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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 27 Nov 2008 15:25:58 -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/2008/Nov/27/t1227824841g8bbcb3dz0efb3z.htm/, Retrieved Sun, 19 May 2024 12:39:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=25928, Retrieved Sun, 19 May 2024 12:39:43 +0000

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Original text written by user:

d=0 D=0

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

182

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

F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:40:39] [b98453cac15ba1066b407e146608df68]
F       [Law of Averages] [Random Walk Simul...] [2008-11-27 19:45:04] [58bf45a666dc5198906262e8815a9722]
F RMPD    [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-11-27 22:08:29] [58bf45a666dc5198906262e8815a9722]
- RMP         [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2008-11-27 22:25:58] [63db34dadd44fb018112addcdefe949f] [Current]
F   P           [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2008-11-28 10:12:46] [58bf45a666dc5198906262e8815a9722] 
F   P           [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2008-11-28 10:15:39] [58bf45a666dc5198906262e8815a9722] 
F   P           [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2008-11-28 10:17:42] [58bf45a666dc5198906262e8815a9722] 
F   P           [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2008-11-28 10:20:24] [58bf45a666dc5198906262e8815a9722] 
-   PD          [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2008-11-28 10:23:41] [58bf45a666dc5198906262e8815a9722] 
-   PD          [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2008-11-28 10:26:03] [58bf45a666dc5198906262e8815a9722] 
-   PD          [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2008-11-28 10:26:03] [58bf45a666dc5198906262e8815a9722] 
-   PD          [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2008-11-28 10:29:39] [58bf45a666dc5198906262e8815a9722] 
-   PD          [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2008-11-28 10:31:19] [58bf45a666dc5198906262e8815a9722] 

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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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25928&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25928&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25928&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.095247	0.7378	0.231763
2	-0.150608	-1.1666	0.123993
3	0.168679	1.3066	0.09817
4	0.158939	1.2311	0.111538
5	0.10549	0.8171	0.208546
6	0.266965	2.0679	0.021485
7	-0.024652	-0.191	0.424604
8	0.114606	0.8877	0.189114
9	0.057414	0.4447	0.32906
10	-0.210477	-1.6303	0.054134
11	0.039141	0.3032	0.381399
12	0.528496	4.0937	6.4e-05
13	-0.011068	-0.0857	0.465982
14	-0.171496	-1.3284	0.094537
15	-0.018534	-0.1436	0.443163
16	0.006862	0.0532	0.478893
17	0.043367	0.3359	0.369051

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.095247 & 0.7378 & 0.231763 \tabularnewline
2 & -0.150608 & -1.1666 & 0.123993 \tabularnewline
3 & 0.168679 & 1.3066 & 0.09817 \tabularnewline
4 & 0.158939 & 1.2311 & 0.111538 \tabularnewline
5 & 0.10549 & 0.8171 & 0.208546 \tabularnewline
6 & 0.266965 & 2.0679 & 0.021485 \tabularnewline
7 & -0.024652 & -0.191 & 0.424604 \tabularnewline
8 & 0.114606 & 0.8877 & 0.189114 \tabularnewline
9 & 0.057414 & 0.4447 & 0.32906 \tabularnewline
10 & -0.210477 & -1.6303 & 0.054134 \tabularnewline
11 & 0.039141 & 0.3032 & 0.381399 \tabularnewline
12 & 0.528496 & 4.0937 & 6.4e-05 \tabularnewline
13 & -0.011068 & -0.0857 & 0.465982 \tabularnewline
14 & -0.171496 & -1.3284 & 0.094537 \tabularnewline
15 & -0.018534 & -0.1436 & 0.443163 \tabularnewline
16 & 0.006862 & 0.0532 & 0.478893 \tabularnewline
17 & 0.043367 & 0.3359 & 0.369051 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25928&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]0.095247[/C][C]0.7378[/C][C]0.231763[/C][/ROW]
[ROW][C]2[/C][C]-0.150608[/C][C]-1.1666[/C][C]0.123993[/C][/ROW]
[ROW][C]3[/C][C]0.168679[/C][C]1.3066[/C][C]0.09817[/C][/ROW]
[ROW][C]4[/C][C]0.158939[/C][C]1.2311[/C][C]0.111538[/C][/ROW]
[ROW][C]5[/C][C]0.10549[/C][C]0.8171[/C][C]0.208546[/C][/ROW]
[ROW][C]6[/C][C]0.266965[/C][C]2.0679[/C][C]0.021485[/C][/ROW]
[ROW][C]7[/C][C]-0.024652[/C][C]-0.191[/C][C]0.424604[/C][/ROW]
[ROW][C]8[/C][C]0.114606[/C][C]0.8877[/C][C]0.189114[/C][/ROW]
[ROW][C]9[/C][C]0.057414[/C][C]0.4447[/C][C]0.32906[/C][/ROW]
[ROW][C]10[/C][C]-0.210477[/C][C]-1.6303[/C][C]0.054134[/C][/ROW]
[ROW][C]11[/C][C]0.039141[/C][C]0.3032[/C][C]0.381399[/C][/ROW]
[ROW][C]12[/C][C]0.528496[/C][C]4.0937[/C][C]6.4e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.011068[/C][C]-0.0857[/C][C]0.465982[/C][/ROW]
[ROW][C]14[/C][C]-0.171496[/C][C]-1.3284[/C][C]0.094537[/C][/ROW]
[ROW][C]15[/C][C]-0.018534[/C][C]-0.1436[/C][C]0.443163[/C][/ROW]
[ROW][C]16[/C][C]0.006862[/C][C]0.0532[/C][C]0.478893[/C][/ROW]
[ROW][C]17[/C][C]0.043367[/C][C]0.3359[/C][C]0.369051[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25928&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25928&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	0.095247	0.7378	0.231763
2	-0.150608	-1.1666	0.123993
3	0.168679	1.3066	0.09817
4	0.158939	1.2311	0.111538
5	0.10549	0.8171	0.208546
6	0.266965	2.0679	0.021485
7	-0.024652	-0.191	0.424604
8	0.114606	0.8877	0.189114
9	0.057414	0.4447	0.32906
10	-0.210477	-1.6303	0.054134
11	0.039141	0.3032	0.381399
12	0.528496	4.0937	6.4e-05
13	-0.011068	-0.0857	0.465982
14	-0.171496	-1.3284	0.094537
15	-0.018534	-0.1436	0.443163
16	0.006862	0.0532	0.478893
17	0.043367	0.3359	0.369051

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.095247	0.7378	0.231763
2	-0.161142	-1.2482	0.108404
3	0.20792	1.6105	0.056264
4	0.094314	0.7306	0.233947
5	0.146537	1.1351	0.130431
6	0.275703	2.1356	0.018402
7	-0.092425	-0.7159	0.23841
8	0.202296	1.567	0.06119
9	-0.146351	-1.1336	0.130729
10	-0.267591	-2.0727	0.02125
11	-0.007167	-0.0555	0.477956
12	0.43508	3.3701	0.000659
13	0.000712	0.0055	0.497808
14	-0.0355	-0.275	0.392138
15	-0.136098	-1.0542	0.148007
16	-0.109612	-0.849	0.199615
17	-0.090598	-0.7018	0.242769

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.095247 & 0.7378 & 0.231763 \tabularnewline
2 & -0.161142 & -1.2482 & 0.108404 \tabularnewline
3 & 0.20792 & 1.6105 & 0.056264 \tabularnewline
4 & 0.094314 & 0.7306 & 0.233947 \tabularnewline
5 & 0.146537 & 1.1351 & 0.130431 \tabularnewline
6 & 0.275703 & 2.1356 & 0.018402 \tabularnewline
7 & -0.092425 & -0.7159 & 0.23841 \tabularnewline
8 & 0.202296 & 1.567 & 0.06119 \tabularnewline
9 & -0.146351 & -1.1336 & 0.130729 \tabularnewline
10 & -0.267591 & -2.0727 & 0.02125 \tabularnewline
11 & -0.007167 & -0.0555 & 0.477956 \tabularnewline
12 & 0.43508 & 3.3701 & 0.000659 \tabularnewline
13 & 0.000712 & 0.0055 & 0.497808 \tabularnewline
14 & -0.0355 & -0.275 & 0.392138 \tabularnewline
15 & -0.136098 & -1.0542 & 0.148007 \tabularnewline
16 & -0.109612 & -0.849 & 0.199615 \tabularnewline
17 & -0.090598 & -0.7018 & 0.242769 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=25928&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]0.095247[/C][C]0.7378[/C][C]0.231763[/C][/ROW]
[ROW][C]2[/C][C]-0.161142[/C][C]-1.2482[/C][C]0.108404[/C][/ROW]
[ROW][C]3[/C][C]0.20792[/C][C]1.6105[/C][C]0.056264[/C][/ROW]
[ROW][C]4[/C][C]0.094314[/C][C]0.7306[/C][C]0.233947[/C][/ROW]
[ROW][C]5[/C][C]0.146537[/C][C]1.1351[/C][C]0.130431[/C][/ROW]
[ROW][C]6[/C][C]0.275703[/C][C]2.1356[/C][C]0.018402[/C][/ROW]
[ROW][C]7[/C][C]-0.092425[/C][C]-0.7159[/C][C]0.23841[/C][/ROW]
[ROW][C]8[/C][C]0.202296[/C][C]1.567[/C][C]0.06119[/C][/ROW]
[ROW][C]9[/C][C]-0.146351[/C][C]-1.1336[/C][C]0.130729[/C][/ROW]
[ROW][C]10[/C][C]-0.267591[/C][C]-2.0727[/C][C]0.02125[/C][/ROW]
[ROW][C]11[/C][C]-0.007167[/C][C]-0.0555[/C][C]0.477956[/C][/ROW]
[ROW][C]12[/C][C]0.43508[/C][C]3.3701[/C][C]0.000659[/C][/ROW]
[ROW][C]13[/C][C]0.000712[/C][C]0.0055[/C][C]0.497808[/C][/ROW]
[ROW][C]14[/C][C]-0.0355[/C][C]-0.275[/C][C]0.392138[/C][/ROW]
[ROW][C]15[/C][C]-0.136098[/C][C]-1.0542[/C][C]0.148007[/C][/ROW]
[ROW][C]16[/C][C]-0.109612[/C][C]-0.849[/C][C]0.199615[/C][/ROW]
[ROW][C]17[/C][C]-0.090598[/C][C]-0.7018[/C][C]0.242769[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=25928&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=25928&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	0.095247	0.7378	0.231763
2	-0.161142	-1.2482	0.108404
3	0.20792	1.6105	0.056264
4	0.094314	0.7306	0.233947
5	0.146537	1.1351	0.130431
6	0.275703	2.1356	0.018402
7	-0.092425	-0.7159	0.23841
8	0.202296	1.567	0.06119
9	-0.146351	-1.1336	0.130729
10	-0.267591	-2.0727	0.02125
11	-0.007167	-0.0555	0.477956
12	0.43508	3.3701	0.000659
13	0.000712	0.0055	0.497808
14	-0.0355	-0.275	0.392138
15	-0.136098	-1.0542	0.148007
16	-0.109612	-0.849	0.199615
17	-0.090598	-0.7018	0.242769

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 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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code