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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 20 Dec 2009 06:38:04 -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/20/t1261316373pfedp7epmbz83qt.htm/, Retrieved Sat, 27 Apr 2024 09:14:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69880, Retrieved Sat, 27 Apr 2024 09:14:02 +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 1] [2009-12-20 13:38:04] [e458b4e05bf28a297f8af8d9f96e59d6] [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=69880&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=69880&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69880&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	0.804718	6.1812	0
2	0.712194	5.4705	0
3	0.690553	5.3042	1e-06
4	0.624572	4.7974	6e-06
5	0.58077	4.461	1.9e-05
6	0.482716	3.7078	0.000232
7	0.429842	3.3017	0.000818
8	0.370336	2.8446	0.003052
9	0.230936	1.7739	0.040624
10	0.162172	1.2457	0.108906
11	0.160055	1.2294	0.1119
12	0.115285	0.8855	0.189735
13	0.061281	0.4707	0.319793
14	-0.012012	-0.0923	0.463399
15	-0.083341	-0.6402	0.262276
16	-0.064834	-0.498	0.310167
17	-0.087305	-0.6706	0.252546

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.804718 & 6.1812 & 0 \tabularnewline
2 & 0.712194 & 5.4705 & 0 \tabularnewline
3 & 0.690553 & 5.3042 & 1e-06 \tabularnewline
4 & 0.624572 & 4.7974 & 6e-06 \tabularnewline
5 & 0.58077 & 4.461 & 1.9e-05 \tabularnewline
6 & 0.482716 & 3.7078 & 0.000232 \tabularnewline
7 & 0.429842 & 3.3017 & 0.000818 \tabularnewline
8 & 0.370336 & 2.8446 & 0.003052 \tabularnewline
9 & 0.230936 & 1.7739 & 0.040624 \tabularnewline
10 & 0.162172 & 1.2457 & 0.108906 \tabularnewline
11 & 0.160055 & 1.2294 & 0.1119 \tabularnewline
12 & 0.115285 & 0.8855 & 0.189735 \tabularnewline
13 & 0.061281 & 0.4707 & 0.319793 \tabularnewline
14 & -0.012012 & -0.0923 & 0.463399 \tabularnewline
15 & -0.083341 & -0.6402 & 0.262276 \tabularnewline
16 & -0.064834 & -0.498 & 0.310167 \tabularnewline
17 & -0.087305 & -0.6706 & 0.252546 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69880&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]0.804718[/C][C]6.1812[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.712194[/C][C]5.4705[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.690553[/C][C]5.3042[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]0.624572[/C][C]4.7974[/C][C]6e-06[/C][/ROW]
[ROW][C]5[/C][C]0.58077[/C][C]4.461[/C][C]1.9e-05[/C][/ROW]
[ROW][C]6[/C][C]0.482716[/C][C]3.7078[/C][C]0.000232[/C][/ROW]
[ROW][C]7[/C][C]0.429842[/C][C]3.3017[/C][C]0.000818[/C][/ROW]
[ROW][C]8[/C][C]0.370336[/C][C]2.8446[/C][C]0.003052[/C][/ROW]
[ROW][C]9[/C][C]0.230936[/C][C]1.7739[/C][C]0.040624[/C][/ROW]
[ROW][C]10[/C][C]0.162172[/C][C]1.2457[/C][C]0.108906[/C][/ROW]
[ROW][C]11[/C][C]0.160055[/C][C]1.2294[/C][C]0.1119[/C][/ROW]
[ROW][C]12[/C][C]0.115285[/C][C]0.8855[/C][C]0.189735[/C][/ROW]
[ROW][C]13[/C][C]0.061281[/C][C]0.4707[/C][C]0.319793[/C][/ROW]
[ROW][C]14[/C][C]-0.012012[/C][C]-0.0923[/C][C]0.463399[/C][/ROW]
[ROW][C]15[/C][C]-0.083341[/C][C]-0.6402[/C][C]0.262276[/C][/ROW]
[ROW][C]16[/C][C]-0.064834[/C][C]-0.498[/C][C]0.310167[/C][/ROW]
[ROW][C]17[/C][C]-0.087305[/C][C]-0.6706[/C][C]0.252546[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69880&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69880&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	0.804718	6.1812	0
2	0.712194	5.4705	0
3	0.690553	5.3042	1e-06
4	0.624572	4.7974	6e-06
5	0.58077	4.461	1.9e-05
6	0.482716	3.7078	0.000232
7	0.429842	3.3017	0.000818
8	0.370336	2.8446	0.003052
9	0.230936	1.7739	0.040624
10	0.162172	1.2457	0.108906
11	0.160055	1.2294	0.1119
12	0.115285	0.8855	0.189735
13	0.061281	0.4707	0.319793
14	-0.012012	-0.0923	0.463399
15	-0.083341	-0.6402	0.262276
16	-0.064834	-0.498	0.310167
17	-0.087305	-0.6706	0.252546

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.804718	6.1812	0
2	0.183364	1.4084	0.082124
3	0.220126	1.6908	0.048074
4	-0.018714	-0.1437	0.443096
5	0.04877	0.3746	0.354647
6	-0.182546	-1.4022	0.083053
7	0.019705	0.1514	0.440105
8	-0.084518	-0.6492	0.259365
9	-0.25014	-1.9214	0.029761
10	-0.037897	-0.2911	0.386
11	0.161442	1.2401	0.109932
12	0.023172	0.178	0.429671
13	-0.004507	-0.0346	0.486252
14	-0.096309	-0.7398	0.231189
15	-0.154673	-1.1881	0.119784
16	0.150586	1.1567	0.126034
17	0.044587	0.3425	0.366605

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.804718 & 6.1812 & 0 \tabularnewline
2 & 0.183364 & 1.4084 & 0.082124 \tabularnewline
3 & 0.220126 & 1.6908 & 0.048074 \tabularnewline
4 & -0.018714 & -0.1437 & 0.443096 \tabularnewline
5 & 0.04877 & 0.3746 & 0.354647 \tabularnewline
6 & -0.182546 & -1.4022 & 0.083053 \tabularnewline
7 & 0.019705 & 0.1514 & 0.440105 \tabularnewline
8 & -0.084518 & -0.6492 & 0.259365 \tabularnewline
9 & -0.25014 & -1.9214 & 0.029761 \tabularnewline
10 & -0.037897 & -0.2911 & 0.386 \tabularnewline
11 & 0.161442 & 1.2401 & 0.109932 \tabularnewline
12 & 0.023172 & 0.178 & 0.429671 \tabularnewline
13 & -0.004507 & -0.0346 & 0.486252 \tabularnewline
14 & -0.096309 & -0.7398 & 0.231189 \tabularnewline
15 & -0.154673 & -1.1881 & 0.119784 \tabularnewline
16 & 0.150586 & 1.1567 & 0.126034 \tabularnewline
17 & 0.044587 & 0.3425 & 0.366605 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69880&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]0.804718[/C][C]6.1812[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.183364[/C][C]1.4084[/C][C]0.082124[/C][/ROW]
[ROW][C]3[/C][C]0.220126[/C][C]1.6908[/C][C]0.048074[/C][/ROW]
[ROW][C]4[/C][C]-0.018714[/C][C]-0.1437[/C][C]0.443096[/C][/ROW]
[ROW][C]5[/C][C]0.04877[/C][C]0.3746[/C][C]0.354647[/C][/ROW]
[ROW][C]6[/C][C]-0.182546[/C][C]-1.4022[/C][C]0.083053[/C][/ROW]
[ROW][C]7[/C][C]0.019705[/C][C]0.1514[/C][C]0.440105[/C][/ROW]
[ROW][C]8[/C][C]-0.084518[/C][C]-0.6492[/C][C]0.259365[/C][/ROW]
[ROW][C]9[/C][C]-0.25014[/C][C]-1.9214[/C][C]0.029761[/C][/ROW]
[ROW][C]10[/C][C]-0.037897[/C][C]-0.2911[/C][C]0.386[/C][/ROW]
[ROW][C]11[/C][C]0.161442[/C][C]1.2401[/C][C]0.109932[/C][/ROW]
[ROW][C]12[/C][C]0.023172[/C][C]0.178[/C][C]0.429671[/C][/ROW]
[ROW][C]13[/C][C]-0.004507[/C][C]-0.0346[/C][C]0.486252[/C][/ROW]
[ROW][C]14[/C][C]-0.096309[/C][C]-0.7398[/C][C]0.231189[/C][/ROW]
[ROW][C]15[/C][C]-0.154673[/C][C]-1.1881[/C][C]0.119784[/C][/ROW]
[ROW][C]16[/C][C]0.150586[/C][C]1.1567[/C][C]0.126034[/C][/ROW]
[ROW][C]17[/C][C]0.044587[/C][C]0.3425[/C][C]0.366605[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69880&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69880&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	0.804718	6.1812	0
2	0.183364	1.4084	0.082124
3	0.220126	1.6908	0.048074
4	-0.018714	-0.1437	0.443096
5	0.04877	0.3746	0.354647
6	-0.182546	-1.4022	0.083053
7	0.019705	0.1514	0.440105
8	-0.084518	-0.6492	0.259365
9	-0.25014	-1.9214	0.029761
10	-0.037897	-0.2911	0.386
11	0.161442	1.2401	0.109932
12	0.023172	0.178	0.429671
13	-0.004507	-0.0346	0.486252
14	-0.096309	-0.7398	0.231189
15	-0.154673	-1.1881	0.119784
16	0.150586	1.1567	0.126034
17	0.044587	0.3425	0.366605

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 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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