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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 30 Dec 2009 15:42:06 -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/Dec/30/t1262212985i0rwesgbmsje1nu.htm/, Retrieved Mon, 29 Apr 2024 02:41:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71391, Retrieved Mon, 29 Apr 2024 02:41:01 +0000

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

-       [(Partial) Autocorrelation Function] [paper ACF] [2009-12-30 22:42:06] [3ebad5d90a5c8606f133189c73066208] [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=71391&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=71391&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71391&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	0.26824	2.0778	0.021009
2	0.010628	0.0823	0.467332
3	0.136888	1.0603	0.146622
4	0.13548	1.0494	0.149096
5	0.107827	0.8352	0.203452
6	-0.099236	-0.7687	0.222549
7	-0.328168	-2.542	0.006811
8	-0.08623	-0.6679	0.253369
9	-0.060062	-0.4652	0.321723
10	-0.203047	-1.5728	0.060513
11	-0.179688	-1.3919	0.084552
12	-0.176779	-1.3693	0.088
13	-0.139596	-1.0813	0.141944
14	0.015865	0.1229	0.451303
15	0.036627	0.2837	0.388803
16	0.006712	0.052	0.479353
17	0.008818	0.0683	0.472887

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.26824 & 2.0778 & 0.021009 \tabularnewline
2 & 0.010628 & 0.0823 & 0.467332 \tabularnewline
3 & 0.136888 & 1.0603 & 0.146622 \tabularnewline
4 & 0.13548 & 1.0494 & 0.149096 \tabularnewline
5 & 0.107827 & 0.8352 & 0.203452 \tabularnewline
6 & -0.099236 & -0.7687 & 0.222549 \tabularnewline
7 & -0.328168 & -2.542 & 0.006811 \tabularnewline
8 & -0.08623 & -0.6679 & 0.253369 \tabularnewline
9 & -0.060062 & -0.4652 & 0.321723 \tabularnewline
10 & -0.203047 & -1.5728 & 0.060513 \tabularnewline
11 & -0.179688 & -1.3919 & 0.084552 \tabularnewline
12 & -0.176779 & -1.3693 & 0.088 \tabularnewline
13 & -0.139596 & -1.0813 & 0.141944 \tabularnewline
14 & 0.015865 & 0.1229 & 0.451303 \tabularnewline
15 & 0.036627 & 0.2837 & 0.388803 \tabularnewline
16 & 0.006712 & 0.052 & 0.479353 \tabularnewline
17 & 0.008818 & 0.0683 & 0.472887 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71391&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]0.26824[/C][C]2.0778[/C][C]0.021009[/C][/ROW]
[ROW][C]2[/C][C]0.010628[/C][C]0.0823[/C][C]0.467332[/C][/ROW]
[ROW][C]3[/C][C]0.136888[/C][C]1.0603[/C][C]0.146622[/C][/ROW]
[ROW][C]4[/C][C]0.13548[/C][C]1.0494[/C][C]0.149096[/C][/ROW]
[ROW][C]5[/C][C]0.107827[/C][C]0.8352[/C][C]0.203452[/C][/ROW]
[ROW][C]6[/C][C]-0.099236[/C][C]-0.7687[/C][C]0.222549[/C][/ROW]
[ROW][C]7[/C][C]-0.328168[/C][C]-2.542[/C][C]0.006811[/C][/ROW]
[ROW][C]8[/C][C]-0.08623[/C][C]-0.6679[/C][C]0.253369[/C][/ROW]
[ROW][C]9[/C][C]-0.060062[/C][C]-0.4652[/C][C]0.321723[/C][/ROW]
[ROW][C]10[/C][C]-0.203047[/C][C]-1.5728[/C][C]0.060513[/C][/ROW]
[ROW][C]11[/C][C]-0.179688[/C][C]-1.3919[/C][C]0.084552[/C][/ROW]
[ROW][C]12[/C][C]-0.176779[/C][C]-1.3693[/C][C]0.088[/C][/ROW]
[ROW][C]13[/C][C]-0.139596[/C][C]-1.0813[/C][C]0.141944[/C][/ROW]
[ROW][C]14[/C][C]0.015865[/C][C]0.1229[/C][C]0.451303[/C][/ROW]
[ROW][C]15[/C][C]0.036627[/C][C]0.2837[/C][C]0.388803[/C][/ROW]
[ROW][C]16[/C][C]0.006712[/C][C]0.052[/C][C]0.479353[/C][/ROW]
[ROW][C]17[/C][C]0.008818[/C][C]0.0683[/C][C]0.472887[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71391&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71391&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	0.26824	2.0778	0.021009
2	0.010628	0.0823	0.467332
3	0.136888	1.0603	0.146622
4	0.13548	1.0494	0.149096
5	0.107827	0.8352	0.203452
6	-0.099236	-0.7687	0.222549
7	-0.328168	-2.542	0.006811
8	-0.08623	-0.6679	0.253369
9	-0.060062	-0.4652	0.321723
10	-0.203047	-1.5728	0.060513
11	-0.179688	-1.3919	0.084552
12	-0.176779	-1.3693	0.088
13	-0.139596	-1.0813	0.141944
14	0.015865	0.1229	0.451303
15	0.036627	0.2837	0.388803
16	0.006712	0.052	0.479353
17	0.008818	0.0683	0.472887

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.26824	2.0778	0.021009
2	-0.066079	-0.5118	0.305319
3	0.164042	1.2707	0.104377
4	0.057889	0.4484	0.327738
5	0.074081	0.5738	0.284114
6	-0.174261	-1.3498	0.091072
7	-0.31041	-2.4044	0.009651
8	0.035757	0.277	0.391378
9	-0.072932	-0.5649	0.287113
10	-0.086265	-0.6682	0.253283
11	-0.03032	-0.2349	0.40756
12	-0.089665	-0.6945	0.245011
13	-0.116879	-0.9053	0.184453
14	0.023376	0.1811	0.42846
15	0.09319	0.7218	0.236595
16	0.003864	0.0299	0.488111
17	-0.069011	-0.5346	0.297467

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.26824 & 2.0778 & 0.021009 \tabularnewline
2 & -0.066079 & -0.5118 & 0.305319 \tabularnewline
3 & 0.164042 & 1.2707 & 0.104377 \tabularnewline
4 & 0.057889 & 0.4484 & 0.327738 \tabularnewline
5 & 0.074081 & 0.5738 & 0.284114 \tabularnewline
6 & -0.174261 & -1.3498 & 0.091072 \tabularnewline
7 & -0.31041 & -2.4044 & 0.009651 \tabularnewline
8 & 0.035757 & 0.277 & 0.391378 \tabularnewline
9 & -0.072932 & -0.5649 & 0.287113 \tabularnewline
10 & -0.086265 & -0.6682 & 0.253283 \tabularnewline
11 & -0.03032 & -0.2349 & 0.40756 \tabularnewline
12 & -0.089665 & -0.6945 & 0.245011 \tabularnewline
13 & -0.116879 & -0.9053 & 0.184453 \tabularnewline
14 & 0.023376 & 0.1811 & 0.42846 \tabularnewline
15 & 0.09319 & 0.7218 & 0.236595 \tabularnewline
16 & 0.003864 & 0.0299 & 0.488111 \tabularnewline
17 & -0.069011 & -0.5346 & 0.297467 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71391&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]0.26824[/C][C]2.0778[/C][C]0.021009[/C][/ROW]
[ROW][C]2[/C][C]-0.066079[/C][C]-0.5118[/C][C]0.305319[/C][/ROW]
[ROW][C]3[/C][C]0.164042[/C][C]1.2707[/C][C]0.104377[/C][/ROW]
[ROW][C]4[/C][C]0.057889[/C][C]0.4484[/C][C]0.327738[/C][/ROW]
[ROW][C]5[/C][C]0.074081[/C][C]0.5738[/C][C]0.284114[/C][/ROW]
[ROW][C]6[/C][C]-0.174261[/C][C]-1.3498[/C][C]0.091072[/C][/ROW]
[ROW][C]7[/C][C]-0.31041[/C][C]-2.4044[/C][C]0.009651[/C][/ROW]
[ROW][C]8[/C][C]0.035757[/C][C]0.277[/C][C]0.391378[/C][/ROW]
[ROW][C]9[/C][C]-0.072932[/C][C]-0.5649[/C][C]0.287113[/C][/ROW]
[ROW][C]10[/C][C]-0.086265[/C][C]-0.6682[/C][C]0.253283[/C][/ROW]
[ROW][C]11[/C][C]-0.03032[/C][C]-0.2349[/C][C]0.40756[/C][/ROW]
[ROW][C]12[/C][C]-0.089665[/C][C]-0.6945[/C][C]0.245011[/C][/ROW]
[ROW][C]13[/C][C]-0.116879[/C][C]-0.9053[/C][C]0.184453[/C][/ROW]
[ROW][C]14[/C][C]0.023376[/C][C]0.1811[/C][C]0.42846[/C][/ROW]
[ROW][C]15[/C][C]0.09319[/C][C]0.7218[/C][C]0.236595[/C][/ROW]
[ROW][C]16[/C][C]0.003864[/C][C]0.0299[/C][C]0.488111[/C][/ROW]
[ROW][C]17[/C][C]-0.069011[/C][C]-0.5346[/C][C]0.297467[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=71391&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71391&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	0.26824	2.0778	0.021009
2	-0.066079	-0.5118	0.305319
3	0.164042	1.2707	0.104377
4	0.057889	0.4484	0.327738
5	0.074081	0.5738	0.284114
6	-0.174261	-1.3498	0.091072
7	-0.31041	-2.4044	0.009651
8	0.035757	0.277	0.391378
9	-0.072932	-0.5649	0.287113
10	-0.086265	-0.6682	0.253283
11	-0.03032	-0.2349	0.40756
12	-0.089665	-0.6945	0.245011
13	-0.116879	-0.9053	0.184453
14	0.023376	0.1811	0.42846
15	0.09319	0.7218	0.236595
16	0.003864	0.0299	0.488111
17	-0.069011	-0.5346	0.297467

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 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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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Input Parameters & R Code