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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Nov 2007 03:21:31 -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/Nov/23/t1195812782sok9nwolx8gd5kc.htm/, Retrieved Mon, 29 Apr 2024 04:58:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6129, Retrieved Mon, 29 Apr 2024 04:58:55 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Q2, groep 1

Estimated Impact

208

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

-       [(Partial) Autocorrelation Function] [Q2, groep 1] [2007-11-23 10:21:31] [ce556af355e2eff84137e549c6ea8397] [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=6129&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=6129&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6129&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	8.9443	0
1	0.632623	5.6584	0
2	0.48402	4.3292	2.1e-05
3	0.643082	5.7519	0
4	0.450469	4.0291	6.3e-05
5	0.449076	4.0167	6.6e-05
6	0.626648	5.6049	0
7	0.391452	3.5013	0.00038
8	0.295657	2.6444	0.004923
9	0.414018	3.7031	0.000195
10	0.212745	1.9029	0.030329
11	0.273792	2.4489	0.008258
12	0.524841	4.6943	5e-06
13	0.286666	2.564	0.006109
14	0.176823	1.5816	0.058848
15	0.291893	2.6108	0.005391
16	0.13568	1.2136	0.114243
17	0.132598	1.186	0.119568
18	0.303597	2.7155	0.004053

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.9443 & 0 \tabularnewline
1 & 0.632623 & 5.6584 & 0 \tabularnewline
2 & 0.48402 & 4.3292 & 2.1e-05 \tabularnewline
3 & 0.643082 & 5.7519 & 0 \tabularnewline
4 & 0.450469 & 4.0291 & 6.3e-05 \tabularnewline
5 & 0.449076 & 4.0167 & 6.6e-05 \tabularnewline
6 & 0.626648 & 5.6049 & 0 \tabularnewline
7 & 0.391452 & 3.5013 & 0.00038 \tabularnewline
8 & 0.295657 & 2.6444 & 0.004923 \tabularnewline
9 & 0.414018 & 3.7031 & 0.000195 \tabularnewline
10 & 0.212745 & 1.9029 & 0.030329 \tabularnewline
11 & 0.273792 & 2.4489 & 0.008258 \tabularnewline
12 & 0.524841 & 4.6943 & 5e-06 \tabularnewline
13 & 0.286666 & 2.564 & 0.006109 \tabularnewline
14 & 0.176823 & 1.5816 & 0.058848 \tabularnewline
15 & 0.291893 & 2.6108 & 0.005391 \tabularnewline
16 & 0.13568 & 1.2136 & 0.114243 \tabularnewline
17 & 0.132598 & 1.186 & 0.119568 \tabularnewline
18 & 0.303597 & 2.7155 & 0.004053 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6129&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]8.9443[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.632623[/C][C]5.6584[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.48402[/C][C]4.3292[/C][C]2.1e-05[/C][/ROW]
[ROW][C]3[/C][C]0.643082[/C][C]5.7519[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.450469[/C][C]4.0291[/C][C]6.3e-05[/C][/ROW]
[ROW][C]5[/C][C]0.449076[/C][C]4.0167[/C][C]6.6e-05[/C][/ROW]
[ROW][C]6[/C][C]0.626648[/C][C]5.6049[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.391452[/C][C]3.5013[/C][C]0.00038[/C][/ROW]
[ROW][C]8[/C][C]0.295657[/C][C]2.6444[/C][C]0.004923[/C][/ROW]
[ROW][C]9[/C][C]0.414018[/C][C]3.7031[/C][C]0.000195[/C][/ROW]
[ROW][C]10[/C][C]0.212745[/C][C]1.9029[/C][C]0.030329[/C][/ROW]
[ROW][C]11[/C][C]0.273792[/C][C]2.4489[/C][C]0.008258[/C][/ROW]
[ROW][C]12[/C][C]0.524841[/C][C]4.6943[/C][C]5e-06[/C][/ROW]
[ROW][C]13[/C][C]0.286666[/C][C]2.564[/C][C]0.006109[/C][/ROW]
[ROW][C]14[/C][C]0.176823[/C][C]1.5816[/C][C]0.058848[/C][/ROW]
[ROW][C]15[/C][C]0.291893[/C][C]2.6108[/C][C]0.005391[/C][/ROW]
[ROW][C]16[/C][C]0.13568[/C][C]1.2136[/C][C]0.114243[/C][/ROW]
[ROW][C]17[/C][C]0.132598[/C][C]1.186[/C][C]0.119568[/C][/ROW]
[ROW][C]18[/C][C]0.303597[/C][C]2.7155[/C][C]0.004053[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6129&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6129&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	8.9443	0
1	0.632623	5.6584	0
2	0.48402	4.3292	2.1e-05
3	0.643082	5.7519	0
4	0.450469	4.0291	6.3e-05
5	0.449076	4.0167	6.6e-05
6	0.626648	5.6049	0
7	0.391452	3.5013	0.00038
8	0.295657	2.6444	0.004923
9	0.414018	3.7031	0.000195
10	0.212745	1.9029	0.030329
11	0.273792	2.4489	0.008258
12	0.524841	4.6943	5e-06
13	0.286666	2.564	0.006109
14	0.176823	1.5816	0.058848
15	0.291893	2.6108	0.005391
16	0.13568	1.2136	0.114243
17	0.132598	1.186	0.119568
18	0.303597	2.7155	0.004053

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.632623	5.6584	0
1	0.13973	1.2498	0.107511
2	0.495289	4.43	1.5e-05
3	-0.23772	-2.1262	0.981716
4	0.337652	3.0201	0.001696
5	0.166068	1.4854	0.07069
6	-0.233377	-2.0874	0.979982
7	-0.031376	-0.2806	0.610144
8	-0.045992	-0.4114	0.659048
9	-0.182705	-1.6342	0.946923
10	0.32743	2.9286	0.002217
11	0.248923	2.2264	0.014399
12	-0.170641	-1.5263	0.934555
13	-0.097619	-0.8731	0.807398
14	-0.152562	-1.3646	0.911891
15	0.009113	0.0815	0.46762
16	-0.05672	-0.5073	0.693336
17	0.017288	0.1546	0.438751
18	-0.006186	-0.0553	0.521992

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.632623 & 5.6584 & 0 \tabularnewline
1 & 0.13973 & 1.2498 & 0.107511 \tabularnewline
2 & 0.495289 & 4.43 & 1.5e-05 \tabularnewline
3 & -0.23772 & -2.1262 & 0.981716 \tabularnewline
4 & 0.337652 & 3.0201 & 0.001696 \tabularnewline
5 & 0.166068 & 1.4854 & 0.07069 \tabularnewline
6 & -0.233377 & -2.0874 & 0.979982 \tabularnewline
7 & -0.031376 & -0.2806 & 0.610144 \tabularnewline
8 & -0.045992 & -0.4114 & 0.659048 \tabularnewline
9 & -0.182705 & -1.6342 & 0.946923 \tabularnewline
10 & 0.32743 & 2.9286 & 0.002217 \tabularnewline
11 & 0.248923 & 2.2264 & 0.014399 \tabularnewline
12 & -0.170641 & -1.5263 & 0.934555 \tabularnewline
13 & -0.097619 & -0.8731 & 0.807398 \tabularnewline
14 & -0.152562 & -1.3646 & 0.911891 \tabularnewline
15 & 0.009113 & 0.0815 & 0.46762 \tabularnewline
16 & -0.05672 & -0.5073 & 0.693336 \tabularnewline
17 & 0.017288 & 0.1546 & 0.438751 \tabularnewline
18 & -0.006186 & -0.0553 & 0.521992 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6129&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]0.632623[/C][C]5.6584[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.13973[/C][C]1.2498[/C][C]0.107511[/C][/ROW]
[ROW][C]2[/C][C]0.495289[/C][C]4.43[/C][C]1.5e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.23772[/C][C]-2.1262[/C][C]0.981716[/C][/ROW]
[ROW][C]4[/C][C]0.337652[/C][C]3.0201[/C][C]0.001696[/C][/ROW]
[ROW][C]5[/C][C]0.166068[/C][C]1.4854[/C][C]0.07069[/C][/ROW]
[ROW][C]6[/C][C]-0.233377[/C][C]-2.0874[/C][C]0.979982[/C][/ROW]
[ROW][C]7[/C][C]-0.031376[/C][C]-0.2806[/C][C]0.610144[/C][/ROW]
[ROW][C]8[/C][C]-0.045992[/C][C]-0.4114[/C][C]0.659048[/C][/ROW]
[ROW][C]9[/C][C]-0.182705[/C][C]-1.6342[/C][C]0.946923[/C][/ROW]
[ROW][C]10[/C][C]0.32743[/C][C]2.9286[/C][C]0.002217[/C][/ROW]
[ROW][C]11[/C][C]0.248923[/C][C]2.2264[/C][C]0.014399[/C][/ROW]
[ROW][C]12[/C][C]-0.170641[/C][C]-1.5263[/C][C]0.934555[/C][/ROW]
[ROW][C]13[/C][C]-0.097619[/C][C]-0.8731[/C][C]0.807398[/C][/ROW]
[ROW][C]14[/C][C]-0.152562[/C][C]-1.3646[/C][C]0.911891[/C][/ROW]
[ROW][C]15[/C][C]0.009113[/C][C]0.0815[/C][C]0.46762[/C][/ROW]
[ROW][C]16[/C][C]-0.05672[/C][C]-0.5073[/C][C]0.693336[/C][/ROW]
[ROW][C]17[/C][C]0.017288[/C][C]0.1546[/C][C]0.438751[/C][/ROW]
[ROW][C]18[/C][C]-0.006186[/C][C]-0.0553[/C][C]0.521992[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6129&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6129&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	0.632623	5.6584	0
1	0.13973	1.2498	0.107511
2	0.495289	4.43	1.5e-05
3	-0.23772	-2.1262	0.981716
4	0.337652	3.0201	0.001696
5	0.166068	1.4854	0.07069
6	-0.233377	-2.0874	0.979982
7	-0.031376	-0.2806	0.610144
8	-0.045992	-0.4114	0.659048
9	-0.182705	-1.6342	0.946923
10	0.32743	2.9286	0.002217
11	0.248923	2.2264	0.014399
12	-0.170641	-1.5263	0.934555
13	-0.097619	-0.8731	0.807398
14	-0.152562	-1.3646	0.911891
15	0.009113	0.0815	0.46762
16	-0.05672	-0.5073	0.693336
17	0.017288	0.1546	0.438751
18	-0.006186	-0.0553	0.521992

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 ;

Parameters (R input):

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