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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 28 Dec 2009 07:34:38 -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/28/t12620109476ru71qdegeczs1m.htm/, Retrieved Sat, 04 May 2024 21:46:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70981, Retrieved Sat, 04 May 2024 21:46:33 +0000

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No (this computation is public)

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Estimated Impact

103

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-       [(Partial) Autocorrelation Function] [paper acf export] [2009-12-28 14:34:38] [90d336e5f53609c0c5a6217e988a780d] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70981&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]2 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=70981&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70981&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.251757	1.7623	0.042128
2	0.281763	1.9723	0.027114
3	0.158031	1.1062	0.137017
4	0.019317	0.1352	0.446495
5	0.152338	1.0664	0.145742
6	-0.04233	-0.2963	0.384123
7	-0.09467	-0.6627	0.255317
8	0.124303	0.8701	0.194239
9	-0.002524	-0.0177	0.492989
10	0.193139	1.352	0.091296
11	0.003429	0.024	0.490473
12	-0.111055	-0.7774	0.220335
13	-0.084051	-0.5884	0.279498
14	-0.084149	-0.589	0.27927
15	-0.014036	-0.0983	0.461067
16	-0.174243	-1.2197	0.114208
17	-0.044852	-0.314	0.377439

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.251757 & 1.7623 & 0.042128 \tabularnewline
2 & 0.281763 & 1.9723 & 0.027114 \tabularnewline
3 & 0.158031 & 1.1062 & 0.137017 \tabularnewline
4 & 0.019317 & 0.1352 & 0.446495 \tabularnewline
5 & 0.152338 & 1.0664 & 0.145742 \tabularnewline
6 & -0.04233 & -0.2963 & 0.384123 \tabularnewline
7 & -0.09467 & -0.6627 & 0.255317 \tabularnewline
8 & 0.124303 & 0.8701 & 0.194239 \tabularnewline
9 & -0.002524 & -0.0177 & 0.492989 \tabularnewline
10 & 0.193139 & 1.352 & 0.091296 \tabularnewline
11 & 0.003429 & 0.024 & 0.490473 \tabularnewline
12 & -0.111055 & -0.7774 & 0.220335 \tabularnewline
13 & -0.084051 & -0.5884 & 0.279498 \tabularnewline
14 & -0.084149 & -0.589 & 0.27927 \tabularnewline
15 & -0.014036 & -0.0983 & 0.461067 \tabularnewline
16 & -0.174243 & -1.2197 & 0.114208 \tabularnewline
17 & -0.044852 & -0.314 & 0.377439 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70981&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]0.251757[/C][C]1.7623[/C][C]0.042128[/C][/ROW]
[ROW][C]2[/C][C]0.281763[/C][C]1.9723[/C][C]0.027114[/C][/ROW]
[ROW][C]3[/C][C]0.158031[/C][C]1.1062[/C][C]0.137017[/C][/ROW]
[ROW][C]4[/C][C]0.019317[/C][C]0.1352[/C][C]0.446495[/C][/ROW]
[ROW][C]5[/C][C]0.152338[/C][C]1.0664[/C][C]0.145742[/C][/ROW]
[ROW][C]6[/C][C]-0.04233[/C][C]-0.2963[/C][C]0.384123[/C][/ROW]
[ROW][C]7[/C][C]-0.09467[/C][C]-0.6627[/C][C]0.255317[/C][/ROW]
[ROW][C]8[/C][C]0.124303[/C][C]0.8701[/C][C]0.194239[/C][/ROW]
[ROW][C]9[/C][C]-0.002524[/C][C]-0.0177[/C][C]0.492989[/C][/ROW]
[ROW][C]10[/C][C]0.193139[/C][C]1.352[/C][C]0.091296[/C][/ROW]
[ROW][C]11[/C][C]0.003429[/C][C]0.024[/C][C]0.490473[/C][/ROW]
[ROW][C]12[/C][C]-0.111055[/C][C]-0.7774[/C][C]0.220335[/C][/ROW]
[ROW][C]13[/C][C]-0.084051[/C][C]-0.5884[/C][C]0.279498[/C][/ROW]
[ROW][C]14[/C][C]-0.084149[/C][C]-0.589[/C][C]0.27927[/C][/ROW]
[ROW][C]15[/C][C]-0.014036[/C][C]-0.0983[/C][C]0.461067[/C][/ROW]
[ROW][C]16[/C][C]-0.174243[/C][C]-1.2197[/C][C]0.114208[/C][/ROW]
[ROW][C]17[/C][C]-0.044852[/C][C]-0.314[/C][C]0.377439[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70981&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70981&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	0.251757	1.7623	0.042128
2	0.281763	1.9723	0.027114
3	0.158031	1.1062	0.137017
4	0.019317	0.1352	0.446495
5	0.152338	1.0664	0.145742
6	-0.04233	-0.2963	0.384123
7	-0.09467	-0.6627	0.255317
8	0.124303	0.8701	0.194239
9	-0.002524	-0.0177	0.492989
10	0.193139	1.352	0.091296
11	0.003429	0.024	0.490473
12	-0.111055	-0.7774	0.220335
13	-0.084051	-0.5884	0.279498
14	-0.084149	-0.589	0.27927
15	-0.014036	-0.0983	0.461067
16	-0.174243	-1.2197	0.114208
17	-0.044852	-0.314	0.377439

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.251757	1.7623	0.042128
2	0.23316	1.6321	0.054533
3	0.050734	0.3551	0.362006
4	-0.096252	-0.6738	0.251814
5	0.131472	0.9203	0.180961
6	-0.095265	-0.6669	0.253997
7	-0.144951	-1.0147	0.157627
8	0.212332	1.4863	0.0718
9	0.023195	0.1624	0.435844
10	0.122822	0.8598	0.197055
11	-0.0978	-0.6846	0.24841
12	-0.167417	-1.1719	0.123448
13	-0.125313	-0.8772	0.192331
14	0.060403	0.4228	0.337138
15	0.08757	0.613	0.271358
16	-0.189974	-1.3298	0.094868
17	0.11969	0.8378	0.203098

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.251757 & 1.7623 & 0.042128 \tabularnewline
2 & 0.23316 & 1.6321 & 0.054533 \tabularnewline
3 & 0.050734 & 0.3551 & 0.362006 \tabularnewline
4 & -0.096252 & -0.6738 & 0.251814 \tabularnewline
5 & 0.131472 & 0.9203 & 0.180961 \tabularnewline
6 & -0.095265 & -0.6669 & 0.253997 \tabularnewline
7 & -0.144951 & -1.0147 & 0.157627 \tabularnewline
8 & 0.212332 & 1.4863 & 0.0718 \tabularnewline
9 & 0.023195 & 0.1624 & 0.435844 \tabularnewline
10 & 0.122822 & 0.8598 & 0.197055 \tabularnewline
11 & -0.0978 & -0.6846 & 0.24841 \tabularnewline
12 & -0.167417 & -1.1719 & 0.123448 \tabularnewline
13 & -0.125313 & -0.8772 & 0.192331 \tabularnewline
14 & 0.060403 & 0.4228 & 0.337138 \tabularnewline
15 & 0.08757 & 0.613 & 0.271358 \tabularnewline
16 & -0.189974 & -1.3298 & 0.094868 \tabularnewline
17 & 0.11969 & 0.8378 & 0.203098 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70981&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]0.251757[/C][C]1.7623[/C][C]0.042128[/C][/ROW]
[ROW][C]2[/C][C]0.23316[/C][C]1.6321[/C][C]0.054533[/C][/ROW]
[ROW][C]3[/C][C]0.050734[/C][C]0.3551[/C][C]0.362006[/C][/ROW]
[ROW][C]4[/C][C]-0.096252[/C][C]-0.6738[/C][C]0.251814[/C][/ROW]
[ROW][C]5[/C][C]0.131472[/C][C]0.9203[/C][C]0.180961[/C][/ROW]
[ROW][C]6[/C][C]-0.095265[/C][C]-0.6669[/C][C]0.253997[/C][/ROW]
[ROW][C]7[/C][C]-0.144951[/C][C]-1.0147[/C][C]0.157627[/C][/ROW]
[ROW][C]8[/C][C]0.212332[/C][C]1.4863[/C][C]0.0718[/C][/ROW]
[ROW][C]9[/C][C]0.023195[/C][C]0.1624[/C][C]0.435844[/C][/ROW]
[ROW][C]10[/C][C]0.122822[/C][C]0.8598[/C][C]0.197055[/C][/ROW]
[ROW][C]11[/C][C]-0.0978[/C][C]-0.6846[/C][C]0.24841[/C][/ROW]
[ROW][C]12[/C][C]-0.167417[/C][C]-1.1719[/C][C]0.123448[/C][/ROW]
[ROW][C]13[/C][C]-0.125313[/C][C]-0.8772[/C][C]0.192331[/C][/ROW]
[ROW][C]14[/C][C]0.060403[/C][C]0.4228[/C][C]0.337138[/C][/ROW]
[ROW][C]15[/C][C]0.08757[/C][C]0.613[/C][C]0.271358[/C][/ROW]
[ROW][C]16[/C][C]-0.189974[/C][C]-1.3298[/C][C]0.094868[/C][/ROW]
[ROW][C]17[/C][C]0.11969[/C][C]0.8378[/C][C]0.203098[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70981&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70981&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	0.251757	1.7623	0.042128
2	0.23316	1.6321	0.054533
3	0.050734	0.3551	0.362006
4	-0.096252	-0.6738	0.251814
5	0.131472	0.9203	0.180961
6	-0.095265	-0.6669	0.253997
7	-0.144951	-1.0147	0.157627
8	0.212332	1.4863	0.0718
9	0.023195	0.1624	0.435844
10	0.122822	0.8598	0.197055
11	-0.0978	-0.6846	0.24841
12	-0.167417	-1.1719	0.123448
13	-0.125313	-0.8772	0.192331
14	0.060403	0.4228	0.337138
15	0.08757	0.613	0.271358
16	-0.189974	-1.3298	0.094868
17	0.11969	0.8378	0.203098

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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Tables (Output of Computation)

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Input Parameters & R Code