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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 24 Nov 2007 12:56:44 -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/24/t1195933773pto58px91akiate.htm/, Retrieved Fri, 03 May 2024 08:52:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6364, Retrieved Fri, 03 May 2024 08:52:05 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

197

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

-       [(Partial) Autocorrelation Function] [ws9q2afcfs1e] [2007-11-24 19:56:44] [142ab5472309a9ae9a3b52678758dc4a] [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	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=6364&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=6364&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6364&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	7.746	0
1	0.612197	4.7421	7e-06
2	0.478264	3.7046	0.000232
3	0.350446	2.7145	0.004327
4	0.335358	2.5977	0.005895
5	0.233249	1.8067	0.037909
6	0.210476	1.6303	0.054134
7	0.087397	0.677	0.250511
8	0.033493	0.2594	0.398095
9	0.045462	0.3522	0.36298
10	0.105197	0.8149	0.209189
11	0.137868	1.0679	0.144917
12	0.109464	0.8479	0.19993
13	0.036606	0.2835	0.388866
14	-0.057853	-0.4481	0.672162
15	-0.10099	-0.7823	0.781433
16	-0.099473	-0.7705	0.77799

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.612197 & 4.7421 & 7e-06 \tabularnewline
2 & 0.478264 & 3.7046 & 0.000232 \tabularnewline
3 & 0.350446 & 2.7145 & 0.004327 \tabularnewline
4 & 0.335358 & 2.5977 & 0.005895 \tabularnewline
5 & 0.233249 & 1.8067 & 0.037909 \tabularnewline
6 & 0.210476 & 1.6303 & 0.054134 \tabularnewline
7 & 0.087397 & 0.677 & 0.250511 \tabularnewline
8 & 0.033493 & 0.2594 & 0.398095 \tabularnewline
9 & 0.045462 & 0.3522 & 0.36298 \tabularnewline
10 & 0.105197 & 0.8149 & 0.209189 \tabularnewline
11 & 0.137868 & 1.0679 & 0.144917 \tabularnewline
12 & 0.109464 & 0.8479 & 0.19993 \tabularnewline
13 & 0.036606 & 0.2835 & 0.388866 \tabularnewline
14 & -0.057853 & -0.4481 & 0.672162 \tabularnewline
15 & -0.10099 & -0.7823 & 0.781433 \tabularnewline
16 & -0.099473 & -0.7705 & 0.77799 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6364&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.612197[/C][C]4.7421[/C][C]7e-06[/C][/ROW]
[ROW][C]2[/C][C]0.478264[/C][C]3.7046[/C][C]0.000232[/C][/ROW]
[ROW][C]3[/C][C]0.350446[/C][C]2.7145[/C][C]0.004327[/C][/ROW]
[ROW][C]4[/C][C]0.335358[/C][C]2.5977[/C][C]0.005895[/C][/ROW]
[ROW][C]5[/C][C]0.233249[/C][C]1.8067[/C][C]0.037909[/C][/ROW]
[ROW][C]6[/C][C]0.210476[/C][C]1.6303[/C][C]0.054134[/C][/ROW]
[ROW][C]7[/C][C]0.087397[/C][C]0.677[/C][C]0.250511[/C][/ROW]
[ROW][C]8[/C][C]0.033493[/C][C]0.2594[/C][C]0.398095[/C][/ROW]
[ROW][C]9[/C][C]0.045462[/C][C]0.3522[/C][C]0.36298[/C][/ROW]
[ROW][C]10[/C][C]0.105197[/C][C]0.8149[/C][C]0.209189[/C][/ROW]
[ROW][C]11[/C][C]0.137868[/C][C]1.0679[/C][C]0.144917[/C][/ROW]
[ROW][C]12[/C][C]0.109464[/C][C]0.8479[/C][C]0.19993[/C][/ROW]
[ROW][C]13[/C][C]0.036606[/C][C]0.2835[/C][C]0.388866[/C][/ROW]
[ROW][C]14[/C][C]-0.057853[/C][C]-0.4481[/C][C]0.672162[/C][/ROW]
[ROW][C]15[/C][C]-0.10099[/C][C]-0.7823[/C][C]0.781433[/C][/ROW]
[ROW][C]16[/C][C]-0.099473[/C][C]-0.7705[/C][C]0.77799[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6364&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6364&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	7.746	0
1	0.612197	4.7421	7e-06
2	0.478264	3.7046	0.000232
3	0.350446	2.7145	0.004327
4	0.335358	2.5977	0.005895
5	0.233249	1.8067	0.037909
6	0.210476	1.6303	0.054134
7	0.087397	0.677	0.250511
8	0.033493	0.2594	0.398095
9	0.045462	0.3522	0.36298
10	0.105197	0.8149	0.209189
11	0.137868	1.0679	0.144917
12	0.109464	0.8479	0.19993
13	0.036606	0.2835	0.388866
14	-0.057853	-0.4481	0.672162
15	-0.10099	-0.7823	0.781433
16	-0.099473	-0.7705	0.77799

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.612197	4.7421	7e-06
1	0.165511	1.282	0.10238
2	0.007876	0.061	0.475779
3	0.122895	0.9519	0.172473
4	-0.060119	-0.4657	0.678434
5	0.039102	0.3029	0.381514
6	-0.126045	-0.9763	0.833591
7	-0.051547	-0.3993	0.654449
8	0.085646	0.6634	0.254805
9	0.102878	0.7969	0.214328
10	0.09303	0.7206	0.236976
11	-0.035494	-0.2749	0.607844
12	-0.104478	-0.8093	0.789226
13	-0.159786	-1.2377	0.889676
14	-0.098493	-0.7629	0.775751
15	0.003527	0.0273	0.489148
16	0.006663	0.0516	0.479504

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.612197 & 4.7421 & 7e-06 \tabularnewline
1 & 0.165511 & 1.282 & 0.10238 \tabularnewline
2 & 0.007876 & 0.061 & 0.475779 \tabularnewline
3 & 0.122895 & 0.9519 & 0.172473 \tabularnewline
4 & -0.060119 & -0.4657 & 0.678434 \tabularnewline
5 & 0.039102 & 0.3029 & 0.381514 \tabularnewline
6 & -0.126045 & -0.9763 & 0.833591 \tabularnewline
7 & -0.051547 & -0.3993 & 0.654449 \tabularnewline
8 & 0.085646 & 0.6634 & 0.254805 \tabularnewline
9 & 0.102878 & 0.7969 & 0.214328 \tabularnewline
10 & 0.09303 & 0.7206 & 0.236976 \tabularnewline
11 & -0.035494 & -0.2749 & 0.607844 \tabularnewline
12 & -0.104478 & -0.8093 & 0.789226 \tabularnewline
13 & -0.159786 & -1.2377 & 0.889676 \tabularnewline
14 & -0.098493 & -0.7629 & 0.775751 \tabularnewline
15 & 0.003527 & 0.0273 & 0.489148 \tabularnewline
16 & 0.006663 & 0.0516 & 0.479504 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6364&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]0.612197[/C][C]4.7421[/C][C]7e-06[/C][/ROW]
[ROW][C]1[/C][C]0.165511[/C][C]1.282[/C][C]0.10238[/C][/ROW]
[ROW][C]2[/C][C]0.007876[/C][C]0.061[/C][C]0.475779[/C][/ROW]
[ROW][C]3[/C][C]0.122895[/C][C]0.9519[/C][C]0.172473[/C][/ROW]
[ROW][C]4[/C][C]-0.060119[/C][C]-0.4657[/C][C]0.678434[/C][/ROW]
[ROW][C]5[/C][C]0.039102[/C][C]0.3029[/C][C]0.381514[/C][/ROW]
[ROW][C]6[/C][C]-0.126045[/C][C]-0.9763[/C][C]0.833591[/C][/ROW]
[ROW][C]7[/C][C]-0.051547[/C][C]-0.3993[/C][C]0.654449[/C][/ROW]
[ROW][C]8[/C][C]0.085646[/C][C]0.6634[/C][C]0.254805[/C][/ROW]
[ROW][C]9[/C][C]0.102878[/C][C]0.7969[/C][C]0.214328[/C][/ROW]
[ROW][C]10[/C][C]0.09303[/C][C]0.7206[/C][C]0.236976[/C][/ROW]
[ROW][C]11[/C][C]-0.035494[/C][C]-0.2749[/C][C]0.607844[/C][/ROW]
[ROW][C]12[/C][C]-0.104478[/C][C]-0.8093[/C][C]0.789226[/C][/ROW]
[ROW][C]13[/C][C]-0.159786[/C][C]-1.2377[/C][C]0.889676[/C][/ROW]
[ROW][C]14[/C][C]-0.098493[/C][C]-0.7629[/C][C]0.775751[/C][/ROW]
[ROW][C]15[/C][C]0.003527[/C][C]0.0273[/C][C]0.489148[/C][/ROW]
[ROW][C]16[/C][C]0.006663[/C][C]0.0516[/C][C]0.479504[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6364&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6364&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	0.612197	4.7421	7e-06
1	0.165511	1.282	0.10238
2	0.007876	0.061	0.475779
3	0.122895	0.9519	0.172473
4	-0.060119	-0.4657	0.678434
5	0.039102	0.3029	0.381514
6	-0.126045	-0.9763	0.833591
7	-0.051547	-0.3993	0.654449
8	0.085646	0.6634	0.254805
9	0.102878	0.7969	0.214328
10	0.09303	0.7206	0.236976
11	-0.035494	-0.2749	0.607844
12	-0.104478	-0.8093	0.789226
13	-0.159786	-1.2377	0.889676
14	-0.098493	-0.7629	0.775751
15	0.003527	0.0273	0.489148
16	0.006663	0.0516	0.479504

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.8 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.8 ; 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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Dataset

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Figures (Output of Computation)

Input Parameters & R Code