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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 25 Nov 2009 11:31:17 -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/Nov/25/t12591739413ac0h78y3slpugy.htm/, Retrieved Tue, 07 May 2024 20:47:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59546, Retrieved Tue, 07 May 2024 20:47:45 +0000

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Estimated Impact

115

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-       [(Partial) Autocorrelation Function] [] [2009-11-25 18:31:17] [6e025b5370bdd3143fbe248190b38274] [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=59546&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=59546&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59546&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	-0.528339	-3.6221	0.000357
2	0.077457	0.531	0.298953
3	0.35951	2.4647	0.008712
4	-0.378655	-2.5959	0.006275
5	0.169358	1.1611	0.12574
6	0.155644	1.067	0.145702
7	-0.423139	-2.9009	0.002822
8	0.317909	2.1795	0.017171
9	-0.197133	-1.3515	0.091506
10	-0.123586	-0.8473	0.200572
11	0.192324	1.3185	0.096862
12	-0.161153	-1.1048	0.137433
13	-5.2e-05	-4e-04	0.49986
14	0.066799	0.4579	0.32455
15	-0.002186	-0.015	0.494052
16	-0.08395	-0.5755	0.283838
17	0.113285	0.7766	0.220631

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.528339 & -3.6221 & 0.000357 \tabularnewline
2 & 0.077457 & 0.531 & 0.298953 \tabularnewline
3 & 0.35951 & 2.4647 & 0.008712 \tabularnewline
4 & -0.378655 & -2.5959 & 0.006275 \tabularnewline
5 & 0.169358 & 1.1611 & 0.12574 \tabularnewline
6 & 0.155644 & 1.067 & 0.145702 \tabularnewline
7 & -0.423139 & -2.9009 & 0.002822 \tabularnewline
8 & 0.317909 & 2.1795 & 0.017171 \tabularnewline
9 & -0.197133 & -1.3515 & 0.091506 \tabularnewline
10 & -0.123586 & -0.8473 & 0.200572 \tabularnewline
11 & 0.192324 & 1.3185 & 0.096862 \tabularnewline
12 & -0.161153 & -1.1048 & 0.137433 \tabularnewline
13 & -5.2e-05 & -4e-04 & 0.49986 \tabularnewline
14 & 0.066799 & 0.4579 & 0.32455 \tabularnewline
15 & -0.002186 & -0.015 & 0.494052 \tabularnewline
16 & -0.08395 & -0.5755 & 0.283838 \tabularnewline
17 & 0.113285 & 0.7766 & 0.220631 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59546&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]-0.528339[/C][C]-3.6221[/C][C]0.000357[/C][/ROW]
[ROW][C]2[/C][C]0.077457[/C][C]0.531[/C][C]0.298953[/C][/ROW]
[ROW][C]3[/C][C]0.35951[/C][C]2.4647[/C][C]0.008712[/C][/ROW]
[ROW][C]4[/C][C]-0.378655[/C][C]-2.5959[/C][C]0.006275[/C][/ROW]
[ROW][C]5[/C][C]0.169358[/C][C]1.1611[/C][C]0.12574[/C][/ROW]
[ROW][C]6[/C][C]0.155644[/C][C]1.067[/C][C]0.145702[/C][/ROW]
[ROW][C]7[/C][C]-0.423139[/C][C]-2.9009[/C][C]0.002822[/C][/ROW]
[ROW][C]8[/C][C]0.317909[/C][C]2.1795[/C][C]0.017171[/C][/ROW]
[ROW][C]9[/C][C]-0.197133[/C][C]-1.3515[/C][C]0.091506[/C][/ROW]
[ROW][C]10[/C][C]-0.123586[/C][C]-0.8473[/C][C]0.200572[/C][/ROW]
[ROW][C]11[/C][C]0.192324[/C][C]1.3185[/C][C]0.096862[/C][/ROW]
[ROW][C]12[/C][C]-0.161153[/C][C]-1.1048[/C][C]0.137433[/C][/ROW]
[ROW][C]13[/C][C]-5.2e-05[/C][C]-4e-04[/C][C]0.49986[/C][/ROW]
[ROW][C]14[/C][C]0.066799[/C][C]0.4579[/C][C]0.32455[/C][/ROW]
[ROW][C]15[/C][C]-0.002186[/C][C]-0.015[/C][C]0.494052[/C][/ROW]
[ROW][C]16[/C][C]-0.08395[/C][C]-0.5755[/C][C]0.283838[/C][/ROW]
[ROW][C]17[/C][C]0.113285[/C][C]0.7766[/C][C]0.220631[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59546&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59546&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	-0.528339	-3.6221	0.000357
2	0.077457	0.531	0.298953
3	0.35951	2.4647	0.008712
4	-0.378655	-2.5959	0.006275
5	0.169358	1.1611	0.12574
6	0.155644	1.067	0.145702
7	-0.423139	-2.9009	0.002822
8	0.317909	2.1795	0.017171
9	-0.197133	-1.3515	0.091506
10	-0.123586	-0.8473	0.200572
11	0.192324	1.3185	0.096862
12	-0.161153	-1.1048	0.137433
13	-5.2e-05	-4e-04	0.49986
14	0.066799	0.4579	0.32455
15	-0.002186	-0.015	0.494052
16	-0.08395	-0.5755	0.283838
17	0.113285	0.7766	0.220631

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.528339	-3.6221	0.000357
2	-0.279785	-1.9181	0.030592
3	0.397427	2.7246	0.004506
4	0.063073	0.4324	0.333711
5	-0.090721	-0.622	0.26849
6	0.111334	0.7633	0.224558
7	-0.246493	-1.6899	0.048838
8	-0.126787	-0.8692	0.194575
9	-0.210241	-1.4413	0.078059
10	-0.114068	-0.782	0.219066
11	-0.054122	-0.371	0.356137
12	0.07351	0.504	0.308322
13	0.084919	0.5822	0.281616
14	-0.118892	-0.8151	0.209568
15	0.152571	1.046	0.150461
16	-0.151024	-1.0354	0.152897
17	-0.128591	-0.8816	0.191247

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.528339 & -3.6221 & 0.000357 \tabularnewline
2 & -0.279785 & -1.9181 & 0.030592 \tabularnewline
3 & 0.397427 & 2.7246 & 0.004506 \tabularnewline
4 & 0.063073 & 0.4324 & 0.333711 \tabularnewline
5 & -0.090721 & -0.622 & 0.26849 \tabularnewline
6 & 0.111334 & 0.7633 & 0.224558 \tabularnewline
7 & -0.246493 & -1.6899 & 0.048838 \tabularnewline
8 & -0.126787 & -0.8692 & 0.194575 \tabularnewline
9 & -0.210241 & -1.4413 & 0.078059 \tabularnewline
10 & -0.114068 & -0.782 & 0.219066 \tabularnewline
11 & -0.054122 & -0.371 & 0.356137 \tabularnewline
12 & 0.07351 & 0.504 & 0.308322 \tabularnewline
13 & 0.084919 & 0.5822 & 0.281616 \tabularnewline
14 & -0.118892 & -0.8151 & 0.209568 \tabularnewline
15 & 0.152571 & 1.046 & 0.150461 \tabularnewline
16 & -0.151024 & -1.0354 & 0.152897 \tabularnewline
17 & -0.128591 & -0.8816 & 0.191247 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59546&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]-0.528339[/C][C]-3.6221[/C][C]0.000357[/C][/ROW]
[ROW][C]2[/C][C]-0.279785[/C][C]-1.9181[/C][C]0.030592[/C][/ROW]
[ROW][C]3[/C][C]0.397427[/C][C]2.7246[/C][C]0.004506[/C][/ROW]
[ROW][C]4[/C][C]0.063073[/C][C]0.4324[/C][C]0.333711[/C][/ROW]
[ROW][C]5[/C][C]-0.090721[/C][C]-0.622[/C][C]0.26849[/C][/ROW]
[ROW][C]6[/C][C]0.111334[/C][C]0.7633[/C][C]0.224558[/C][/ROW]
[ROW][C]7[/C][C]-0.246493[/C][C]-1.6899[/C][C]0.048838[/C][/ROW]
[ROW][C]8[/C][C]-0.126787[/C][C]-0.8692[/C][C]0.194575[/C][/ROW]
[ROW][C]9[/C][C]-0.210241[/C][C]-1.4413[/C][C]0.078059[/C][/ROW]
[ROW][C]10[/C][C]-0.114068[/C][C]-0.782[/C][C]0.219066[/C][/ROW]
[ROW][C]11[/C][C]-0.054122[/C][C]-0.371[/C][C]0.356137[/C][/ROW]
[ROW][C]12[/C][C]0.07351[/C][C]0.504[/C][C]0.308322[/C][/ROW]
[ROW][C]13[/C][C]0.084919[/C][C]0.5822[/C][C]0.281616[/C][/ROW]
[ROW][C]14[/C][C]-0.118892[/C][C]-0.8151[/C][C]0.209568[/C][/ROW]
[ROW][C]15[/C][C]0.152571[/C][C]1.046[/C][C]0.150461[/C][/ROW]
[ROW][C]16[/C][C]-0.151024[/C][C]-1.0354[/C][C]0.152897[/C][/ROW]
[ROW][C]17[/C][C]-0.128591[/C][C]-0.8816[/C][C]0.191247[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59546&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59546&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	-0.528339	-3.6221	0.000357
2	-0.279785	-1.9181	0.030592
3	0.397427	2.7246	0.004506
4	0.063073	0.4324	0.333711
5	-0.090721	-0.622	0.26849
6	0.111334	0.7633	0.224558
7	-0.246493	-1.6899	0.048838
8	-0.126787	-0.8692	0.194575
9	-0.210241	-1.4413	0.078059
10	-0.114068	-0.782	0.219066
11	-0.054122	-0.371	0.356137
12	0.07351	0.504	0.308322
13	0.084919	0.5822	0.281616
14	-0.118892	-0.8151	0.209568
15	0.152571	1.046	0.150461
16	-0.151024	-1.0354	0.152897
17	-0.128591	-0.8816	0.191247

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code