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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 04 Dec 2009 07:07:17 -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/04/t12599356869osll0yn4f844u1.htm/, Retrieved Sun, 28 Apr 2024 17:46:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63555, Retrieved Sun, 28 Apr 2024 17:46:20 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

104

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [] [2009-11-27 14:40:44] [b98453cac15ba1066b407e146608df68]
F RMPD      [(Partial) Autocorrelation Function] [ws9 1] [2009-12-04 14:07:17] [84778c3520b84fd5786bccf2e25a5aef] [Current]

Feedback Forum

2009-12-10 16:51:04 [Brecht Thijs] [reply] 
De opdracht moet starten met het inschatten van de lambda 
waarde. Dit doe je door middel van de Standard Deviation Mean Plo 
SMP: 
http://www.freestatistics.org/blog/index.php?v=date/2009/Dec/10/t1260463665nzm0qe4cy3q1r0t.htm/ 
 
De eerste tabel geeft een p-waarde van 0,72. We nemen de Ho dus aan 
er is geen transformatie nodig en lambda blijft 1.

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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	0 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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63555&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]0 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=63555&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63555&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	0 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.837597	6.5418	0
2	0.673092	5.257	1e-06
3	0.501066	3.9135	0.000116
4	0.363805	2.8414	0.003049
5	0.274226	2.1418	0.018107
6	0.212287	1.658	0.051224
7	0.133986	1.0465	0.149738
8	0.075698	0.5912	0.278278
9	0.082392	0.6435	0.261156
10	0.107076	0.8363	0.203129
11	0.157805	1.2325	0.111246
12	0.177305	1.3848	0.08558
13	0.085601	0.6686	0.253148
14	-0.007776	-0.0607	0.475886
15	-0.112866	-0.8815	0.19075
16	-0.148918	-1.1631	0.124663
17	-0.159735	-1.2476	0.108479

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.837597 & 6.5418 & 0 \tabularnewline
2 & 0.673092 & 5.257 & 1e-06 \tabularnewline
3 & 0.501066 & 3.9135 & 0.000116 \tabularnewline
4 & 0.363805 & 2.8414 & 0.003049 \tabularnewline
5 & 0.274226 & 2.1418 & 0.018107 \tabularnewline
6 & 0.212287 & 1.658 & 0.051224 \tabularnewline
7 & 0.133986 & 1.0465 & 0.149738 \tabularnewline
8 & 0.075698 & 0.5912 & 0.278278 \tabularnewline
9 & 0.082392 & 0.6435 & 0.261156 \tabularnewline
10 & 0.107076 & 0.8363 & 0.203129 \tabularnewline
11 & 0.157805 & 1.2325 & 0.111246 \tabularnewline
12 & 0.177305 & 1.3848 & 0.08558 \tabularnewline
13 & 0.085601 & 0.6686 & 0.253148 \tabularnewline
14 & -0.007776 & -0.0607 & 0.475886 \tabularnewline
15 & -0.112866 & -0.8815 & 0.19075 \tabularnewline
16 & -0.148918 & -1.1631 & 0.124663 \tabularnewline
17 & -0.159735 & -1.2476 & 0.108479 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63555&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]0.837597[/C][C]6.5418[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.673092[/C][C]5.257[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.501066[/C][C]3.9135[/C][C]0.000116[/C][/ROW]
[ROW][C]4[/C][C]0.363805[/C][C]2.8414[/C][C]0.003049[/C][/ROW]
[ROW][C]5[/C][C]0.274226[/C][C]2.1418[/C][C]0.018107[/C][/ROW]
[ROW][C]6[/C][C]0.212287[/C][C]1.658[/C][C]0.051224[/C][/ROW]
[ROW][C]7[/C][C]0.133986[/C][C]1.0465[/C][C]0.149738[/C][/ROW]
[ROW][C]8[/C][C]0.075698[/C][C]0.5912[/C][C]0.278278[/C][/ROW]
[ROW][C]9[/C][C]0.082392[/C][C]0.6435[/C][C]0.261156[/C][/ROW]
[ROW][C]10[/C][C]0.107076[/C][C]0.8363[/C][C]0.203129[/C][/ROW]
[ROW][C]11[/C][C]0.157805[/C][C]1.2325[/C][C]0.111246[/C][/ROW]
[ROW][C]12[/C][C]0.177305[/C][C]1.3848[/C][C]0.08558[/C][/ROW]
[ROW][C]13[/C][C]0.085601[/C][C]0.6686[/C][C]0.253148[/C][/ROW]
[ROW][C]14[/C][C]-0.007776[/C][C]-0.0607[/C][C]0.475886[/C][/ROW]
[ROW][C]15[/C][C]-0.112866[/C][C]-0.8815[/C][C]0.19075[/C][/ROW]
[ROW][C]16[/C][C]-0.148918[/C][C]-1.1631[/C][C]0.124663[/C][/ROW]
[ROW][C]17[/C][C]-0.159735[/C][C]-1.2476[/C][C]0.108479[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63555&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63555&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	0.837597	6.5418	0
2	0.673092	5.257	1e-06
3	0.501066	3.9135	0.000116
4	0.363805	2.8414	0.003049
5	0.274226	2.1418	0.018107
6	0.212287	1.658	0.051224
7	0.133986	1.0465	0.149738
8	0.075698	0.5912	0.278278
9	0.082392	0.6435	0.261156
10	0.107076	0.8363	0.203129
11	0.157805	1.2325	0.111246
12	0.177305	1.3848	0.08558
13	0.085601	0.6686	0.253148
14	-0.007776	-0.0607	0.475886
15	-0.112866	-0.8815	0.19075
16	-0.148918	-1.1631	0.124663
17	-0.159735	-1.2476	0.108479

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.837597	6.5418	0
2	-0.095422	-0.7453	0.229486
3	-0.123719	-0.9663	0.168861
4	0.004908	0.0383	0.484773
5	0.060564	0.473	0.318944
6	0.007364	0.0575	0.47716
7	-0.124267	-0.9706	0.167802
8	0.010399	0.0812	0.467766
9	0.1966	1.5355	0.064917
10	0.04179	0.3264	0.372624
11	0.057021	0.4454	0.328821
12	-0.059895	-0.4678	0.3208
13	-0.323814	-2.5291	0.007019
14	-0.015568	-0.1216	0.451813
15	-0.083271	-0.6504	0.258948
16	0.137436	1.0734	0.143658
17	0.005533	0.0432	0.482837

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.837597 & 6.5418 & 0 \tabularnewline
2 & -0.095422 & -0.7453 & 0.229486 \tabularnewline
3 & -0.123719 & -0.9663 & 0.168861 \tabularnewline
4 & 0.004908 & 0.0383 & 0.484773 \tabularnewline
5 & 0.060564 & 0.473 & 0.318944 \tabularnewline
6 & 0.007364 & 0.0575 & 0.47716 \tabularnewline
7 & -0.124267 & -0.9706 & 0.167802 \tabularnewline
8 & 0.010399 & 0.0812 & 0.467766 \tabularnewline
9 & 0.1966 & 1.5355 & 0.064917 \tabularnewline
10 & 0.04179 & 0.3264 & 0.372624 \tabularnewline
11 & 0.057021 & 0.4454 & 0.328821 \tabularnewline
12 & -0.059895 & -0.4678 & 0.3208 \tabularnewline
13 & -0.323814 & -2.5291 & 0.007019 \tabularnewline
14 & -0.015568 & -0.1216 & 0.451813 \tabularnewline
15 & -0.083271 & -0.6504 & 0.258948 \tabularnewline
16 & 0.137436 & 1.0734 & 0.143658 \tabularnewline
17 & 0.005533 & 0.0432 & 0.482837 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63555&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]0.837597[/C][C]6.5418[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.095422[/C][C]-0.7453[/C][C]0.229486[/C][/ROW]
[ROW][C]3[/C][C]-0.123719[/C][C]-0.9663[/C][C]0.168861[/C][/ROW]
[ROW][C]4[/C][C]0.004908[/C][C]0.0383[/C][C]0.484773[/C][/ROW]
[ROW][C]5[/C][C]0.060564[/C][C]0.473[/C][C]0.318944[/C][/ROW]
[ROW][C]6[/C][C]0.007364[/C][C]0.0575[/C][C]0.47716[/C][/ROW]
[ROW][C]7[/C][C]-0.124267[/C][C]-0.9706[/C][C]0.167802[/C][/ROW]
[ROW][C]8[/C][C]0.010399[/C][C]0.0812[/C][C]0.467766[/C][/ROW]
[ROW][C]9[/C][C]0.1966[/C][C]1.5355[/C][C]0.064917[/C][/ROW]
[ROW][C]10[/C][C]0.04179[/C][C]0.3264[/C][C]0.372624[/C][/ROW]
[ROW][C]11[/C][C]0.057021[/C][C]0.4454[/C][C]0.328821[/C][/ROW]
[ROW][C]12[/C][C]-0.059895[/C][C]-0.4678[/C][C]0.3208[/C][/ROW]
[ROW][C]13[/C][C]-0.323814[/C][C]-2.5291[/C][C]0.007019[/C][/ROW]
[ROW][C]14[/C][C]-0.015568[/C][C]-0.1216[/C][C]0.451813[/C][/ROW]
[ROW][C]15[/C][C]-0.083271[/C][C]-0.6504[/C][C]0.258948[/C][/ROW]
[ROW][C]16[/C][C]0.137436[/C][C]1.0734[/C][C]0.143658[/C][/ROW]
[ROW][C]17[/C][C]0.005533[/C][C]0.0432[/C][C]0.482837[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63555&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63555&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	0.837597	6.5418	0
2	-0.095422	-0.7453	0.229486
3	-0.123719	-0.9663	0.168861
4	0.004908	0.0383	0.484773
5	0.060564	0.473	0.318944
6	0.007364	0.0575	0.47716
7	-0.124267	-0.9706	0.167802
8	0.010399	0.0812	0.467766
9	0.1966	1.5355	0.064917
10	0.04179	0.3264	0.372624
11	0.057021	0.4454	0.328821
12	-0.059895	-0.4678	0.3208
13	-0.323814	-2.5291	0.007019
14	-0.015568	-0.1216	0.451813
15	-0.083271	-0.6504	0.258948
16	0.137436	1.0734	0.143658
17	0.005533	0.0432	0.482837

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; 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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code