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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 04 Dec 2009 12:35:20 -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/t1259955597h1aixsdcu2tefff.htm/, Retrieved Sat, 27 Apr 2024 13:44:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64084, Retrieved Sat, 27 Apr 2024 13:44:47 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

146

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   [(Partial) Autocorrelation Function] [] [2009-11-27 14:47:30] [b98453cac15ba1066b407e146608df68]
- R PD    [(Partial) Autocorrelation Function] [] [2009-12-03 15:49:35] [fa44bc1b850de3469c0e3e9a5981c418]
-   PD        [(Partial) Autocorrelation Function] [autocorrelatie] [2009-12-04 19:35:20] [95bc1f3b1182fbde76c5a24f1f253203] [Current]

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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=64084&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=64084&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64084&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	0.891593	6.9636	0
2	0.811617	6.3389	0
3	0.749489	5.8537	0
4	0.677192	5.289	1e-06
5	0.585023	4.5692	1.2e-05
6	0.50287	3.9275	0.000111
7	0.421532	3.2923	0.000828
8	0.340851	2.6621	0.004957
9	0.253709	1.9815	0.026022
10	0.193053	1.5078	0.068385
11	0.137895	1.077	0.142863
12	0.058103	0.4538	0.325791
13	-0.012414	-0.097	0.461539
14	-0.07236	-0.5652	0.287022
15	-0.086272	-0.6738	0.25149
16	-0.129747	-1.0134	0.157447
17	-0.18768	-1.4658	0.073915

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.891593 & 6.9636 & 0 \tabularnewline
2 & 0.811617 & 6.3389 & 0 \tabularnewline
3 & 0.749489 & 5.8537 & 0 \tabularnewline
4 & 0.677192 & 5.289 & 1e-06 \tabularnewline
5 & 0.585023 & 4.5692 & 1.2e-05 \tabularnewline
6 & 0.50287 & 3.9275 & 0.000111 \tabularnewline
7 & 0.421532 & 3.2923 & 0.000828 \tabularnewline
8 & 0.340851 & 2.6621 & 0.004957 \tabularnewline
9 & 0.253709 & 1.9815 & 0.026022 \tabularnewline
10 & 0.193053 & 1.5078 & 0.068385 \tabularnewline
11 & 0.137895 & 1.077 & 0.142863 \tabularnewline
12 & 0.058103 & 0.4538 & 0.325791 \tabularnewline
13 & -0.012414 & -0.097 & 0.461539 \tabularnewline
14 & -0.07236 & -0.5652 & 0.287022 \tabularnewline
15 & -0.086272 & -0.6738 & 0.25149 \tabularnewline
16 & -0.129747 & -1.0134 & 0.157447 \tabularnewline
17 & -0.18768 & -1.4658 & 0.073915 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64084&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]0.891593[/C][C]6.9636[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.811617[/C][C]6.3389[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.749489[/C][C]5.8537[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.677192[/C][C]5.289[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.585023[/C][C]4.5692[/C][C]1.2e-05[/C][/ROW]
[ROW][C]6[/C][C]0.50287[/C][C]3.9275[/C][C]0.000111[/C][/ROW]
[ROW][C]7[/C][C]0.421532[/C][C]3.2923[/C][C]0.000828[/C][/ROW]
[ROW][C]8[/C][C]0.340851[/C][C]2.6621[/C][C]0.004957[/C][/ROW]
[ROW][C]9[/C][C]0.253709[/C][C]1.9815[/C][C]0.026022[/C][/ROW]
[ROW][C]10[/C][C]0.193053[/C][C]1.5078[/C][C]0.068385[/C][/ROW]
[ROW][C]11[/C][C]0.137895[/C][C]1.077[/C][C]0.142863[/C][/ROW]
[ROW][C]12[/C][C]0.058103[/C][C]0.4538[/C][C]0.325791[/C][/ROW]
[ROW][C]13[/C][C]-0.012414[/C][C]-0.097[/C][C]0.461539[/C][/ROW]
[ROW][C]14[/C][C]-0.07236[/C][C]-0.5652[/C][C]0.287022[/C][/ROW]
[ROW][C]15[/C][C]-0.086272[/C][C]-0.6738[/C][C]0.25149[/C][/ROW]
[ROW][C]16[/C][C]-0.129747[/C][C]-1.0134[/C][C]0.157447[/C][/ROW]
[ROW][C]17[/C][C]-0.18768[/C][C]-1.4658[/C][C]0.073915[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64084&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64084&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	0.891593	6.9636	0
2	0.811617	6.3389	0
3	0.749489	5.8537	0
4	0.677192	5.289	1e-06
5	0.585023	4.5692	1.2e-05
6	0.50287	3.9275	0.000111
7	0.421532	3.2923	0.000828
8	0.340851	2.6621	0.004957
9	0.253709	1.9815	0.026022
10	0.193053	1.5078	0.068385
11	0.137895	1.077	0.142863
12	0.058103	0.4538	0.325791
13	-0.012414	-0.097	0.461539
14	-0.07236	-0.5652	0.287022
15	-0.086272	-0.6738	0.25149
16	-0.129747	-1.0134	0.157447
17	-0.18768	-1.4658	0.073915

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.891593	6.9636	0
2	0.081332	0.6352	0.263829
3	0.059869	0.4676	0.32087
4	-0.062267	-0.4863	0.314242
5	-0.142492	-1.1129	0.13506
6	-0.039865	-0.3114	0.378296
7	-0.058075	-0.4536	0.32587
8	-0.04177	-0.3262	0.372683
9	-0.083626	-0.6531	0.25806
10	0.05488	0.4286	0.334853
11	0.002686	0.021	0.491667
12	-0.146163	-1.1416	0.129047
13	-0.051471	-0.402	0.344545
14	-0.052842	-0.4127	0.340634
15	0.193985	1.5151	0.06746
16	-0.107173	-0.837	0.202916
17	-0.139568	-1.0901	0.139986

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.891593 & 6.9636 & 0 \tabularnewline
2 & 0.081332 & 0.6352 & 0.263829 \tabularnewline
3 & 0.059869 & 0.4676 & 0.32087 \tabularnewline
4 & -0.062267 & -0.4863 & 0.314242 \tabularnewline
5 & -0.142492 & -1.1129 & 0.13506 \tabularnewline
6 & -0.039865 & -0.3114 & 0.378296 \tabularnewline
7 & -0.058075 & -0.4536 & 0.32587 \tabularnewline
8 & -0.04177 & -0.3262 & 0.372683 \tabularnewline
9 & -0.083626 & -0.6531 & 0.25806 \tabularnewline
10 & 0.05488 & 0.4286 & 0.334853 \tabularnewline
11 & 0.002686 & 0.021 & 0.491667 \tabularnewline
12 & -0.146163 & -1.1416 & 0.129047 \tabularnewline
13 & -0.051471 & -0.402 & 0.344545 \tabularnewline
14 & -0.052842 & -0.4127 & 0.340634 \tabularnewline
15 & 0.193985 & 1.5151 & 0.06746 \tabularnewline
16 & -0.107173 & -0.837 & 0.202916 \tabularnewline
17 & -0.139568 & -1.0901 & 0.139986 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64084&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]0.891593[/C][C]6.9636[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.081332[/C][C]0.6352[/C][C]0.263829[/C][/ROW]
[ROW][C]3[/C][C]0.059869[/C][C]0.4676[/C][C]0.32087[/C][/ROW]
[ROW][C]4[/C][C]-0.062267[/C][C]-0.4863[/C][C]0.314242[/C][/ROW]
[ROW][C]5[/C][C]-0.142492[/C][C]-1.1129[/C][C]0.13506[/C][/ROW]
[ROW][C]6[/C][C]-0.039865[/C][C]-0.3114[/C][C]0.378296[/C][/ROW]
[ROW][C]7[/C][C]-0.058075[/C][C]-0.4536[/C][C]0.32587[/C][/ROW]
[ROW][C]8[/C][C]-0.04177[/C][C]-0.3262[/C][C]0.372683[/C][/ROW]
[ROW][C]9[/C][C]-0.083626[/C][C]-0.6531[/C][C]0.25806[/C][/ROW]
[ROW][C]10[/C][C]0.05488[/C][C]0.4286[/C][C]0.334853[/C][/ROW]
[ROW][C]11[/C][C]0.002686[/C][C]0.021[/C][C]0.491667[/C][/ROW]
[ROW][C]12[/C][C]-0.146163[/C][C]-1.1416[/C][C]0.129047[/C][/ROW]
[ROW][C]13[/C][C]-0.051471[/C][C]-0.402[/C][C]0.344545[/C][/ROW]
[ROW][C]14[/C][C]-0.052842[/C][C]-0.4127[/C][C]0.340634[/C][/ROW]
[ROW][C]15[/C][C]0.193985[/C][C]1.5151[/C][C]0.06746[/C][/ROW]
[ROW][C]16[/C][C]-0.107173[/C][C]-0.837[/C][C]0.202916[/C][/ROW]
[ROW][C]17[/C][C]-0.139568[/C][C]-1.0901[/C][C]0.139986[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64084&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64084&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	0.891593	6.9636	0
2	0.081332	0.6352	0.263829
3	0.059869	0.4676	0.32087
4	-0.062267	-0.4863	0.314242
5	-0.142492	-1.1129	0.13506
6	-0.039865	-0.3114	0.378296
7	-0.058075	-0.4536	0.32587
8	-0.04177	-0.3262	0.372683
9	-0.083626	-0.6531	0.25806
10	0.05488	0.4286	0.334853
11	0.002686	0.021	0.491667
12	-0.146163	-1.1416	0.129047
13	-0.051471	-0.402	0.344545
14	-0.052842	-0.4127	0.340634
15	0.193985	1.5151	0.06746
16	-0.107173	-0.837	0.202916
17	-0.139568	-1.0901	0.139986

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