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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 27 Nov 2009 12:05:54 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/27/t1259348804xfg40nqjgaown3u.htm/, Retrieved Sun, 28 Apr 2024 21:49:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61142, Retrieved Sun, 28 Apr 2024 21:49:55 +0000

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

-       [(Partial) Autocorrelation Function] [ACF] [2009-11-27 19:05:54] [99bf2a1e962091d45abf4c2600a412f9] [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=61142&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=61142&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61142&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	-0.008365	-0.0573	0.477256
2	0.12948	0.8877	0.189619
3	0.183813	1.2602	0.106917
4	0.119196	0.8172	0.208979
5	-0.002604	-0.0179	0.492916
6	0.1365	0.9358	0.177081
7	-0.0144	-0.0987	0.460888
8	0.102288	0.7012	0.243303
9	-0.061087	-0.4188	0.338639
10	-0.06703	-0.4595	0.323985
11	0.289419	1.9842	0.026548
12	-0.112498	-0.7712	0.22221
13	-0.067868	-0.4653	0.32194
14	0.092824	0.6364	0.263812
15	-0.094013	-0.6445	0.261185
16	-0.074858	-0.5132	0.305108
17	0.010854	0.0744	0.470499

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.008365 & -0.0573 & 0.477256 \tabularnewline
2 & 0.12948 & 0.8877 & 0.189619 \tabularnewline
3 & 0.183813 & 1.2602 & 0.106917 \tabularnewline
4 & 0.119196 & 0.8172 & 0.208979 \tabularnewline
5 & -0.002604 & -0.0179 & 0.492916 \tabularnewline
6 & 0.1365 & 0.9358 & 0.177081 \tabularnewline
7 & -0.0144 & -0.0987 & 0.460888 \tabularnewline
8 & 0.102288 & 0.7012 & 0.243303 \tabularnewline
9 & -0.061087 & -0.4188 & 0.338639 \tabularnewline
10 & -0.06703 & -0.4595 & 0.323985 \tabularnewline
11 & 0.289419 & 1.9842 & 0.026548 \tabularnewline
12 & -0.112498 & -0.7712 & 0.22221 \tabularnewline
13 & -0.067868 & -0.4653 & 0.32194 \tabularnewline
14 & 0.092824 & 0.6364 & 0.263812 \tabularnewline
15 & -0.094013 & -0.6445 & 0.261185 \tabularnewline
16 & -0.074858 & -0.5132 & 0.305108 \tabularnewline
17 & 0.010854 & 0.0744 & 0.470499 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61142&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]-0.008365[/C][C]-0.0573[/C][C]0.477256[/C][/ROW]
[ROW][C]2[/C][C]0.12948[/C][C]0.8877[/C][C]0.189619[/C][/ROW]
[ROW][C]3[/C][C]0.183813[/C][C]1.2602[/C][C]0.106917[/C][/ROW]
[ROW][C]4[/C][C]0.119196[/C][C]0.8172[/C][C]0.208979[/C][/ROW]
[ROW][C]5[/C][C]-0.002604[/C][C]-0.0179[/C][C]0.492916[/C][/ROW]
[ROW][C]6[/C][C]0.1365[/C][C]0.9358[/C][C]0.177081[/C][/ROW]
[ROW][C]7[/C][C]-0.0144[/C][C]-0.0987[/C][C]0.460888[/C][/ROW]
[ROW][C]8[/C][C]0.102288[/C][C]0.7012[/C][C]0.243303[/C][/ROW]
[ROW][C]9[/C][C]-0.061087[/C][C]-0.4188[/C][C]0.338639[/C][/ROW]
[ROW][C]10[/C][C]-0.06703[/C][C]-0.4595[/C][C]0.323985[/C][/ROW]
[ROW][C]11[/C][C]0.289419[/C][C]1.9842[/C][C]0.026548[/C][/ROW]
[ROW][C]12[/C][C]-0.112498[/C][C]-0.7712[/C][C]0.22221[/C][/ROW]
[ROW][C]13[/C][C]-0.067868[/C][C]-0.4653[/C][C]0.32194[/C][/ROW]
[ROW][C]14[/C][C]0.092824[/C][C]0.6364[/C][C]0.263812[/C][/ROW]
[ROW][C]15[/C][C]-0.094013[/C][C]-0.6445[/C][C]0.261185[/C][/ROW]
[ROW][C]16[/C][C]-0.074858[/C][C]-0.5132[/C][C]0.305108[/C][/ROW]
[ROW][C]17[/C][C]0.010854[/C][C]0.0744[/C][C]0.470499[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61142&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61142&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	-0.008365	-0.0573	0.477256
2	0.12948	0.8877	0.189619
3	0.183813	1.2602	0.106917
4	0.119196	0.8172	0.208979
5	-0.002604	-0.0179	0.492916
6	0.1365	0.9358	0.177081
7	-0.0144	-0.0987	0.460888
8	0.102288	0.7012	0.243303
9	-0.061087	-0.4188	0.338639
10	-0.06703	-0.4595	0.323985
11	0.289419	1.9842	0.026548
12	-0.112498	-0.7712	0.22221
13	-0.067868	-0.4653	0.32194
14	0.092824	0.6364	0.263812
15	-0.094013	-0.6445	0.261185
16	-0.074858	-0.5132	0.305108
17	0.010854	0.0744	0.470499

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.008365	-0.0573	0.477256
2	0.129419	0.8873	0.18973
3	0.189017	1.2958	0.10068
4	0.115686	0.7931	0.215852
5	-0.044321	-0.3038	0.381293
6	0.075162	0.5153	0.304384
7	-0.046279	-0.3173	0.376221
8	0.075446	0.5172	0.303709
9	-0.088038	-0.6036	0.27452
10	-0.113913	-0.7809	0.219375
11	0.308878	2.1176	0.019766
12	-0.100813	-0.6911	0.24644
13	-0.099606	-0.6829	0.249021
14	0.022135	0.1517	0.440018
15	-0.107808	-0.7391	0.231763
16	-0.006418	-0.044	0.482545
17	-0.042147	-0.2889	0.386947

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.008365 & -0.0573 & 0.477256 \tabularnewline
2 & 0.129419 & 0.8873 & 0.18973 \tabularnewline
3 & 0.189017 & 1.2958 & 0.10068 \tabularnewline
4 & 0.115686 & 0.7931 & 0.215852 \tabularnewline
5 & -0.044321 & -0.3038 & 0.381293 \tabularnewline
6 & 0.075162 & 0.5153 & 0.304384 \tabularnewline
7 & -0.046279 & -0.3173 & 0.376221 \tabularnewline
8 & 0.075446 & 0.5172 & 0.303709 \tabularnewline
9 & -0.088038 & -0.6036 & 0.27452 \tabularnewline
10 & -0.113913 & -0.7809 & 0.219375 \tabularnewline
11 & 0.308878 & 2.1176 & 0.019766 \tabularnewline
12 & -0.100813 & -0.6911 & 0.24644 \tabularnewline
13 & -0.099606 & -0.6829 & 0.249021 \tabularnewline
14 & 0.022135 & 0.1517 & 0.440018 \tabularnewline
15 & -0.107808 & -0.7391 & 0.231763 \tabularnewline
16 & -0.006418 & -0.044 & 0.482545 \tabularnewline
17 & -0.042147 & -0.2889 & 0.386947 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61142&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]-0.008365[/C][C]-0.0573[/C][C]0.477256[/C][/ROW]
[ROW][C]2[/C][C]0.129419[/C][C]0.8873[/C][C]0.18973[/C][/ROW]
[ROW][C]3[/C][C]0.189017[/C][C]1.2958[/C][C]0.10068[/C][/ROW]
[ROW][C]4[/C][C]0.115686[/C][C]0.7931[/C][C]0.215852[/C][/ROW]
[ROW][C]5[/C][C]-0.044321[/C][C]-0.3038[/C][C]0.381293[/C][/ROW]
[ROW][C]6[/C][C]0.075162[/C][C]0.5153[/C][C]0.304384[/C][/ROW]
[ROW][C]7[/C][C]-0.046279[/C][C]-0.3173[/C][C]0.376221[/C][/ROW]
[ROW][C]8[/C][C]0.075446[/C][C]0.5172[/C][C]0.303709[/C][/ROW]
[ROW][C]9[/C][C]-0.088038[/C][C]-0.6036[/C][C]0.27452[/C][/ROW]
[ROW][C]10[/C][C]-0.113913[/C][C]-0.7809[/C][C]0.219375[/C][/ROW]
[ROW][C]11[/C][C]0.308878[/C][C]2.1176[/C][C]0.019766[/C][/ROW]
[ROW][C]12[/C][C]-0.100813[/C][C]-0.6911[/C][C]0.24644[/C][/ROW]
[ROW][C]13[/C][C]-0.099606[/C][C]-0.6829[/C][C]0.249021[/C][/ROW]
[ROW][C]14[/C][C]0.022135[/C][C]0.1517[/C][C]0.440018[/C][/ROW]
[ROW][C]15[/C][C]-0.107808[/C][C]-0.7391[/C][C]0.231763[/C][/ROW]
[ROW][C]16[/C][C]-0.006418[/C][C]-0.044[/C][C]0.482545[/C][/ROW]
[ROW][C]17[/C][C]-0.042147[/C][C]-0.2889[/C][C]0.386947[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61142&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61142&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	-0.008365	-0.0573	0.477256
2	0.129419	0.8873	0.18973
3	0.189017	1.2958	0.10068
4	0.115686	0.7931	0.215852
5	-0.044321	-0.3038	0.381293
6	0.075162	0.5153	0.304384
7	-0.046279	-0.3173	0.376221
8	0.075446	0.5172	0.303709
9	-0.088038	-0.6036	0.27452
10	-0.113913	-0.7809	0.219375
11	0.308878	2.1176	0.019766
12	-0.100813	-0.6911	0.24644
13	-0.099606	-0.6829	0.249021
14	0.022135	0.1517	0.440018
15	-0.107808	-0.7391	0.231763
16	-0.006418	-0.044	0.482545
17	-0.042147	-0.2889	0.386947

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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