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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 04 Dec 2007 15:11:13 -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/04/t1196805621ly17xxr9rzov8il.htm/, Retrieved Thu, 16 Jan 2025 19:50:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2459, Retrieved Thu, 16 Jan 2025 19:50:50 +0000

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Estimated Impact

221

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-       [(Partial) Autocorrelation Function] [] [2007-12-04 22:11:13] [a5d60d21ad00400c5f1209c78aa5829c] [Current]

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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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2459&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2459&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2459&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	9.5917	0
1	0.134407	1.2892	0.100282
2	-0.11798	-1.1316	0.869634
3	0.162789	1.5614	0.06093
4	-0.041444	-0.3975	0.654046
5	-0.222264	-2.1319	0.982159
6	-0.095278	-0.9139	0.818414
7	0.052544	0.504	0.307739
8	-0.146696	-1.4071	0.91861
9	-0.095177	-0.9129	0.818161
10	0.295614	2.8354	0.002813
11	0.269833	2.5881	0.005607
12	-0.102678	-0.9849	0.83636
13	0.032534	0.3121	0.377853
14	0.125104	1.2	0.116619
15	-0.253383	-2.4304	0.991488
16	-0.10215	-0.9798	0.835119
17	0.05446	0.5224	0.301336
18	-0.060613	-0.5814	0.718796

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.5917 & 0 \tabularnewline
1 & 0.134407 & 1.2892 & 0.100282 \tabularnewline
2 & -0.11798 & -1.1316 & 0.869634 \tabularnewline
3 & 0.162789 & 1.5614 & 0.06093 \tabularnewline
4 & -0.041444 & -0.3975 & 0.654046 \tabularnewline
5 & -0.222264 & -2.1319 & 0.982159 \tabularnewline
6 & -0.095278 & -0.9139 & 0.818414 \tabularnewline
7 & 0.052544 & 0.504 & 0.307739 \tabularnewline
8 & -0.146696 & -1.4071 & 0.91861 \tabularnewline
9 & -0.095177 & -0.9129 & 0.818161 \tabularnewline
10 & 0.295614 & 2.8354 & 0.002813 \tabularnewline
11 & 0.269833 & 2.5881 & 0.005607 \tabularnewline
12 & -0.102678 & -0.9849 & 0.83636 \tabularnewline
13 & 0.032534 & 0.3121 & 0.377853 \tabularnewline
14 & 0.125104 & 1.2 & 0.116619 \tabularnewline
15 & -0.253383 & -2.4304 & 0.991488 \tabularnewline
16 & -0.10215 & -0.9798 & 0.835119 \tabularnewline
17 & 0.05446 & 0.5224 & 0.301336 \tabularnewline
18 & -0.060613 & -0.5814 & 0.718796 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2459&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]9.5917[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.134407[/C][C]1.2892[/C][C]0.100282[/C][/ROW]
[ROW][C]2[/C][C]-0.11798[/C][C]-1.1316[/C][C]0.869634[/C][/ROW]
[ROW][C]3[/C][C]0.162789[/C][C]1.5614[/C][C]0.06093[/C][/ROW]
[ROW][C]4[/C][C]-0.041444[/C][C]-0.3975[/C][C]0.654046[/C][/ROW]
[ROW][C]5[/C][C]-0.222264[/C][C]-2.1319[/C][C]0.982159[/C][/ROW]
[ROW][C]6[/C][C]-0.095278[/C][C]-0.9139[/C][C]0.818414[/C][/ROW]
[ROW][C]7[/C][C]0.052544[/C][C]0.504[/C][C]0.307739[/C][/ROW]
[ROW][C]8[/C][C]-0.146696[/C][C]-1.4071[/C][C]0.91861[/C][/ROW]
[ROW][C]9[/C][C]-0.095177[/C][C]-0.9129[/C][C]0.818161[/C][/ROW]
[ROW][C]10[/C][C]0.295614[/C][C]2.8354[/C][C]0.002813[/C][/ROW]
[ROW][C]11[/C][C]0.269833[/C][C]2.5881[/C][C]0.005607[/C][/ROW]
[ROW][C]12[/C][C]-0.102678[/C][C]-0.9849[/C][C]0.83636[/C][/ROW]
[ROW][C]13[/C][C]0.032534[/C][C]0.3121[/C][C]0.377853[/C][/ROW]
[ROW][C]14[/C][C]0.125104[/C][C]1.2[/C][C]0.116619[/C][/ROW]
[ROW][C]15[/C][C]-0.253383[/C][C]-2.4304[/C][C]0.991488[/C][/ROW]
[ROW][C]16[/C][C]-0.10215[/C][C]-0.9798[/C][C]0.835119[/C][/ROW]
[ROW][C]17[/C][C]0.05446[/C][C]0.5224[/C][C]0.301336[/C][/ROW]
[ROW][C]18[/C][C]-0.060613[/C][C]-0.5814[/C][C]0.718796[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2459&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2459&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	9.5917	0
1	0.134407	1.2892	0.100282
2	-0.11798	-1.1316	0.869634
3	0.162789	1.5614	0.06093
4	-0.041444	-0.3975	0.654046
5	-0.222264	-2.1319	0.982159
6	-0.095278	-0.9139	0.818414
7	0.052544	0.504	0.307739
8	-0.146696	-1.4071	0.91861
9	-0.095177	-0.9129	0.818161
10	0.295614	2.8354	0.002813
11	0.269833	2.5881	0.005607
12	-0.102678	-0.9849	0.83636
13	0.032534	0.3121	0.377853
14	0.125104	1.2	0.116619
15	-0.253383	-2.4304	0.991488
16	-0.10215	-0.9798	0.835119
17	0.05446	0.5224	0.301336
18	-0.060613	-0.5814	0.718796

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.134407	1.2892	0.100282
1	-0.138548	-1.3289	0.906418
2	0.20711	1.9865	0.024975
3	-0.129043	-1.2377	0.890519
4	-0.152014	-1.4581	0.925886
5	-0.094469	-0.9061	0.81638
6	0.064333	0.6171	0.26936
7	-0.145183	-1.3925	0.916443
8	-0.026928	-0.2583	0.601617
9	0.246203	2.3615	0.010155
10	0.227777	2.1848	0.015724
11	-0.129775	-1.2448	0.891809
12	-0.01985	-0.1904	0.57529
13	0.021272	0.204	0.419388
14	-0.163543	-1.5686	0.939918
15	0.054171	0.5196	0.302298
16	-0.030451	-0.2921	0.614558
17	0.055651	0.5338	0.297389
18	-0.060154	-0.577	0.717318

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.134407 & 1.2892 & 0.100282 \tabularnewline
1 & -0.138548 & -1.3289 & 0.906418 \tabularnewline
2 & 0.20711 & 1.9865 & 0.024975 \tabularnewline
3 & -0.129043 & -1.2377 & 0.890519 \tabularnewline
4 & -0.152014 & -1.4581 & 0.925886 \tabularnewline
5 & -0.094469 & -0.9061 & 0.81638 \tabularnewline
6 & 0.064333 & 0.6171 & 0.26936 \tabularnewline
7 & -0.145183 & -1.3925 & 0.916443 \tabularnewline
8 & -0.026928 & -0.2583 & 0.601617 \tabularnewline
9 & 0.246203 & 2.3615 & 0.010155 \tabularnewline
10 & 0.227777 & 2.1848 & 0.015724 \tabularnewline
11 & -0.129775 & -1.2448 & 0.891809 \tabularnewline
12 & -0.01985 & -0.1904 & 0.57529 \tabularnewline
13 & 0.021272 & 0.204 & 0.419388 \tabularnewline
14 & -0.163543 & -1.5686 & 0.939918 \tabularnewline
15 & 0.054171 & 0.5196 & 0.302298 \tabularnewline
16 & -0.030451 & -0.2921 & 0.614558 \tabularnewline
17 & 0.055651 & 0.5338 & 0.297389 \tabularnewline
18 & -0.060154 & -0.577 & 0.717318 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2459&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]0.134407[/C][C]1.2892[/C][C]0.100282[/C][/ROW]
[ROW][C]1[/C][C]-0.138548[/C][C]-1.3289[/C][C]0.906418[/C][/ROW]
[ROW][C]2[/C][C]0.20711[/C][C]1.9865[/C][C]0.024975[/C][/ROW]
[ROW][C]3[/C][C]-0.129043[/C][C]-1.2377[/C][C]0.890519[/C][/ROW]
[ROW][C]4[/C][C]-0.152014[/C][C]-1.4581[/C][C]0.925886[/C][/ROW]
[ROW][C]5[/C][C]-0.094469[/C][C]-0.9061[/C][C]0.81638[/C][/ROW]
[ROW][C]6[/C][C]0.064333[/C][C]0.6171[/C][C]0.26936[/C][/ROW]
[ROW][C]7[/C][C]-0.145183[/C][C]-1.3925[/C][C]0.916443[/C][/ROW]
[ROW][C]8[/C][C]-0.026928[/C][C]-0.2583[/C][C]0.601617[/C][/ROW]
[ROW][C]9[/C][C]0.246203[/C][C]2.3615[/C][C]0.010155[/C][/ROW]
[ROW][C]10[/C][C]0.227777[/C][C]2.1848[/C][C]0.015724[/C][/ROW]
[ROW][C]11[/C][C]-0.129775[/C][C]-1.2448[/C][C]0.891809[/C][/ROW]
[ROW][C]12[/C][C]-0.01985[/C][C]-0.1904[/C][C]0.57529[/C][/ROW]
[ROW][C]13[/C][C]0.021272[/C][C]0.204[/C][C]0.419388[/C][/ROW]
[ROW][C]14[/C][C]-0.163543[/C][C]-1.5686[/C][C]0.939918[/C][/ROW]
[ROW][C]15[/C][C]0.054171[/C][C]0.5196[/C][C]0.302298[/C][/ROW]
[ROW][C]16[/C][C]-0.030451[/C][C]-0.2921[/C][C]0.614558[/C][/ROW]
[ROW][C]17[/C][C]0.055651[/C][C]0.5338[/C][C]0.297389[/C][/ROW]
[ROW][C]18[/C][C]-0.060154[/C][C]-0.577[/C][C]0.717318[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2459&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2459&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	0.134407	1.2892	0.100282
1	-0.138548	-1.3289	0.906418
2	0.20711	1.9865	0.024975
3	-0.129043	-1.2377	0.890519
4	-0.152014	-1.4581	0.925886
5	-0.094469	-0.9061	0.81638
6	0.064333	0.6171	0.26936
7	-0.145183	-1.3925	0.916443
8	-0.026928	-0.2583	0.601617
9	0.246203	2.3615	0.010155
10	0.227777	2.1848	0.015724
11	-0.129775	-1.2448	0.891809
12	-0.01985	-0.1904	0.57529
13	0.021272	0.204	0.419388
14	-0.163543	-1.5686	0.939918
15	0.054171	0.5196	0.302298
16	-0.030451	-0.2921	0.614558
17	0.055651	0.5338	0.297389
18	-0.060154	-0.577	0.717318

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 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; 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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