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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 17 Dec 2007 11:51:05 -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/17/t1197916469wnxmneih1o8fe5j.htm/, Retrieved Fri, 03 May 2024 20:25:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4404, Retrieved Fri, 03 May 2024 20:25:49 +0000

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User-defined keywords

Personenwagens

Estimated Impact

176

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-       [(Partial) Autocorrelation Function] [Paper XVI AcorF] [2007-12-17 18:51:05] [fd802f308f037a9692de8c23f8b60e49] [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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4404&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]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=4404&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4404&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	9.3274	0
1	0.146654	1.3679	0.087434
2	0.175541	1.6373	0.052586
3	0.113077	1.0547	0.147238
4	0.101238	0.9443	0.17382
5	0.008213	0.0766	0.469557
6	0.010287	0.096	0.46189
7	-0.19165	-1.7876	0.961338
8	-0.094493	-0.8814	0.809727
9	-0.040796	-0.3805	0.647757
10	-0.237791	-2.218	0.985419
11	-0.09284	-0.866	0.805552
12	-0.173439	-1.6177	0.94533
13	-0.206573	-1.9268	0.971365
14	-0.055719	-0.5197	0.697707
15	-0.01901	-0.1773	0.570162
16	-0.176724	-1.6484	0.948558
17	0.040483	0.3776	0.353323
18	-0.035483	-0.331	0.629267

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.3274 & 0 \tabularnewline
1 & 0.146654 & 1.3679 & 0.087434 \tabularnewline
2 & 0.175541 & 1.6373 & 0.052586 \tabularnewline
3 & 0.113077 & 1.0547 & 0.147238 \tabularnewline
4 & 0.101238 & 0.9443 & 0.17382 \tabularnewline
5 & 0.008213 & 0.0766 & 0.469557 \tabularnewline
6 & 0.010287 & 0.096 & 0.46189 \tabularnewline
7 & -0.19165 & -1.7876 & 0.961338 \tabularnewline
8 & -0.094493 & -0.8814 & 0.809727 \tabularnewline
9 & -0.040796 & -0.3805 & 0.647757 \tabularnewline
10 & -0.237791 & -2.218 & 0.985419 \tabularnewline
11 & -0.09284 & -0.866 & 0.805552 \tabularnewline
12 & -0.173439 & -1.6177 & 0.94533 \tabularnewline
13 & -0.206573 & -1.9268 & 0.971365 \tabularnewline
14 & -0.055719 & -0.5197 & 0.697707 \tabularnewline
15 & -0.01901 & -0.1773 & 0.570162 \tabularnewline
16 & -0.176724 & -1.6484 & 0.948558 \tabularnewline
17 & 0.040483 & 0.3776 & 0.353323 \tabularnewline
18 & -0.035483 & -0.331 & 0.629267 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4404&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]9.3274[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.146654[/C][C]1.3679[/C][C]0.087434[/C][/ROW]
[ROW][C]2[/C][C]0.175541[/C][C]1.6373[/C][C]0.052586[/C][/ROW]
[ROW][C]3[/C][C]0.113077[/C][C]1.0547[/C][C]0.147238[/C][/ROW]
[ROW][C]4[/C][C]0.101238[/C][C]0.9443[/C][C]0.17382[/C][/ROW]
[ROW][C]5[/C][C]0.008213[/C][C]0.0766[/C][C]0.469557[/C][/ROW]
[ROW][C]6[/C][C]0.010287[/C][C]0.096[/C][C]0.46189[/C][/ROW]
[ROW][C]7[/C][C]-0.19165[/C][C]-1.7876[/C][C]0.961338[/C][/ROW]
[ROW][C]8[/C][C]-0.094493[/C][C]-0.8814[/C][C]0.809727[/C][/ROW]
[ROW][C]9[/C][C]-0.040796[/C][C]-0.3805[/C][C]0.647757[/C][/ROW]
[ROW][C]10[/C][C]-0.237791[/C][C]-2.218[/C][C]0.985419[/C][/ROW]
[ROW][C]11[/C][C]-0.09284[/C][C]-0.866[/C][C]0.805552[/C][/ROW]
[ROW][C]12[/C][C]-0.173439[/C][C]-1.6177[/C][C]0.94533[/C][/ROW]
[ROW][C]13[/C][C]-0.206573[/C][C]-1.9268[/C][C]0.971365[/C][/ROW]
[ROW][C]14[/C][C]-0.055719[/C][C]-0.5197[/C][C]0.697707[/C][/ROW]
[ROW][C]15[/C][C]-0.01901[/C][C]-0.1773[/C][C]0.570162[/C][/ROW]
[ROW][C]16[/C][C]-0.176724[/C][C]-1.6484[/C][C]0.948558[/C][/ROW]
[ROW][C]17[/C][C]0.040483[/C][C]0.3776[/C][C]0.353323[/C][/ROW]
[ROW][C]18[/C][C]-0.035483[/C][C]-0.331[/C][C]0.629267[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4404&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4404&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	9.3274	0
1	0.146654	1.3679	0.087434
2	0.175541	1.6373	0.052586
3	0.113077	1.0547	0.147238
4	0.101238	0.9443	0.17382
5	0.008213	0.0766	0.469557
6	0.010287	0.096	0.46189
7	-0.19165	-1.7876	0.961338
8	-0.094493	-0.8814	0.809727
9	-0.040796	-0.3805	0.647757
10	-0.237791	-2.218	0.985419
11	-0.09284	-0.866	0.805552
12	-0.173439	-1.6177	0.94533
13	-0.206573	-1.9268	0.971365
14	-0.055719	-0.5197	0.697707
15	-0.01901	-0.1773	0.570162
16	-0.176724	-1.6484	0.948558
17	0.040483	0.3776	0.353323
18	-0.035483	-0.331	0.629267

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.146654	1.3679	0.087434
1	0.157419	1.4683	0.072814
2	0.071575	0.6676	0.253077
3	0.054734	0.5105	0.30549
4	-0.040309	-0.376	0.646075
5	-0.018634	-0.1738	0.568788
6	-0.210484	-1.9633	0.973595
7	-0.058837	-0.5488	0.707725
8	0.040014	0.3732	0.354943
9	-0.196959	-1.8371	0.965196
10	-0.001023	-0.0095	0.503796
11	-0.105789	-0.9867	0.836745
12	-0.152709	-1.4244	0.921042
13	0.023927	0.2232	0.41196
14	0.027798	0.2593	0.398015
15	-0.14996	-1.3987	0.917277
16	0.028972	0.2702	0.39381
17	-0.048891	-0.456	0.675245
18	-0.089232	-0.8323	0.796241

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.146654 & 1.3679 & 0.087434 \tabularnewline
1 & 0.157419 & 1.4683 & 0.072814 \tabularnewline
2 & 0.071575 & 0.6676 & 0.253077 \tabularnewline
3 & 0.054734 & 0.5105 & 0.30549 \tabularnewline
4 & -0.040309 & -0.376 & 0.646075 \tabularnewline
5 & -0.018634 & -0.1738 & 0.568788 \tabularnewline
6 & -0.210484 & -1.9633 & 0.973595 \tabularnewline
7 & -0.058837 & -0.5488 & 0.707725 \tabularnewline
8 & 0.040014 & 0.3732 & 0.354943 \tabularnewline
9 & -0.196959 & -1.8371 & 0.965196 \tabularnewline
10 & -0.001023 & -0.0095 & 0.503796 \tabularnewline
11 & -0.105789 & -0.9867 & 0.836745 \tabularnewline
12 & -0.152709 & -1.4244 & 0.921042 \tabularnewline
13 & 0.023927 & 0.2232 & 0.41196 \tabularnewline
14 & 0.027798 & 0.2593 & 0.398015 \tabularnewline
15 & -0.14996 & -1.3987 & 0.917277 \tabularnewline
16 & 0.028972 & 0.2702 & 0.39381 \tabularnewline
17 & -0.048891 & -0.456 & 0.675245 \tabularnewline
18 & -0.089232 & -0.8323 & 0.796241 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4404&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]0.146654[/C][C]1.3679[/C][C]0.087434[/C][/ROW]
[ROW][C]1[/C][C]0.157419[/C][C]1.4683[/C][C]0.072814[/C][/ROW]
[ROW][C]2[/C][C]0.071575[/C][C]0.6676[/C][C]0.253077[/C][/ROW]
[ROW][C]3[/C][C]0.054734[/C][C]0.5105[/C][C]0.30549[/C][/ROW]
[ROW][C]4[/C][C]-0.040309[/C][C]-0.376[/C][C]0.646075[/C][/ROW]
[ROW][C]5[/C][C]-0.018634[/C][C]-0.1738[/C][C]0.568788[/C][/ROW]
[ROW][C]6[/C][C]-0.210484[/C][C]-1.9633[/C][C]0.973595[/C][/ROW]
[ROW][C]7[/C][C]-0.058837[/C][C]-0.5488[/C][C]0.707725[/C][/ROW]
[ROW][C]8[/C][C]0.040014[/C][C]0.3732[/C][C]0.354943[/C][/ROW]
[ROW][C]9[/C][C]-0.196959[/C][C]-1.8371[/C][C]0.965196[/C][/ROW]
[ROW][C]10[/C][C]-0.001023[/C][C]-0.0095[/C][C]0.503796[/C][/ROW]
[ROW][C]11[/C][C]-0.105789[/C][C]-0.9867[/C][C]0.836745[/C][/ROW]
[ROW][C]12[/C][C]-0.152709[/C][C]-1.4244[/C][C]0.921042[/C][/ROW]
[ROW][C]13[/C][C]0.023927[/C][C]0.2232[/C][C]0.41196[/C][/ROW]
[ROW][C]14[/C][C]0.027798[/C][C]0.2593[/C][C]0.398015[/C][/ROW]
[ROW][C]15[/C][C]-0.14996[/C][C]-1.3987[/C][C]0.917277[/C][/ROW]
[ROW][C]16[/C][C]0.028972[/C][C]0.2702[/C][C]0.39381[/C][/ROW]
[ROW][C]17[/C][C]-0.048891[/C][C]-0.456[/C][C]0.675245[/C][/ROW]
[ROW][C]18[/C][C]-0.089232[/C][C]-0.8323[/C][C]0.796241[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4404&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4404&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	0.146654	1.3679	0.087434
1	0.157419	1.4683	0.072814
2	0.071575	0.6676	0.253077
3	0.054734	0.5105	0.30549
4	-0.040309	-0.376	0.646075
5	-0.018634	-0.1738	0.568788
6	-0.210484	-1.9633	0.973595
7	-0.058837	-0.5488	0.707725
8	0.040014	0.3732	0.354943
9	-0.196959	-1.8371	0.965196
10	-0.001023	-0.0095	0.503796
11	-0.105789	-0.9867	0.836745
12	-0.152709	-1.4244	0.921042
13	0.023927	0.2232	0.41196
14	0.027798	0.2593	0.398015
15	-0.14996	-1.3987	0.917277
16	0.028972	0.2702	0.39381
17	-0.048891	-0.456	0.675245
18	-0.089232	-0.8323	0.796241

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -1.7 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = -1.7 ; par3 = 0 ; par4 = 1 ; 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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