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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 06 Dec 2007 07:49:30 -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/06/t1196951793t9mh4j0v3757uqs.htm/, Retrieved Fri, 03 May 2024 05:57:18 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2638, Retrieved Fri, 03 May 2024 05:57:18 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

192

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

-       [(Partial) Autocorrelation Function] [WS4: Q2 Invoer] [2007-12-06 14:49:30] [9b75aacdafaeee3fe66fbd4de075ccd6] [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=2638&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=2638&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2638&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	6.8557	0
1	-0.523114	-3.5863	0.999602
2	0.224162	1.5368	0.065526
3	0.070876	0.4859	0.314648
4	-0.260227	-1.784	0.959562
5	0.07046	0.483	0.315653
6	0.054815	0.3758	0.354381
7	-0.030763	-0.2109	0.583061
8	0.226136	1.5503	0.063888
9	-0.199125	-1.3651	0.910644
10	0.002019	0.0138	0.494508
11	-0.043552	-0.2986	0.616711
12	-0.275459	-1.8884	0.967427
13	0.20122	1.3795	0.087136
14	-0.17682	-1.2122	0.884256
15	0.212308	1.4555	0.076087
16	-0.143069	-0.9808	0.834151

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.8557 & 0 \tabularnewline
1 & -0.523114 & -3.5863 & 0.999602 \tabularnewline
2 & 0.224162 & 1.5368 & 0.065526 \tabularnewline
3 & 0.070876 & 0.4859 & 0.314648 \tabularnewline
4 & -0.260227 & -1.784 & 0.959562 \tabularnewline
5 & 0.07046 & 0.483 & 0.315653 \tabularnewline
6 & 0.054815 & 0.3758 & 0.354381 \tabularnewline
7 & -0.030763 & -0.2109 & 0.583061 \tabularnewline
8 & 0.226136 & 1.5503 & 0.063888 \tabularnewline
9 & -0.199125 & -1.3651 & 0.910644 \tabularnewline
10 & 0.002019 & 0.0138 & 0.494508 \tabularnewline
11 & -0.043552 & -0.2986 & 0.616711 \tabularnewline
12 & -0.275459 & -1.8884 & 0.967427 \tabularnewline
13 & 0.20122 & 1.3795 & 0.087136 \tabularnewline
14 & -0.17682 & -1.2122 & 0.884256 \tabularnewline
15 & 0.212308 & 1.4555 & 0.076087 \tabularnewline
16 & -0.143069 & -0.9808 & 0.834151 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2638&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]6.8557[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.523114[/C][C]-3.5863[/C][C]0.999602[/C][/ROW]
[ROW][C]2[/C][C]0.224162[/C][C]1.5368[/C][C]0.065526[/C][/ROW]
[ROW][C]3[/C][C]0.070876[/C][C]0.4859[/C][C]0.314648[/C][/ROW]
[ROW][C]4[/C][C]-0.260227[/C][C]-1.784[/C][C]0.959562[/C][/ROW]
[ROW][C]5[/C][C]0.07046[/C][C]0.483[/C][C]0.315653[/C][/ROW]
[ROW][C]6[/C][C]0.054815[/C][C]0.3758[/C][C]0.354381[/C][/ROW]
[ROW][C]7[/C][C]-0.030763[/C][C]-0.2109[/C][C]0.583061[/C][/ROW]
[ROW][C]8[/C][C]0.226136[/C][C]1.5503[/C][C]0.063888[/C][/ROW]
[ROW][C]9[/C][C]-0.199125[/C][C]-1.3651[/C][C]0.910644[/C][/ROW]
[ROW][C]10[/C][C]0.002019[/C][C]0.0138[/C][C]0.494508[/C][/ROW]
[ROW][C]11[/C][C]-0.043552[/C][C]-0.2986[/C][C]0.616711[/C][/ROW]
[ROW][C]12[/C][C]-0.275459[/C][C]-1.8884[/C][C]0.967427[/C][/ROW]
[ROW][C]13[/C][C]0.20122[/C][C]1.3795[/C][C]0.087136[/C][/ROW]
[ROW][C]14[/C][C]-0.17682[/C][C]-1.2122[/C][C]0.884256[/C][/ROW]
[ROW][C]15[/C][C]0.212308[/C][C]1.4555[/C][C]0.076087[/C][/ROW]
[ROW][C]16[/C][C]-0.143069[/C][C]-0.9808[/C][C]0.834151[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2638&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2638&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	6.8557	0
1	-0.523114	-3.5863	0.999602
2	0.224162	1.5368	0.065526
3	0.070876	0.4859	0.314648
4	-0.260227	-1.784	0.959562
5	0.07046	0.483	0.315653
6	0.054815	0.3758	0.354381
7	-0.030763	-0.2109	0.583061
8	0.226136	1.5503	0.063888
9	-0.199125	-1.3651	0.910644
10	0.002019	0.0138	0.494508
11	-0.043552	-0.2986	0.616711
12	-0.275459	-1.8884	0.967427
13	0.20122	1.3795	0.087136
14	-0.17682	-1.2122	0.884256
15	0.212308	1.4555	0.076087
16	-0.143069	-0.9808	0.834151

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.523114	-3.5863	0.999602
1	-0.06813	-0.4671	0.678697
2	0.221981	1.5218	0.067377
3	-0.171827	-1.178	0.877634
4	-0.276483	-1.8955	0.967905
5	0.056639	0.3883	0.349773
6	0.217248	1.4894	0.071534
7	0.322648	2.212	0.015933
8	-0.135307	-0.9276	0.820827
9	-0.412609	-2.8287	0.996575
10	-0.216412	-1.4836	0.927711
11	-0.203455	-1.3948	0.915186
12	-0.026256	-0.18	0.571037
13	-0.278847	-1.9117	0.968987
14	-0.024816	-0.1701	0.56718
15	-0.127042	-0.871	0.805896
16	0.031782	0.2179	0.41423

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.523114 & -3.5863 & 0.999602 \tabularnewline
1 & -0.06813 & -0.4671 & 0.678697 \tabularnewline
2 & 0.221981 & 1.5218 & 0.067377 \tabularnewline
3 & -0.171827 & -1.178 & 0.877634 \tabularnewline
4 & -0.276483 & -1.8955 & 0.967905 \tabularnewline
5 & 0.056639 & 0.3883 & 0.349773 \tabularnewline
6 & 0.217248 & 1.4894 & 0.071534 \tabularnewline
7 & 0.322648 & 2.212 & 0.015933 \tabularnewline
8 & -0.135307 & -0.9276 & 0.820827 \tabularnewline
9 & -0.412609 & -2.8287 & 0.996575 \tabularnewline
10 & -0.216412 & -1.4836 & 0.927711 \tabularnewline
11 & -0.203455 & -1.3948 & 0.915186 \tabularnewline
12 & -0.026256 & -0.18 & 0.571037 \tabularnewline
13 & -0.278847 & -1.9117 & 0.968987 \tabularnewline
14 & -0.024816 & -0.1701 & 0.56718 \tabularnewline
15 & -0.127042 & -0.871 & 0.805896 \tabularnewline
16 & 0.031782 & 0.2179 & 0.41423 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2638&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]-0.523114[/C][C]-3.5863[/C][C]0.999602[/C][/ROW]
[ROW][C]1[/C][C]-0.06813[/C][C]-0.4671[/C][C]0.678697[/C][/ROW]
[ROW][C]2[/C][C]0.221981[/C][C]1.5218[/C][C]0.067377[/C][/ROW]
[ROW][C]3[/C][C]-0.171827[/C][C]-1.178[/C][C]0.877634[/C][/ROW]
[ROW][C]4[/C][C]-0.276483[/C][C]-1.8955[/C][C]0.967905[/C][/ROW]
[ROW][C]5[/C][C]0.056639[/C][C]0.3883[/C][C]0.349773[/C][/ROW]
[ROW][C]6[/C][C]0.217248[/C][C]1.4894[/C][C]0.071534[/C][/ROW]
[ROW][C]7[/C][C]0.322648[/C][C]2.212[/C][C]0.015933[/C][/ROW]
[ROW][C]8[/C][C]-0.135307[/C][C]-0.9276[/C][C]0.820827[/C][/ROW]
[ROW][C]9[/C][C]-0.412609[/C][C]-2.8287[/C][C]0.996575[/C][/ROW]
[ROW][C]10[/C][C]-0.216412[/C][C]-1.4836[/C][C]0.927711[/C][/ROW]
[ROW][C]11[/C][C]-0.203455[/C][C]-1.3948[/C][C]0.915186[/C][/ROW]
[ROW][C]12[/C][C]-0.026256[/C][C]-0.18[/C][C]0.571037[/C][/ROW]
[ROW][C]13[/C][C]-0.278847[/C][C]-1.9117[/C][C]0.968987[/C][/ROW]
[ROW][C]14[/C][C]-0.024816[/C][C]-0.1701[/C][C]0.56718[/C][/ROW]
[ROW][C]15[/C][C]-0.127042[/C][C]-0.871[/C][C]0.805896[/C][/ROW]
[ROW][C]16[/C][C]0.031782[/C][C]0.2179[/C][C]0.41423[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2638&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2638&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	-0.523114	-3.5863	0.999602
1	-0.06813	-0.4671	0.678697
2	0.221981	1.5218	0.067377
3	-0.171827	-1.178	0.877634
4	-0.276483	-1.8955	0.967905
5	0.056639	0.3883	0.349773
6	0.217248	1.4894	0.071534
7	0.322648	2.212	0.015933
8	-0.135307	-0.9276	0.820827
9	-0.412609	-2.8287	0.996575
10	-0.216412	-1.4836	0.927711
11	-0.203455	-1.3948	0.915186
12	-0.026256	-0.18	0.571037
13	-0.278847	-1.9117	0.968987
14	-0.024816	-0.1701	0.56718
15	-0.127042	-0.871	0.805896
16	0.031782	0.2179	0.41423

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 = 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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Input Parameters & R Code