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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 08 Dec 2007 02:27:32 -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/08/t11971057472dvf0t9iq35deop.htm/, Retrieved Mon, 29 Apr 2024 02:56:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2903, Retrieved Mon, 29 Apr 2024 02:56:58 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

PAF-25dD1

Estimated Impact

250

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

-       [(Partial) Autocorrelation Function] [autocorrelation f...] [2007-12-08 09:27:32] [65108f21b143a71c6470aac06bd65b08] [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=2903&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=2903&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2903&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	7.746	0
1	0.001015	0.0079	0.496877
2	-0.013408	-0.1039	0.541185
3	-0.078645	-0.6092	0.727648
4	-0.13552	-1.0497	0.850975
5	-0.11821	-0.9157	0.818243
6	-0.009563	-0.0741	0.5294
7	0.34008	2.6342	0.005356
8	-0.009248	-0.0716	0.528435
9	-0.025815	-0.2	0.578906
10	-0.092553	-0.7169	0.761895
11	0.106361	0.8239	0.206639
12	-0.127187	-0.9852	0.835756
13	-0.003959	-0.0307	0.512183
14	0.132133	1.0235	0.155091
15	0.03988	0.3089	0.379231
16	-0.121841	-0.9438	0.825466
17	-0.127902	-0.9907	0.8371

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.001015 & 0.0079 & 0.496877 \tabularnewline
2 & -0.013408 & -0.1039 & 0.541185 \tabularnewline
3 & -0.078645 & -0.6092 & 0.727648 \tabularnewline
4 & -0.13552 & -1.0497 & 0.850975 \tabularnewline
5 & -0.11821 & -0.9157 & 0.818243 \tabularnewline
6 & -0.009563 & -0.0741 & 0.5294 \tabularnewline
7 & 0.34008 & 2.6342 & 0.005356 \tabularnewline
8 & -0.009248 & -0.0716 & 0.528435 \tabularnewline
9 & -0.025815 & -0.2 & 0.578906 \tabularnewline
10 & -0.092553 & -0.7169 & 0.761895 \tabularnewline
11 & 0.106361 & 0.8239 & 0.206639 \tabularnewline
12 & -0.127187 & -0.9852 & 0.835756 \tabularnewline
13 & -0.003959 & -0.0307 & 0.512183 \tabularnewline
14 & 0.132133 & 1.0235 & 0.155091 \tabularnewline
15 & 0.03988 & 0.3089 & 0.379231 \tabularnewline
16 & -0.121841 & -0.9438 & 0.825466 \tabularnewline
17 & -0.127902 & -0.9907 & 0.8371 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2903&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.001015[/C][C]0.0079[/C][C]0.496877[/C][/ROW]
[ROW][C]2[/C][C]-0.013408[/C][C]-0.1039[/C][C]0.541185[/C][/ROW]
[ROW][C]3[/C][C]-0.078645[/C][C]-0.6092[/C][C]0.727648[/C][/ROW]
[ROW][C]4[/C][C]-0.13552[/C][C]-1.0497[/C][C]0.850975[/C][/ROW]
[ROW][C]5[/C][C]-0.11821[/C][C]-0.9157[/C][C]0.818243[/C][/ROW]
[ROW][C]6[/C][C]-0.009563[/C][C]-0.0741[/C][C]0.5294[/C][/ROW]
[ROW][C]7[/C][C]0.34008[/C][C]2.6342[/C][C]0.005356[/C][/ROW]
[ROW][C]8[/C][C]-0.009248[/C][C]-0.0716[/C][C]0.528435[/C][/ROW]
[ROW][C]9[/C][C]-0.025815[/C][C]-0.2[/C][C]0.578906[/C][/ROW]
[ROW][C]10[/C][C]-0.092553[/C][C]-0.7169[/C][C]0.761895[/C][/ROW]
[ROW][C]11[/C][C]0.106361[/C][C]0.8239[/C][C]0.206639[/C][/ROW]
[ROW][C]12[/C][C]-0.127187[/C][C]-0.9852[/C][C]0.835756[/C][/ROW]
[ROW][C]13[/C][C]-0.003959[/C][C]-0.0307[/C][C]0.512183[/C][/ROW]
[ROW][C]14[/C][C]0.132133[/C][C]1.0235[/C][C]0.155091[/C][/ROW]
[ROW][C]15[/C][C]0.03988[/C][C]0.3089[/C][C]0.379231[/C][/ROW]
[ROW][C]16[/C][C]-0.121841[/C][C]-0.9438[/C][C]0.825466[/C][/ROW]
[ROW][C]17[/C][C]-0.127902[/C][C]-0.9907[/C][C]0.8371[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2903&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2903&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	7.746	0
1	0.001015	0.0079	0.496877
2	-0.013408	-0.1039	0.541185
3	-0.078645	-0.6092	0.727648
4	-0.13552	-1.0497	0.850975
5	-0.11821	-0.9157	0.818243
6	-0.009563	-0.0741	0.5294
7	0.34008	2.6342	0.005356
8	-0.009248	-0.0716	0.528435
9	-0.025815	-0.2	0.578906
10	-0.092553	-0.7169	0.761895
11	0.106361	0.8239	0.206639
12	-0.127187	-0.9852	0.835756
13	-0.003959	-0.0307	0.512183
14	0.132133	1.0235	0.155091
15	0.03988	0.3089	0.379231
16	-0.121841	-0.9438	0.825466
17	-0.127902	-0.9907	0.8371

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.001015	0.0079	0.496877
1	-0.013409	-0.1039	0.541188
2	-0.078632	-0.6091	0.727614
3	-0.13649	-1.0572	0.852681
4	-0.124882	-0.9673	0.831369
5	-0.025301	-0.196	0.577357
6	0.325948	2.5248	0.007119
7	-0.035723	-0.2767	0.608521
8	-0.066264	-0.5133	0.695179
9	-0.083597	-0.6475	0.740124
10	0.216548	1.6774	0.049336
11	-0.062842	-0.4868	0.685902
12	-0.0365	-0.2827	0.610822
13	-0.001859	-0.0144	0.50572
14	0.101404	0.7855	0.217634
15	-0.115795	-0.8969	0.813334
16	-0.126606	-0.9807	0.834657
17	-0.178595	-1.3834	0.914165

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.001015 & 0.0079 & 0.496877 \tabularnewline
1 & -0.013409 & -0.1039 & 0.541188 \tabularnewline
2 & -0.078632 & -0.6091 & 0.727614 \tabularnewline
3 & -0.13649 & -1.0572 & 0.852681 \tabularnewline
4 & -0.124882 & -0.9673 & 0.831369 \tabularnewline
5 & -0.025301 & -0.196 & 0.577357 \tabularnewline
6 & 0.325948 & 2.5248 & 0.007119 \tabularnewline
7 & -0.035723 & -0.2767 & 0.608521 \tabularnewline
8 & -0.066264 & -0.5133 & 0.695179 \tabularnewline
9 & -0.083597 & -0.6475 & 0.740124 \tabularnewline
10 & 0.216548 & 1.6774 & 0.049336 \tabularnewline
11 & -0.062842 & -0.4868 & 0.685902 \tabularnewline
12 & -0.0365 & -0.2827 & 0.610822 \tabularnewline
13 & -0.001859 & -0.0144 & 0.50572 \tabularnewline
14 & 0.101404 & 0.7855 & 0.217634 \tabularnewline
15 & -0.115795 & -0.8969 & 0.813334 \tabularnewline
16 & -0.126606 & -0.9807 & 0.834657 \tabularnewline
17 & -0.178595 & -1.3834 & 0.914165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2903&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]0.001015[/C][C]0.0079[/C][C]0.496877[/C][/ROW]
[ROW][C]1[/C][C]-0.013409[/C][C]-0.1039[/C][C]0.541188[/C][/ROW]
[ROW][C]2[/C][C]-0.078632[/C][C]-0.6091[/C][C]0.727614[/C][/ROW]
[ROW][C]3[/C][C]-0.13649[/C][C]-1.0572[/C][C]0.852681[/C][/ROW]
[ROW][C]4[/C][C]-0.124882[/C][C]-0.9673[/C][C]0.831369[/C][/ROW]
[ROW][C]5[/C][C]-0.025301[/C][C]-0.196[/C][C]0.577357[/C][/ROW]
[ROW][C]6[/C][C]0.325948[/C][C]2.5248[/C][C]0.007119[/C][/ROW]
[ROW][C]7[/C][C]-0.035723[/C][C]-0.2767[/C][C]0.608521[/C][/ROW]
[ROW][C]8[/C][C]-0.066264[/C][C]-0.5133[/C][C]0.695179[/C][/ROW]
[ROW][C]9[/C][C]-0.083597[/C][C]-0.6475[/C][C]0.740124[/C][/ROW]
[ROW][C]10[/C][C]0.216548[/C][C]1.6774[/C][C]0.049336[/C][/ROW]
[ROW][C]11[/C][C]-0.062842[/C][C]-0.4868[/C][C]0.685902[/C][/ROW]
[ROW][C]12[/C][C]-0.0365[/C][C]-0.2827[/C][C]0.610822[/C][/ROW]
[ROW][C]13[/C][C]-0.001859[/C][C]-0.0144[/C][C]0.50572[/C][/ROW]
[ROW][C]14[/C][C]0.101404[/C][C]0.7855[/C][C]0.217634[/C][/ROW]
[ROW][C]15[/C][C]-0.115795[/C][C]-0.8969[/C][C]0.813334[/C][/ROW]
[ROW][C]16[/C][C]-0.126606[/C][C]-0.9807[/C][C]0.834657[/C][/ROW]
[ROW][C]17[/C][C]-0.178595[/C][C]-1.3834[/C][C]0.914165[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2903&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2903&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	0.001015	0.0079	0.496877
1	-0.013409	-0.1039	0.541188
2	-0.078632	-0.6091	0.727614
3	-0.13649	-1.0572	0.852681
4	-0.124882	-0.9673	0.831369
5	-0.025301	-0.196	0.577357
6	0.325948	2.5248	0.007119
7	-0.035723	-0.2767	0.608521
8	-0.066264	-0.5133	0.695179
9	-0.083597	-0.6475	0.740124
10	0.216548	1.6774	0.049336
11	-0.062842	-0.4868	0.685902
12	-0.0365	-0.2827	0.610822
13	-0.001859	-0.0144	0.50572
14	0.101404	0.7855	0.217634
15	-0.115795	-0.8969	0.813334
16	-0.126606	-0.9807	0.834657
17	-0.178595	-1.3834	0.914165

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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