnewline
16 & -0.168451 & -1.3048 & 0.098469 \tabularnewline
17 & -0.082963 & -0.6426 & 0.261457 \tabularnewline
18 & -0.009601 & -0.0744 & 0.470481 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59837&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]-0.609906[/C][C]-4.7243[/C][C]7e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.370042[/C][C]-2.8663[/C][C]0.00286[/C][/ROW]
[ROW][C]3[/C][C]-0.256687[/C][C]-1.9883[/C][C]0.025674[/C][/ROW]
[ROW][C]4[/C][C]-0.196583[/C][C]-1.5227[/C][C]0.066541[/C][/ROW]
[ROW][C]5[/C][C]-0.288759[/C][C]-2.2367[/C][C]0.014517[/C][/ROW]
[ROW][C]6[/C][C]0.045607[/C][C]0.3533[/C][C]0.362563[/C][/ROW]
[ROW][C]7[/C][C]-0.127969[/C][C]-0.9912[/C][C]0.162774[/C][/ROW]
[ROW][C]8[/C][C]-0.184519[/C][C]-1.4293[/C][C]0.079056[/C][/ROW]
[ROW][C]9[/C][C]0.08845[/C][C]0.6851[/C][C]0.247949[/C][/ROW]
[ROW][C]10[/C][C]-0.095056[/C][C]-0.7363[/C][C]0.232208[/C][/ROW]
[ROW][C]11[/C][C]0.160796[/C][C]1.2455[/C][C]0.108891[/C][/ROW]
[ROW][C]12[/C][C]-0.010273[/C][C]-0.0796[/C][C]0.468421[/C][/ROW]
[ROW][C]13[/C][C]0.005609[/C][C]0.0434[/C][C]0.482744[/C][/ROW]
[ROW][C]14[/C][C]-0.208631[/C][C]-1.6161[/C][C]0.055665[/C][/ROW]
[ROW][C]15[/C][C]-0.057152[/C][C]-0.4427[/C][C]0.32979[/C][/ROW]
[ROW][C]16[/C][C]-0.168451[/C][C]-1.3048[/C][C]0.098469[/C][/ROW]
[ROW][C]17[/C][C]-0.082963[/C][C]-0.6426[/C][C]0.261457[/C][/ROW]
[ROW][C]18[/C][C]-0.009601[/C][C]-0.0744[/C][C]0.470481[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59837&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59837&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	-0.609906	-4.7243	7e-06
2	-0.370042	-2.8663	0.00286
3	-0.256687	-1.9883	0.025674
4	-0.196583	-1.5227	0.066541
5	-0.288759	-2.2367	0.014517
6	0.045607	0.3533	0.362563
7	-0.127969	-0.9912	0.162774
8	-0.184519	-1.4293	0.079056
9	0.08845	0.6851	0.247949
10	-0.095056	-0.7363	0.232208
11	0.160796	1.2455	0.108891
12	-0.010273	-0.0796	0.468421
13	0.005609	0.0434	0.482744
14	-0.208631	-1.6161	0.055665
15	-0.057152	-0.4427	0.32979
16	-0.168451	-1.3048	0.098469
17	-0.082963	-0.6426	0.261457
18	-0.009601	-0.0744	0.470481

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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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Figures (Output of Computation)

Input Parameters & R Code