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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 19 Dec 2007 11:54:54 -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/2007/Dec/19/t11980894374moi1ro8roo9xjo.htm/, Retrieved Tue, 07 May 2024 02:22:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4697, Retrieved Tue, 07 May 2024 02:22:49 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

196

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

-       [(Partial) Autocorrelation Function] [] [2007-12-19 18:54:54] [dd38921fafddee0dfc20da83e9650a2a] [Current]

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Dataseries X:

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Histogram

Boxplots

8.1
8.3
8.2
8.1
7.7
7.6
7.7
8.2
8.4
8.4
8.6
8.4
8.5
8.7
8.7
8.6
7.4
7.3
7.4
9
9.2
9.2
8.5
8.3
8.3
8.6
8.6
8.5
8.1
8.1
8
8.6
8.7
8.7
8.6
8.4
8.4
8.7
8.7
8.5
8.3
8.3
8.3
8.1
8.2
8.1
8.1
7.9
7.7
8.1
8
7.7
7.8
7.6
7.4
7.7
7.8
7.5
7.2
7

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4697&T=0

[TABLE]
[ROW][C]Summary of compuational 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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4697&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4697&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	6.8557	0
1	0.015407	0.1056	0.458163
2	-0.082912	-0.5684	0.713772
3	-0.564447	-3.8697	0.999833
4	-0.03565	-0.2444	0.596009
5	0.009841	0.0675	0.473248
6	0.099825	0.6844	0.248552
7	-0.008476	-0.0581	0.523045
8	0.051143	0.3506	0.36372
9	0.152233	1.0437	0.150991
10	0.036095	0.2475	0.402817
11	-0.043774	-0.3001	0.617288
12	-0.27378	-1.8769	0.96663
13	-0.00347	-0.0238	0.50944
14	0.052107	0.3572	0.36126
15	0.191188	1.3107	0.098161
16	-0.025674	-0.176	0.56948

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.8557 & 0 \tabularnewline
1 & 0.015407 & 0.1056 & 0.458163 \tabularnewline
2 & -0.082912 & -0.5684 & 0.713772 \tabularnewline
3 & -0.564447 & -3.8697 & 0.999833 \tabularnewline
4 & -0.03565 & -0.2444 & 0.596009 \tabularnewline
5 & 0.009841 & 0.0675 & 0.473248 \tabularnewline
6 & 0.099825 & 0.6844 & 0.248552 \tabularnewline
7 & -0.008476 & -0.0581 & 0.523045 \tabularnewline
8 & 0.051143 & 0.3506 & 0.36372 \tabularnewline
9 & 0.152233 & 1.0437 & 0.150991 \tabularnewline
10 & 0.036095 & 0.2475 & 0.402817 \tabularnewline
11 & -0.043774 & -0.3001 & 0.617288 \tabularnewline
12 & -0.27378 & -1.8769 & 0.96663 \tabularnewline
13 & -0.00347 & -0.0238 & 0.50944 \tabularnewline
14 & 0.052107 & 0.3572 & 0.36126 \tabularnewline
15 & 0.191188 & 1.3107 & 0.098161 \tabularnewline
16 & -0.025674 & -0.176 & 0.56948 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4697&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]0[/C][C]1[/C][C]6.8557[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.015407[/C][C]0.1056[/C][C]0.458163[/C][/ROW]
[ROW][C]2[/C][C]-0.082912[/C][C]-0.5684[/C][C]0.713772[/C][/ROW]
[ROW][C]3[/C][C]-0.564447[/C][C]-3.8697[/C][C]0.999833[/C][/ROW]
[ROW][C]4[/C][C]-0.03565[/C][C]-0.2444[/C][C]0.596009[/C][/ROW]
[ROW][C]5[/C][C]0.009841[/C][C]0.0675[/C][C]0.473248[/C][/ROW]
[ROW][C]6[/C][C]0.099825[/C][C]0.6844[/C][C]0.248552[/C][/ROW]
[ROW][C]7[/C][C]-0.008476[/C][C]-0.0581[/C][C]0.523045[/C][/ROW]
[ROW][C]8[/C][C]0.051143[/C][C]0.3506[/C][C]0.36372[/C][/ROW]
[ROW][C]9[/C][C]0.152233[/C][C]1.0437[/C][C]0.150991[/C][/ROW]
[ROW][C]10[/C][C]0.036095[/C][C]0.2475[/C][C]0.402817[/C][/ROW]
[ROW][C]11[/C][C]-0.043774[/C][C]-0.3001[/C][C]0.617288[/C][/ROW]
[ROW][C]12[/C][C]-0.27378[/C][C]-1.8769[/C][C]0.96663[/C][/ROW]
[ROW][C]13[/C][C]-0.00347[/C][C]-0.0238[/C][C]0.50944[/C][/ROW]
[ROW][C]14[/C][C]0.052107[/C][C]0.3572[/C][C]0.36126[/C][/ROW]
[ROW][C]15[/C][C]0.191188[/C][C]1.3107[/C][C]0.098161[/C][/ROW]
[ROW][C]16[/C][C]-0.025674[/C][C]-0.176[/C][C]0.56948[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4697&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4697&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
0	1	6.8557	0
1	0.015407	0.1056	0.458163
2	-0.082912	-0.5684	0.713772
3	-0.564447	-3.8697	0.999833
4	-0.03565	-0.2444	0.596009
5	0.009841	0.0675	0.473248
6	0.099825	0.6844	0.248552
7	-0.008476	-0.0581	0.523045
8	0.051143	0.3506	0.36372
9	0.152233	1.0437	0.150991
10	0.036095	0.2475	0.402817
11	-0.043774	-0.3001	0.617288
12	-0.27378	-1.8769	0.96663
13	-0.00347	-0.0238	0.50944
14	0.052107	0.3572	0.36126
15	0.191188	1.3107	0.098161
16	-0.025674	-0.176	0.56948

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.015407	0.1056	0.458163
1	-0.08317	-0.5702	0.714365
2	-0.56583	-3.8791	0.999837
3	-0.074355	-0.5098	0.693694
4	-0.124257	-0.8519	0.800694
5	-0.356978	-2.4473	0.990908
6	-0.184751	-1.2666	0.894228
7	-0.118153	-0.81	0.788993
8	-0.012395	-0.085	0.53368
9	-0.061972	-0.4249	0.66356
10	-0.015469	-0.1061	0.542004
11	-0.200696	-1.3759	0.912314
12	-0.026015	-0.1784	0.570393
13	-0.003618	-0.0248	0.509841
14	-0.074164	-0.5084	0.69324
15	-0.052265	-0.3583	0.639142
16	0.024783	0.1699	0.432908

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.015407 & 0.1056 & 0.458163 \tabularnewline
1 & -0.08317 & -0.5702 & 0.714365 \tabularnewline
2 & -0.56583 & -3.8791 & 0.999837 \tabularnewline
3 & -0.074355 & -0.5098 & 0.693694 \tabularnewline
4 & -0.124257 & -0.8519 & 0.800694 \tabularnewline
5 & -0.356978 & -2.4473 & 0.990908 \tabularnewline
6 & -0.184751 & -1.2666 & 0.894228 \tabularnewline
7 & -0.118153 & -0.81 & 0.788993 \tabularnewline
8 & -0.012395 & -0.085 & 0.53368 \tabularnewline
9 & -0.061972 & -0.4249 & 0.66356 \tabularnewline
10 & -0.015469 & -0.1061 & 0.542004 \tabularnewline
11 & -0.200696 & -1.3759 & 0.912314 \tabularnewline
12 & -0.026015 & -0.1784 & 0.570393 \tabularnewline
13 & -0.003618 & -0.0248 & 0.509841 \tabularnewline
14 & -0.074164 & -0.5084 & 0.69324 \tabularnewline
15 & -0.052265 & -0.3583 & 0.639142 \tabularnewline
16 & 0.024783 & 0.1699 & 0.432908 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4697&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]0[/C][C]0.015407[/C][C]0.1056[/C][C]0.458163[/C][/ROW]
[ROW][C]1[/C][C]-0.08317[/C][C]-0.5702[/C][C]0.714365[/C][/ROW]
[ROW][C]2[/C][C]-0.56583[/C][C]-3.8791[/C][C]0.999837[/C][/ROW]
[ROW][C]3[/C][C]-0.074355[/C][C]-0.5098[/C][C]0.693694[/C][/ROW]
[ROW][C]4[/C][C]-0.124257[/C][C]-0.8519[/C][C]0.800694[/C][/ROW]
[ROW][C]5[/C][C]-0.356978[/C][C]-2.4473[/C][C]0.990908[/C][/ROW]
[ROW][C]6[/C][C]-0.184751[/C][C]-1.2666[/C][C]0.894228[/C][/ROW]
[ROW][C]7[/C][C]-0.118153[/C][C]-0.81[/C][C]0.788993[/C][/ROW]
[ROW][C]8[/C][C]-0.012395[/C][C]-0.085[/C][C]0.53368[/C][/ROW]
[ROW][C]9[/C][C]-0.061972[/C][C]-0.4249[/C][C]0.66356[/C][/ROW]
[ROW][C]10[/C][C]-0.015469[/C][C]-0.1061[/C][C]0.542004[/C][/ROW]
[ROW][C]11[/C][C]-0.200696[/C][C]-1.3759[/C][C]0.912314[/C][/ROW]
[ROW][C]12[/C][C]-0.026015[/C][C]-0.1784[/C][C]0.570393[/C][/ROW]
[ROW][C]13[/C][C]-0.003618[/C][C]-0.0248[/C][C]0.509841[/C][/ROW]
[ROW][C]14[/C][C]-0.074164[/C][C]-0.5084[/C][C]0.69324[/C][/ROW]
[ROW][C]15[/C][C]-0.052265[/C][C]-0.3583[/C][C]0.639142[/C][/ROW]
[ROW][C]16[/C][C]0.024783[/C][C]0.1699[/C][C]0.432908[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4697&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4697&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
0	0.015407	0.1056	0.458163
1	-0.08317	-0.5702	0.714365
2	-0.56583	-3.8791	0.999837
3	-0.074355	-0.5098	0.693694
4	-0.124257	-0.8519	0.800694
5	-0.356978	-2.4473	0.990908
6	-0.184751	-1.2666	0.894228
7	-0.118153	-0.81	0.788993
8	-0.012395	-0.085	0.53368
9	-0.061972	-0.4249	0.66356
10	-0.015469	-0.1061	0.542004
11	-0.200696	-1.3759	0.912314
12	-0.026015	-0.1784	0.570393
13	-0.003618	-0.0248	0.509841
14	-0.074164	-0.5084	0.69324
15	-0.052265	-0.3583	0.639142
16	0.024783	0.1699	0.432908

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

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 (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='lags',ylab='ACF')
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 1:par1) {
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(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-1,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(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)

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Input Parameters & R Code