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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 04 Dec 2009 05:02:14 -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/t125992825030snhg5fql4vh6m.htm/, Retrieved Sun, 28 Apr 2024 05:46:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63342, Retrieved Sun, 28 Apr 2024 05:46:35 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

103

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 14:46:03] [b98453cac15ba1066b407e146608df68]
- R PD      [(Partial) Autocorrelation Function] [] [2009-12-04 12:02:14] [1c773da0103d9327c2f1f790e2d74438] [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=63342&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=63342&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63342&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	0.932734	7.2249	0
2	0.845899	6.5523	0
3	0.762017	5.9026	0
4	0.666946	5.1661	1e-06
5	0.560436	4.3411	2.8e-05
6	0.448915	3.4773	0.000474
7	0.355705	2.7553	0.003877
8	0.295001	2.2851	0.012929
9	0.247588	1.9178	0.029949
10	0.197328	1.5285	0.065822
11	0.162123	1.2558	0.107029
12	0.158896	1.2308	0.111599
13	0.158259	1.2259	0.112518
14	0.147808	1.1449	0.128396
15	0.122393	0.9481	0.173453
16	0.072627	0.5626	0.287914
17	0.02553	0.1978	0.421952

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.932734 & 7.2249 & 0 \tabularnewline
2 & 0.845899 & 6.5523 & 0 \tabularnewline
3 & 0.762017 & 5.9026 & 0 \tabularnewline
4 & 0.666946 & 5.1661 & 1e-06 \tabularnewline
5 & 0.560436 & 4.3411 & 2.8e-05 \tabularnewline
6 & 0.448915 & 3.4773 & 0.000474 \tabularnewline
7 & 0.355705 & 2.7553 & 0.003877 \tabularnewline
8 & 0.295001 & 2.2851 & 0.012929 \tabularnewline
9 & 0.247588 & 1.9178 & 0.029949 \tabularnewline
10 & 0.197328 & 1.5285 & 0.065822 \tabularnewline
11 & 0.162123 & 1.2558 & 0.107029 \tabularnewline
12 & 0.158896 & 1.2308 & 0.111599 \tabularnewline
13 & 0.158259 & 1.2259 & 0.112518 \tabularnewline
14 & 0.147808 & 1.1449 & 0.128396 \tabularnewline
15 & 0.122393 & 0.9481 & 0.173453 \tabularnewline
16 & 0.072627 & 0.5626 & 0.287914 \tabularnewline
17 & 0.02553 & 0.1978 & 0.421952 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63342&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]0.932734[/C][C]7.2249[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.845899[/C][C]6.5523[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.762017[/C][C]5.9026[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.666946[/C][C]5.1661[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.560436[/C][C]4.3411[/C][C]2.8e-05[/C][/ROW]
[ROW][C]6[/C][C]0.448915[/C][C]3.4773[/C][C]0.000474[/C][/ROW]
[ROW][C]7[/C][C]0.355705[/C][C]2.7553[/C][C]0.003877[/C][/ROW]
[ROW][C]8[/C][C]0.295001[/C][C]2.2851[/C][C]0.012929[/C][/ROW]
[ROW][C]9[/C][C]0.247588[/C][C]1.9178[/C][C]0.029949[/C][/ROW]
[ROW][C]10[/C][C]0.197328[/C][C]1.5285[/C][C]0.065822[/C][/ROW]
[ROW][C]11[/C][C]0.162123[/C][C]1.2558[/C][C]0.107029[/C][/ROW]
[ROW][C]12[/C][C]0.158896[/C][C]1.2308[/C][C]0.111599[/C][/ROW]
[ROW][C]13[/C][C]0.158259[/C][C]1.2259[/C][C]0.112518[/C][/ROW]
[ROW][C]14[/C][C]0.147808[/C][C]1.1449[/C][C]0.128396[/C][/ROW]
[ROW][C]15[/C][C]0.122393[/C][C]0.9481[/C][C]0.173453[/C][/ROW]
[ROW][C]16[/C][C]0.072627[/C][C]0.5626[/C][C]0.287914[/C][/ROW]
[ROW][C]17[/C][C]0.02553[/C][C]0.1978[/C][C]0.421952[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63342&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63342&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	0.932734	7.2249	0
2	0.845899	6.5523	0
3	0.762017	5.9026	0
4	0.666946	5.1661	1e-06
5	0.560436	4.3411	2.8e-05
6	0.448915	3.4773	0.000474
7	0.355705	2.7553	0.003877
8	0.295001	2.2851	0.012929
9	0.247588	1.9178	0.029949
10	0.197328	1.5285	0.065822
11	0.162123	1.2558	0.107029
12	0.158896	1.2308	0.111599
13	0.158259	1.2259	0.112518
14	0.147808	1.1449	0.128396
15	0.122393	0.9481	0.173453
16	0.072627	0.5626	0.287914
17	0.02553	0.1978	0.421952

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.932734	7.2249	0
2	-0.185326	-1.4355	0.078164
3	-0.002747	-0.0213	0.491547
4	-0.146461	-1.1345	0.130553
5	-0.12254	-0.9492	0.173166
6	-0.097484	-0.7551	0.22657
7	0.081802	0.6336	0.264364
8	0.170927	1.324	0.095263
9	0.025232	0.1954	0.422852
10	-0.090654	-0.7022	0.242634
11	0.026659	0.2065	0.418551
12	0.14028	1.0866	0.140779
13	-0.057222	-0.4432	0.329594
14	-0.057965	-0.449	0.327526
15	-0.128892	-0.9984	0.16105
16	-0.248347	-1.9237	0.029571
17	0.001047	0.0081	0.496777

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.932734 & 7.2249 & 0 \tabularnewline
2 & -0.185326 & -1.4355 & 0.078164 \tabularnewline
3 & -0.002747 & -0.0213 & 0.491547 \tabularnewline
4 & -0.146461 & -1.1345 & 0.130553 \tabularnewline
5 & -0.12254 & -0.9492 & 0.173166 \tabularnewline
6 & -0.097484 & -0.7551 & 0.22657 \tabularnewline
7 & 0.081802 & 0.6336 & 0.264364 \tabularnewline
8 & 0.170927 & 1.324 & 0.095263 \tabularnewline
9 & 0.025232 & 0.1954 & 0.422852 \tabularnewline
10 & -0.090654 & -0.7022 & 0.242634 \tabularnewline
11 & 0.026659 & 0.2065 & 0.418551 \tabularnewline
12 & 0.14028 & 1.0866 & 0.140779 \tabularnewline
13 & -0.057222 & -0.4432 & 0.329594 \tabularnewline
14 & -0.057965 & -0.449 & 0.327526 \tabularnewline
15 & -0.128892 & -0.9984 & 0.16105 \tabularnewline
16 & -0.248347 & -1.9237 & 0.029571 \tabularnewline
17 & 0.001047 & 0.0081 & 0.496777 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63342&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]0.932734[/C][C]7.2249[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.185326[/C][C]-1.4355[/C][C]0.078164[/C][/ROW]
[ROW][C]3[/C][C]-0.002747[/C][C]-0.0213[/C][C]0.491547[/C][/ROW]
[ROW][C]4[/C][C]-0.146461[/C][C]-1.1345[/C][C]0.130553[/C][/ROW]
[ROW][C]5[/C][C]-0.12254[/C][C]-0.9492[/C][C]0.173166[/C][/ROW]
[ROW][C]6[/C][C]-0.097484[/C][C]-0.7551[/C][C]0.22657[/C][/ROW]
[ROW][C]7[/C][C]0.081802[/C][C]0.6336[/C][C]0.264364[/C][/ROW]
[ROW][C]8[/C][C]0.170927[/C][C]1.324[/C][C]0.095263[/C][/ROW]
[ROW][C]9[/C][C]0.025232[/C][C]0.1954[/C][C]0.422852[/C][/ROW]
[ROW][C]10[/C][C]-0.090654[/C][C]-0.7022[/C][C]0.242634[/C][/ROW]
[ROW][C]11[/C][C]0.026659[/C][C]0.2065[/C][C]0.418551[/C][/ROW]
[ROW][C]12[/C][C]0.14028[/C][C]1.0866[/C][C]0.140779[/C][/ROW]
[ROW][C]13[/C][C]-0.057222[/C][C]-0.4432[/C][C]0.329594[/C][/ROW]
[ROW][C]14[/C][C]-0.057965[/C][C]-0.449[/C][C]0.327526[/C][/ROW]
[ROW][C]15[/C][C]-0.128892[/C][C]-0.9984[/C][C]0.16105[/C][/ROW]
[ROW][C]16[/C][C]-0.248347[/C][C]-1.9237[/C][C]0.029571[/C][/ROW]
[ROW][C]17[/C][C]0.001047[/C][C]0.0081[/C][C]0.496777[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63342&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63342&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	0.932734	7.2249	0
2	-0.185326	-1.4355	0.078164
3	-0.002747	-0.0213	0.491547
4	-0.146461	-1.1345	0.130553
5	-0.12254	-0.9492	0.173166
6	-0.097484	-0.7551	0.22657
7	0.081802	0.6336	0.264364
8	0.170927	1.324	0.095263
9	0.025232	0.1954	0.422852
10	-0.090654	-0.7022	0.242634
11	0.026659	0.2065	0.418551
12	0.14028	1.0866	0.140779
13	-0.057222	-0.4432	0.329594
14	-0.057965	-0.449	0.327526
15	-0.128892	-0.9984	0.16105
16	-0.248347	-1.9237	0.029571
17	0.001047	0.0081	0.496777

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code