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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 28 Nov 2009 03:01:54 -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/Nov/28/t12594026223s26xpmhgsvc3o6.htm/, Retrieved Fri, 03 May 2024 08:01:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61398, Retrieved Fri, 03 May 2024 08:01:23 +0000

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No (this computation is public)

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Estimated Impact

124

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

-       [(Partial) Autocorrelation Function] [Autocorrelatie fu...] [2009-11-28 10:01:54] [762da55b2e2304daaed24a7cc507d14d] [Current]
-   P     [(Partial) Autocorrelation Function] [verbetering 3] [2009-11-30 18:47:20] [42ad1186d39724f834063794eac7cea3] 

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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=61398&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=61398&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61398&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	0.908388	6.2935	0
2	0.809623	5.6092	0
3	0.707154	4.8993	6e-06
4	0.593914	4.1148	7.6e-05
5	0.470108	3.257	0.001035
6	0.364011	2.5219	0.007521
7	0.266105	1.8436	0.035708
8	0.181348	1.2564	0.107523
9	0.096648	0.6696	0.253161
10	0.023484	0.1627	0.435718
11	-0.041148	-0.2851	0.388404
12	-0.113498	-0.7863	0.217768
13	-0.185492	-1.2851	0.102458
14	-0.261458	-1.8114	0.038167
15	-0.30784	-2.1328	0.019042
16	-0.362694	-2.5128	0.007695
17	-0.405188	-2.8072	0.003601

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.908388 & 6.2935 & 0 \tabularnewline
2 & 0.809623 & 5.6092 & 0 \tabularnewline
3 & 0.707154 & 4.8993 & 6e-06 \tabularnewline
4 & 0.593914 & 4.1148 & 7.6e-05 \tabularnewline
5 & 0.470108 & 3.257 & 0.001035 \tabularnewline
6 & 0.364011 & 2.5219 & 0.007521 \tabularnewline
7 & 0.266105 & 1.8436 & 0.035708 \tabularnewline
8 & 0.181348 & 1.2564 & 0.107523 \tabularnewline
9 & 0.096648 & 0.6696 & 0.253161 \tabularnewline
10 & 0.023484 & 0.1627 & 0.435718 \tabularnewline
11 & -0.041148 & -0.2851 & 0.388404 \tabularnewline
12 & -0.113498 & -0.7863 & 0.217768 \tabularnewline
13 & -0.185492 & -1.2851 & 0.102458 \tabularnewline
14 & -0.261458 & -1.8114 & 0.038167 \tabularnewline
15 & -0.30784 & -2.1328 & 0.019042 \tabularnewline
16 & -0.362694 & -2.5128 & 0.007695 \tabularnewline
17 & -0.405188 & -2.8072 & 0.003601 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61398&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]0.908388[/C][C]6.2935[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.809623[/C][C]5.6092[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.707154[/C][C]4.8993[/C][C]6e-06[/C][/ROW]
[ROW][C]4[/C][C]0.593914[/C][C]4.1148[/C][C]7.6e-05[/C][/ROW]
[ROW][C]5[/C][C]0.470108[/C][C]3.257[/C][C]0.001035[/C][/ROW]
[ROW][C]6[/C][C]0.364011[/C][C]2.5219[/C][C]0.007521[/C][/ROW]
[ROW][C]7[/C][C]0.266105[/C][C]1.8436[/C][C]0.035708[/C][/ROW]
[ROW][C]8[/C][C]0.181348[/C][C]1.2564[/C][C]0.107523[/C][/ROW]
[ROW][C]9[/C][C]0.096648[/C][C]0.6696[/C][C]0.253161[/C][/ROW]
[ROW][C]10[/C][C]0.023484[/C][C]0.1627[/C][C]0.435718[/C][/ROW]
[ROW][C]11[/C][C]-0.041148[/C][C]-0.2851[/C][C]0.388404[/C][/ROW]
[ROW][C]12[/C][C]-0.113498[/C][C]-0.7863[/C][C]0.217768[/C][/ROW]
[ROW][C]13[/C][C]-0.185492[/C][C]-1.2851[/C][C]0.102458[/C][/ROW]
[ROW][C]14[/C][C]-0.261458[/C][C]-1.8114[/C][C]0.038167[/C][/ROW]
[ROW][C]15[/C][C]-0.30784[/C][C]-2.1328[/C][C]0.019042[/C][/ROW]
[ROW][C]16[/C][C]-0.362694[/C][C]-2.5128[/C][C]0.007695[/C][/ROW]
[ROW][C]17[/C][C]-0.405188[/C][C]-2.8072[/C][C]0.003601[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61398&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61398&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	0.908388	6.2935	0
2	0.809623	5.6092	0
3	0.707154	4.8993	6e-06
4	0.593914	4.1148	7.6e-05
5	0.470108	3.257	0.001035
6	0.364011	2.5219	0.007521
7	0.266105	1.8436	0.035708
8	0.181348	1.2564	0.107523
9	0.096648	0.6696	0.253161
10	0.023484	0.1627	0.435718
11	-0.041148	-0.2851	0.388404
12	-0.113498	-0.7863	0.217768
13	-0.185492	-1.2851	0.102458
14	-0.261458	-1.8114	0.038167
15	-0.30784	-2.1328	0.019042
16	-0.362694	-2.5128	0.007695
17	-0.405188	-2.8072	0.003601

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.908388	6.2935	0
2	-0.088925	-0.6161	0.270373
3	-0.074486	-0.5161	0.304094
4	-0.121109	-0.8391	0.202795
5	-0.129532	-0.8974	0.186986
6	0.024931	0.1727	0.431796
7	-0.030029	-0.208	0.418037
8	0.002253	0.0156	0.493804
9	-0.086328	-0.5981	0.276294
10	-0.029361	-0.2034	0.419833
11	-0.033369	-0.2312	0.409077
12	-0.1269	-0.8792	0.19184
13	-0.075819	-0.5253	0.3009
14	-0.12892	-0.8932	0.188108
15	0.090534	0.6272	0.266738
16	-0.135265	-0.9371	0.176688
17	-0.020014	-0.1387	0.445149

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.908388 & 6.2935 & 0 \tabularnewline
2 & -0.088925 & -0.6161 & 0.270373 \tabularnewline
3 & -0.074486 & -0.5161 & 0.304094 \tabularnewline
4 & -0.121109 & -0.8391 & 0.202795 \tabularnewline
5 & -0.129532 & -0.8974 & 0.186986 \tabularnewline
6 & 0.024931 & 0.1727 & 0.431796 \tabularnewline
7 & -0.030029 & -0.208 & 0.418037 \tabularnewline
8 & 0.002253 & 0.0156 & 0.493804 \tabularnewline
9 & -0.086328 & -0.5981 & 0.276294 \tabularnewline
10 & -0.029361 & -0.2034 & 0.419833 \tabularnewline
11 & -0.033369 & -0.2312 & 0.409077 \tabularnewline
12 & -0.1269 & -0.8792 & 0.19184 \tabularnewline
13 & -0.075819 & -0.5253 & 0.3009 \tabularnewline
14 & -0.12892 & -0.8932 & 0.188108 \tabularnewline
15 & 0.090534 & 0.6272 & 0.266738 \tabularnewline
16 & -0.135265 & -0.9371 & 0.176688 \tabularnewline
17 & -0.020014 & -0.1387 & 0.445149 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61398&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]0.908388[/C][C]6.2935[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.088925[/C][C]-0.6161[/C][C]0.270373[/C][/ROW]
[ROW][C]3[/C][C]-0.074486[/C][C]-0.5161[/C][C]0.304094[/C][/ROW]
[ROW][C]4[/C][C]-0.121109[/C][C]-0.8391[/C][C]0.202795[/C][/ROW]
[ROW][C]5[/C][C]-0.129532[/C][C]-0.8974[/C][C]0.186986[/C][/ROW]
[ROW][C]6[/C][C]0.024931[/C][C]0.1727[/C][C]0.431796[/C][/ROW]
[ROW][C]7[/C][C]-0.030029[/C][C]-0.208[/C][C]0.418037[/C][/ROW]
[ROW][C]8[/C][C]0.002253[/C][C]0.0156[/C][C]0.493804[/C][/ROW]
[ROW][C]9[/C][C]-0.086328[/C][C]-0.5981[/C][C]0.276294[/C][/ROW]
[ROW][C]10[/C][C]-0.029361[/C][C]-0.2034[/C][C]0.419833[/C][/ROW]
[ROW][C]11[/C][C]-0.033369[/C][C]-0.2312[/C][C]0.409077[/C][/ROW]
[ROW][C]12[/C][C]-0.1269[/C][C]-0.8792[/C][C]0.19184[/C][/ROW]
[ROW][C]13[/C][C]-0.075819[/C][C]-0.5253[/C][C]0.3009[/C][/ROW]
[ROW][C]14[/C][C]-0.12892[/C][C]-0.8932[/C][C]0.188108[/C][/ROW]
[ROW][C]15[/C][C]0.090534[/C][C]0.6272[/C][C]0.266738[/C][/ROW]
[ROW][C]16[/C][C]-0.135265[/C][C]-0.9371[/C][C]0.176688[/C][/ROW]
[ROW][C]17[/C][C]-0.020014[/C][C]-0.1387[/C][C]0.445149[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61398&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61398&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	0.908388	6.2935	0
2	-0.088925	-0.6161	0.270373
3	-0.074486	-0.5161	0.304094
4	-0.121109	-0.8391	0.202795
5	-0.129532	-0.8974	0.186986
6	0.024931	0.1727	0.431796
7	-0.030029	-0.208	0.418037
8	0.002253	0.0156	0.493804
9	-0.086328	-0.5981	0.276294
10	-0.029361	-0.2034	0.419833
11	-0.033369	-0.2312	0.409077
12	-0.1269	-0.8792	0.19184
13	-0.075819	-0.5253	0.3009
14	-0.12892	-0.8932	0.188108
15	0.090534	0.6272	0.266738
16	-0.135265	-0.9371	0.176688
17	-0.020014	-0.1387	0.445149

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code