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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 12 Dec 2007 08:49:41 -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/12/t1197473677xijsfw5f8zozb9v.htm/, Retrieved Thu, 02 May 2024 14:34:03 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3225, Retrieved Thu, 02 May 2024 14:34:03 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

222

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

-       [(Partial) Autocorrelation Function] [Inducing stationa...] [2007-12-12 15:49:41] [578856645eee7b4b8f74dcf589866e9b] [Current]
- R PD    [(Partial) Autocorrelation Function] [ACF Energie] [2008-12-21 16:40:39] [dff692ae32125bdbbfc005d665e23b83] 

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Summary of compuational 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 compuational 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=3225&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]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=3225&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3225&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.4261	0
1	0.338828	2.855	0.002819
2	-0.100603	-0.8477	0.800273
3	-0.174268	-1.4684	0.926795
4	0.059681	0.5029	0.308303
5	-0.003171	-0.0267	0.510621
6	-0.160661	-1.3538	0.909946
7	-0.006698	-0.0564	0.522425
8	0.105647	0.8902	0.188183
9	0.144523	1.2178	0.113672
10	0.11952	1.0071	0.158655
11	0.06432	0.542	0.294769
12	-0.04223	-0.3558	0.638492
13	-0.078537	-0.6618	0.744867
14	-0.097246	-0.8194	0.792354
15	-0.15484	-1.3047	0.901896
16	-0.164251	-1.384	0.914654
17	0.104665	0.8819	0.190397

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4261 & 0 \tabularnewline
1 & 0.338828 & 2.855 & 0.002819 \tabularnewline
2 & -0.100603 & -0.8477 & 0.800273 \tabularnewline
3 & -0.174268 & -1.4684 & 0.926795 \tabularnewline
4 & 0.059681 & 0.5029 & 0.308303 \tabularnewline
5 & -0.003171 & -0.0267 & 0.510621 \tabularnewline
6 & -0.160661 & -1.3538 & 0.909946 \tabularnewline
7 & -0.006698 & -0.0564 & 0.522425 \tabularnewline
8 & 0.105647 & 0.8902 & 0.188183 \tabularnewline
9 & 0.144523 & 1.2178 & 0.113672 \tabularnewline
10 & 0.11952 & 1.0071 & 0.158655 \tabularnewline
11 & 0.06432 & 0.542 & 0.294769 \tabularnewline
12 & -0.04223 & -0.3558 & 0.638492 \tabularnewline
13 & -0.078537 & -0.6618 & 0.744867 \tabularnewline
14 & -0.097246 & -0.8194 & 0.792354 \tabularnewline
15 & -0.15484 & -1.3047 & 0.901896 \tabularnewline
16 & -0.164251 & -1.384 & 0.914654 \tabularnewline
17 & 0.104665 & 0.8819 & 0.190397 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3225&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]8.4261[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.338828[/C][C]2.855[/C][C]0.002819[/C][/ROW]
[ROW][C]2[/C][C]-0.100603[/C][C]-0.8477[/C][C]0.800273[/C][/ROW]
[ROW][C]3[/C][C]-0.174268[/C][C]-1.4684[/C][C]0.926795[/C][/ROW]
[ROW][C]4[/C][C]0.059681[/C][C]0.5029[/C][C]0.308303[/C][/ROW]
[ROW][C]5[/C][C]-0.003171[/C][C]-0.0267[/C][C]0.510621[/C][/ROW]
[ROW][C]6[/C][C]-0.160661[/C][C]-1.3538[/C][C]0.909946[/C][/ROW]
[ROW][C]7[/C][C]-0.006698[/C][C]-0.0564[/C][C]0.522425[/C][/ROW]
[ROW][C]8[/C][C]0.105647[/C][C]0.8902[/C][C]0.188183[/C][/ROW]
[ROW][C]9[/C][C]0.144523[/C][C]1.2178[/C][C]0.113672[/C][/ROW]
[ROW][C]10[/C][C]0.11952[/C][C]1.0071[/C][C]0.158655[/C][/ROW]
[ROW][C]11[/C][C]0.06432[/C][C]0.542[/C][C]0.294769[/C][/ROW]
[ROW][C]12[/C][C]-0.04223[/C][C]-0.3558[/C][C]0.638492[/C][/ROW]
[ROW][C]13[/C][C]-0.078537[/C][C]-0.6618[/C][C]0.744867[/C][/ROW]
[ROW][C]14[/C][C]-0.097246[/C][C]-0.8194[/C][C]0.792354[/C][/ROW]
[ROW][C]15[/C][C]-0.15484[/C][C]-1.3047[/C][C]0.901896[/C][/ROW]
[ROW][C]16[/C][C]-0.164251[/C][C]-1.384[/C][C]0.914654[/C][/ROW]
[ROW][C]17[/C][C]0.104665[/C][C]0.8819[/C][C]0.190397[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3225&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3225&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	8.4261	0
1	0.338828	2.855	0.002819
2	-0.100603	-0.8477	0.800273
3	-0.174268	-1.4684	0.926795
4	0.059681	0.5029	0.308303
5	-0.003171	-0.0267	0.510621
6	-0.160661	-1.3538	0.909946
7	-0.006698	-0.0564	0.522425
8	0.105647	0.8902	0.188183
9	0.144523	1.2178	0.113672
10	0.11952	1.0071	0.158655
11	0.06432	0.542	0.294769
12	-0.04223	-0.3558	0.638492
13	-0.078537	-0.6618	0.744867
14	-0.097246	-0.8194	0.792354
15	-0.15484	-1.3047	0.901896
16	-0.164251	-1.384	0.914654
17	0.104665	0.8819	0.190397

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.338828	2.855	0.002819
1	-0.243345	-2.0505	0.977994
2	-0.05936	-0.5002	0.690752
3	0.155122	1.3071	0.097702
4	-0.154379	-1.3008	0.901238
5	-0.125299	-1.0558	0.852678
6	0.175694	1.4804	0.071592
7	-0.029602	-0.2494	0.598127
8	0.08186	0.6898	0.246295
9	0.162828	1.372	0.087189
10	-0.035878	-0.3023	0.618352
11	-0.069517	-0.5858	0.720054
12	0.046933	0.3955	0.346843
13	-0.120586	-1.0161	0.843479
14	-0.151918	-1.2801	0.897659
15	-0.034256	-0.2886	0.613153
16	0.184569	1.5552	0.062172
17	-0.158786	-1.338	0.90741

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.338828 & 2.855 & 0.002819 \tabularnewline
1 & -0.243345 & -2.0505 & 0.977994 \tabularnewline
2 & -0.05936 & -0.5002 & 0.690752 \tabularnewline
3 & 0.155122 & 1.3071 & 0.097702 \tabularnewline
4 & -0.154379 & -1.3008 & 0.901238 \tabularnewline
5 & -0.125299 & -1.0558 & 0.852678 \tabularnewline
6 & 0.175694 & 1.4804 & 0.071592 \tabularnewline
7 & -0.029602 & -0.2494 & 0.598127 \tabularnewline
8 & 0.08186 & 0.6898 & 0.246295 \tabularnewline
9 & 0.162828 & 1.372 & 0.087189 \tabularnewline
10 & -0.035878 & -0.3023 & 0.618352 \tabularnewline
11 & -0.069517 & -0.5858 & 0.720054 \tabularnewline
12 & 0.046933 & 0.3955 & 0.346843 \tabularnewline
13 & -0.120586 & -1.0161 & 0.843479 \tabularnewline
14 & -0.151918 & -1.2801 & 0.897659 \tabularnewline
15 & -0.034256 & -0.2886 & 0.613153 \tabularnewline
16 & 0.184569 & 1.5552 & 0.062172 \tabularnewline
17 & -0.158786 & -1.338 & 0.90741 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3225&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]0.338828[/C][C]2.855[/C][C]0.002819[/C][/ROW]
[ROW][C]1[/C][C]-0.243345[/C][C]-2.0505[/C][C]0.977994[/C][/ROW]
[ROW][C]2[/C][C]-0.05936[/C][C]-0.5002[/C][C]0.690752[/C][/ROW]
[ROW][C]3[/C][C]0.155122[/C][C]1.3071[/C][C]0.097702[/C][/ROW]
[ROW][C]4[/C][C]-0.154379[/C][C]-1.3008[/C][C]0.901238[/C][/ROW]
[ROW][C]5[/C][C]-0.125299[/C][C]-1.0558[/C][C]0.852678[/C][/ROW]
[ROW][C]6[/C][C]0.175694[/C][C]1.4804[/C][C]0.071592[/C][/ROW]
[ROW][C]7[/C][C]-0.029602[/C][C]-0.2494[/C][C]0.598127[/C][/ROW]
[ROW][C]8[/C][C]0.08186[/C][C]0.6898[/C][C]0.246295[/C][/ROW]
[ROW][C]9[/C][C]0.162828[/C][C]1.372[/C][C]0.087189[/C][/ROW]
[ROW][C]10[/C][C]-0.035878[/C][C]-0.3023[/C][C]0.618352[/C][/ROW]
[ROW][C]11[/C][C]-0.069517[/C][C]-0.5858[/C][C]0.720054[/C][/ROW]
[ROW][C]12[/C][C]0.046933[/C][C]0.3955[/C][C]0.346843[/C][/ROW]
[ROW][C]13[/C][C]-0.120586[/C][C]-1.0161[/C][C]0.843479[/C][/ROW]
[ROW][C]14[/C][C]-0.151918[/C][C]-1.2801[/C][C]0.897659[/C][/ROW]
[ROW][C]15[/C][C]-0.034256[/C][C]-0.2886[/C][C]0.613153[/C][/ROW]
[ROW][C]16[/C][C]0.184569[/C][C]1.5552[/C][C]0.062172[/C][/ROW]
[ROW][C]17[/C][C]-0.158786[/C][C]-1.338[/C][C]0.90741[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3225&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3225&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	0.338828	2.855	0.002819
1	-0.243345	-2.0505	0.977994
2	-0.05936	-0.5002	0.690752
3	0.155122	1.3071	0.097702
4	-0.154379	-1.3008	0.901238
5	-0.125299	-1.0558	0.852678
6	0.175694	1.4804	0.071592
7	-0.029602	-0.2494	0.598127
8	0.08186	0.6898	0.246295
9	0.162828	1.372	0.087189
10	-0.035878	-0.3023	0.618352
11	-0.069517	-0.5858	0.720054
12	0.046933	0.3955	0.346843
13	-0.120586	-1.0161	0.843479
14	-0.151918	-1.2801	0.897659
15	-0.034256	-0.2886	0.613153
16	0.184569	1.5552	0.062172
17	-0.158786	-1.338	0.90741

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.2 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.2 ; par3 = 1 ; par4 = 0 ; 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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