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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 16 Dec 2009 09:15:46 -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/Dec/16/t1260980211srh6mu2mosnidrv.htm/, Retrieved Tue, 30 Apr 2024 15:30:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68454, Retrieved Tue, 30 Apr 2024 15:30:08 +0000

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-       [(Partial) Autocorrelation Function] [] [2009-12-16 16:15:46] [df67ec12d4744494b58d8461e1971283] [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=68454&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=68454&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68454&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	-0.362537	-2.7847	0.003595
2	-0.23798	-1.828	0.036306
3	0.16602	1.2752	0.103615
4	-0.197008	-1.5132	0.067778
5	0.124848	0.959	0.170741
6	0.093378	0.7172	0.238025
7	0.02665	0.2047	0.419255
8	-0.061875	-0.4753	0.318175
9	0.062855	0.4828	0.315512
10	-0.276351	-2.1227	0.018993
11	-0.098726	-0.7583	0.225636
12	0.575817	4.4229	2.1e-05
13	-0.193664	-1.4876	0.071096
14	-0.167214	-1.2844	0.102012
15	-0.002451	-0.0188	0.492523
16	-0.054708	-0.4202	0.337925
17	0.142561	1.095	0.138977

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.362537 & -2.7847 & 0.003595 \tabularnewline
2 & -0.23798 & -1.828 & 0.036306 \tabularnewline
3 & 0.16602 & 1.2752 & 0.103615 \tabularnewline
4 & -0.197008 & -1.5132 & 0.067778 \tabularnewline
5 & 0.124848 & 0.959 & 0.170741 \tabularnewline
6 & 0.093378 & 0.7172 & 0.238025 \tabularnewline
7 & 0.02665 & 0.2047 & 0.419255 \tabularnewline
8 & -0.061875 & -0.4753 & 0.318175 \tabularnewline
9 & 0.062855 & 0.4828 & 0.315512 \tabularnewline
10 & -0.276351 & -2.1227 & 0.018993 \tabularnewline
11 & -0.098726 & -0.7583 & 0.225636 \tabularnewline
12 & 0.575817 & 4.4229 & 2.1e-05 \tabularnewline
13 & -0.193664 & -1.4876 & 0.071096 \tabularnewline
14 & -0.167214 & -1.2844 & 0.102012 \tabularnewline
15 & -0.002451 & -0.0188 & 0.492523 \tabularnewline
16 & -0.054708 & -0.4202 & 0.337925 \tabularnewline
17 & 0.142561 & 1.095 & 0.138977 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68454&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]-0.362537[/C][C]-2.7847[/C][C]0.003595[/C][/ROW]
[ROW][C]2[/C][C]-0.23798[/C][C]-1.828[/C][C]0.036306[/C][/ROW]
[ROW][C]3[/C][C]0.16602[/C][C]1.2752[/C][C]0.103615[/C][/ROW]
[ROW][C]4[/C][C]-0.197008[/C][C]-1.5132[/C][C]0.067778[/C][/ROW]
[ROW][C]5[/C][C]0.124848[/C][C]0.959[/C][C]0.170741[/C][/ROW]
[ROW][C]6[/C][C]0.093378[/C][C]0.7172[/C][C]0.238025[/C][/ROW]
[ROW][C]7[/C][C]0.02665[/C][C]0.2047[/C][C]0.419255[/C][/ROW]
[ROW][C]8[/C][C]-0.061875[/C][C]-0.4753[/C][C]0.318175[/C][/ROW]
[ROW][C]9[/C][C]0.062855[/C][C]0.4828[/C][C]0.315512[/C][/ROW]
[ROW][C]10[/C][C]-0.276351[/C][C]-2.1227[/C][C]0.018993[/C][/ROW]
[ROW][C]11[/C][C]-0.098726[/C][C]-0.7583[/C][C]0.225636[/C][/ROW]
[ROW][C]12[/C][C]0.575817[/C][C]4.4229[/C][C]2.1e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.193664[/C][C]-1.4876[/C][C]0.071096[/C][/ROW]
[ROW][C]14[/C][C]-0.167214[/C][C]-1.2844[/C][C]0.102012[/C][/ROW]
[ROW][C]15[/C][C]-0.002451[/C][C]-0.0188[/C][C]0.492523[/C][/ROW]
[ROW][C]16[/C][C]-0.054708[/C][C]-0.4202[/C][C]0.337925[/C][/ROW]
[ROW][C]17[/C][C]0.142561[/C][C]1.095[/C][C]0.138977[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68454&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68454&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	-0.362537	-2.7847	0.003595
2	-0.23798	-1.828	0.036306
3	0.16602	1.2752	0.103615
4	-0.197008	-1.5132	0.067778
5	0.124848	0.959	0.170741
6	0.093378	0.7172	0.238025
7	0.02665	0.2047	0.419255
8	-0.061875	-0.4753	0.318175
9	0.062855	0.4828	0.315512
10	-0.276351	-2.1227	0.018993
11	-0.098726	-0.7583	0.225636
12	0.575817	4.4229	2.1e-05
13	-0.193664	-1.4876	0.071096
14	-0.167214	-1.2844	0.102012
15	-0.002451	-0.0188	0.492523
16	-0.054708	-0.4202	0.337925
17	0.142561	1.095	0.138977

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.362537	-2.7847	0.003595
2	-0.425314	-3.2669	0.000907
3	-0.156222	-1.2	0.117475
4	-0.399451	-3.0682	0.001625
5	-0.209476	-1.609	0.056476
6	-0.152583	-1.172	0.122952
7	0.113041	0.8683	0.194379
8	0.094449	0.7255	0.235515
9	0.366901	2.8182	0.003281
10	-0.101025	-0.776	0.220429
11	-0.486168	-3.7343	0.000213
12	0.008593	0.066	0.4738
13	0.088639	0.6808	0.249315
14	0.046796	0.3595	0.360271
15	-0.242145	-1.8599	0.03394
16	-0.084232	-0.647	0.26007
17	0.120288	0.9239	0.179639

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.362537 & -2.7847 & 0.003595 \tabularnewline
2 & -0.425314 & -3.2669 & 0.000907 \tabularnewline
3 & -0.156222 & -1.2 & 0.117475 \tabularnewline
4 & -0.399451 & -3.0682 & 0.001625 \tabularnewline
5 & -0.209476 & -1.609 & 0.056476 \tabularnewline
6 & -0.152583 & -1.172 & 0.122952 \tabularnewline
7 & 0.113041 & 0.8683 & 0.194379 \tabularnewline
8 & 0.094449 & 0.7255 & 0.235515 \tabularnewline
9 & 0.366901 & 2.8182 & 0.003281 \tabularnewline
10 & -0.101025 & -0.776 & 0.220429 \tabularnewline
11 & -0.486168 & -3.7343 & 0.000213 \tabularnewline
12 & 0.008593 & 0.066 & 0.4738 \tabularnewline
13 & 0.088639 & 0.6808 & 0.249315 \tabularnewline
14 & 0.046796 & 0.3595 & 0.360271 \tabularnewline
15 & -0.242145 & -1.8599 & 0.03394 \tabularnewline
16 & -0.084232 & -0.647 & 0.26007 \tabularnewline
17 & 0.120288 & 0.9239 & 0.179639 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68454&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]-0.362537[/C][C]-2.7847[/C][C]0.003595[/C][/ROW]
[ROW][C]2[/C][C]-0.425314[/C][C]-3.2669[/C][C]0.000907[/C][/ROW]
[ROW][C]3[/C][C]-0.156222[/C][C]-1.2[/C][C]0.117475[/C][/ROW]
[ROW][C]4[/C][C]-0.399451[/C][C]-3.0682[/C][C]0.001625[/C][/ROW]
[ROW][C]5[/C][C]-0.209476[/C][C]-1.609[/C][C]0.056476[/C][/ROW]
[ROW][C]6[/C][C]-0.152583[/C][C]-1.172[/C][C]0.122952[/C][/ROW]
[ROW][C]7[/C][C]0.113041[/C][C]0.8683[/C][C]0.194379[/C][/ROW]
[ROW][C]8[/C][C]0.094449[/C][C]0.7255[/C][C]0.235515[/C][/ROW]
[ROW][C]9[/C][C]0.366901[/C][C]2.8182[/C][C]0.003281[/C][/ROW]
[ROW][C]10[/C][C]-0.101025[/C][C]-0.776[/C][C]0.220429[/C][/ROW]
[ROW][C]11[/C][C]-0.486168[/C][C]-3.7343[/C][C]0.000213[/C][/ROW]
[ROW][C]12[/C][C]0.008593[/C][C]0.066[/C][C]0.4738[/C][/ROW]
[ROW][C]13[/C][C]0.088639[/C][C]0.6808[/C][C]0.249315[/C][/ROW]
[ROW][C]14[/C][C]0.046796[/C][C]0.3595[/C][C]0.360271[/C][/ROW]
[ROW][C]15[/C][C]-0.242145[/C][C]-1.8599[/C][C]0.03394[/C][/ROW]
[ROW][C]16[/C][C]-0.084232[/C][C]-0.647[/C][C]0.26007[/C][/ROW]
[ROW][C]17[/C][C]0.120288[/C][C]0.9239[/C][C]0.179639[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68454&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68454&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	-0.362537	-2.7847	0.003595
2	-0.425314	-3.2669	0.000907
3	-0.156222	-1.2	0.117475
4	-0.399451	-3.0682	0.001625
5	-0.209476	-1.609	0.056476
6	-0.152583	-1.172	0.122952
7	0.113041	0.8683	0.194379
8	0.094449	0.7255	0.235515
9	0.366901	2.8182	0.003281
10	-0.101025	-0.776	0.220429
11	-0.486168	-3.7343	0.000213
12	0.008593	0.066	0.4738
13	0.088639	0.6808	0.249315
14	0.046796	0.3595	0.360271
15	-0.242145	-1.8599	0.03394
16	-0.084232	-0.647	0.26007
17	0.120288	0.9239	0.179639

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 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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Input Parameters & R Code