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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

Fri, 03 Dec 2010 11:32:19 +0000

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/2010/Dec/03/t1291375825fr38nmvndtbwg4m.htm/, Retrieved Sun, 28 Apr 2024 20:54:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104644, Retrieved Sun, 28 Apr 2024 20:54:28 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

172

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

-     [Univariate Explorative Data Analysis] [Monthly US soldie...] [2010-11-02 12:07:39] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Soldiers] [2010-11-29 09:48:36] [b98453cac15ba1066b407e146608df68]
-   PD      [(Partial) Autocorrelation Function] [] [2010-12-03 11:32:19] [df17410ebb98883e83037e1662207ccb] [Current]
-   PD        [(Partial) Autocorrelation Function] [] [2010-12-03 14:12:17] [8a9a6f7c332640af31ddca253a8ded58] 
-   PD        [(Partial) Autocorrelation Function] [] [2010-12-03 14:14:33] [8a9a6f7c332640af31ddca253a8ded58] 
-    D          [(Partial) Autocorrelation Function] [] [2010-12-07 13:28:58] [f72e5115d7374b3b3f29ba3966e5379d] 
-   P             [(Partial) Autocorrelation Function] [] [2010-12-07 15:13:37] [f72e5115d7374b3b3f29ba3966e5379d] 
-   P             [(Partial) Autocorrelation Function] [] [2010-12-07 15:20:07] [f72e5115d7374b3b3f29ba3966e5379d] 
- RMP             [Variance Reduction Matrix] [] [2010-12-07 15:29:14] [f72e5115d7374b3b3f29ba3966e5379d] 
- RMP             [Standard Deviation-Mean Plot] [] [2010-12-07 15:39:58] [f72e5115d7374b3b3f29ba3966e5379d] 
- RMP             [Spectral Analysis] [] [2010-12-07 16:29:36] [f72e5115d7374b3b3f29ba3966e5379d] 
- RMP             [Spectral Analysis] [] [2010-12-07 16:34:30] [f72e5115d7374b3b3f29ba3966e5379d] 
-   P           [(Partial) Autocorrelation Function] [] [2010-12-17 14:07:41] [8a9a6f7c332640af31ddca253a8ded58] 
-   P           [(Partial) Autocorrelation Function] [] [2010-12-17 14:09:32] [8a9a6f7c332640af31ddca253a8ded58] 
-   P           [(Partial) Autocorrelation Function] [] [2010-12-17 14:11:00] [8a9a6f7c332640af31ddca253a8ded58] 
-   PD        [(Partial) Autocorrelation Function] [] [2010-12-14 12:47:55] [9b13650c94c5192ca5135ec8a1fa39f7] 

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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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104644&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104644&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104644&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.243728	-1.635	0.054515
2	0.138719	0.9306	0.178524
3	0.00837	0.0561	0.477735
4	0.291049	1.9524	0.028563
5	-0.103181	-0.6922	0.246197
6	-0.173061	-1.1609	0.125897
7	0.255001	1.7106	0.047021
8	-0.285695	-1.9165	0.030833
9	0.289763	1.9438	0.029095
10	-0.250304	-1.6791	0.050033
11	0.292178	1.96	0.028103
12	-0.309274	-2.0747	0.021882
13	0.146461	0.9825	0.165556
14	-0.040484	-0.2716	0.393594
15	-0.104534	-0.7012	0.243384
16	-0.055723	-0.3738	0.355153
17	-0.205059	-1.3756	0.08788

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.243728 & -1.635 & 0.054515 \tabularnewline
2 & 0.138719 & 0.9306 & 0.178524 \tabularnewline
3 & 0.00837 & 0.0561 & 0.477735 \tabularnewline
4 & 0.291049 & 1.9524 & 0.028563 \tabularnewline
5 & -0.103181 & -0.6922 & 0.246197 \tabularnewline
6 & -0.173061 & -1.1609 & 0.125897 \tabularnewline
7 & 0.255001 & 1.7106 & 0.047021 \tabularnewline
8 & -0.285695 & -1.9165 & 0.030833 \tabularnewline
9 & 0.289763 & 1.9438 & 0.029095 \tabularnewline
10 & -0.250304 & -1.6791 & 0.050033 \tabularnewline
11 & 0.292178 & 1.96 & 0.028103 \tabularnewline
12 & -0.309274 & -2.0747 & 0.021882 \tabularnewline
13 & 0.146461 & 0.9825 & 0.165556 \tabularnewline
14 & -0.040484 & -0.2716 & 0.393594 \tabularnewline
15 & -0.104534 & -0.7012 & 0.243384 \tabularnewline
16 & -0.055723 & -0.3738 & 0.355153 \tabularnewline
17 & -0.205059 & -1.3756 & 0.08788 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104644&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]-0.243728[/C][C]-1.635[/C][C]0.054515[/C][/ROW]
[ROW][C]2[/C][C]0.138719[/C][C]0.9306[/C][C]0.178524[/C][/ROW]
[ROW][C]3[/C][C]0.00837[/C][C]0.0561[/C][C]0.477735[/C][/ROW]
[ROW][C]4[/C][C]0.291049[/C][C]1.9524[/C][C]0.028563[/C][/ROW]
[ROW][C]5[/C][C]-0.103181[/C][C]-0.6922[/C][C]0.246197[/C][/ROW]
[ROW][C]6[/C][C]-0.173061[/C][C]-1.1609[/C][C]0.125897[/C][/ROW]
[ROW][C]7[/C][C]0.255001[/C][C]1.7106[/C][C]0.047021[/C][/ROW]
[ROW][C]8[/C][C]-0.285695[/C][C]-1.9165[/C][C]0.030833[/C][/ROW]
[ROW][C]9[/C][C]0.289763[/C][C]1.9438[/C][C]0.029095[/C][/ROW]
[ROW][C]10[/C][C]-0.250304[/C][C]-1.6791[/C][C]0.050033[/C][/ROW]
[ROW][C]11[/C][C]0.292178[/C][C]1.96[/C][C]0.028103[/C][/ROW]
[ROW][C]12[/C][C]-0.309274[/C][C]-2.0747[/C][C]0.021882[/C][/ROW]
[ROW][C]13[/C][C]0.146461[/C][C]0.9825[/C][C]0.165556[/C][/ROW]
[ROW][C]14[/C][C]-0.040484[/C][C]-0.2716[/C][C]0.393594[/C][/ROW]
[ROW][C]15[/C][C]-0.104534[/C][C]-0.7012[/C][C]0.243384[/C][/ROW]
[ROW][C]16[/C][C]-0.055723[/C][C]-0.3738[/C][C]0.355153[/C][/ROW]
[ROW][C]17[/C][C]-0.205059[/C][C]-1.3756[/C][C]0.08788[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104644&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104644&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	-0.243728	-1.635	0.054515
2	0.138719	0.9306	0.178524
3	0.00837	0.0561	0.477735
4	0.291049	1.9524	0.028563
5	-0.103181	-0.6922	0.246197
6	-0.173061	-1.1609	0.125897
7	0.255001	1.7106	0.047021
8	-0.285695	-1.9165	0.030833
9	0.289763	1.9438	0.029095
10	-0.250304	-1.6791	0.050033
11	0.292178	1.96	0.028103
12	-0.309274	-2.0747	0.021882
13	0.146461	0.9825	0.165556
14	-0.040484	-0.2716	0.393594
15	-0.104534	-0.7012	0.243384
16	-0.055723	-0.3738	0.355153
17	-0.205059	-1.3756	0.08788

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.243728	-1.635	0.054515
2	0.084325	0.5657	0.287213
3	0.064119	0.4301	0.334579
4	0.317081	2.127	0.019466
5	0.032316	0.2168	0.41468
6	-0.306899	-2.0587	0.022668
7	0.140553	0.9429	0.175395
8	-0.284631	-1.9094	0.031302
9	0.309142	2.0738	0.021926
10	-0.02482	-0.1665	0.434257
11	0.136938	0.9186	0.1816
12	-0.210219	-1.4102	0.082679
13	-0.108258	-0.7262	0.235733
14	-0.035796	-0.2401	0.405661
15	-0.037297	-0.2502	0.401787
16	-0.105714	-0.7092	0.240945
17	-0.074201	-0.4978	0.31054

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.243728 & -1.635 & 0.054515 \tabularnewline
2 & 0.084325 & 0.5657 & 0.287213 \tabularnewline
3 & 0.064119 & 0.4301 & 0.334579 \tabularnewline
4 & 0.317081 & 2.127 & 0.019466 \tabularnewline
5 & 0.032316 & 0.2168 & 0.41468 \tabularnewline
6 & -0.306899 & -2.0587 & 0.022668 \tabularnewline
7 & 0.140553 & 0.9429 & 0.175395 \tabularnewline
8 & -0.284631 & -1.9094 & 0.031302 \tabularnewline
9 & 0.309142 & 2.0738 & 0.021926 \tabularnewline
10 & -0.02482 & -0.1665 & 0.434257 \tabularnewline
11 & 0.136938 & 0.9186 & 0.1816 \tabularnewline
12 & -0.210219 & -1.4102 & 0.082679 \tabularnewline
13 & -0.108258 & -0.7262 & 0.235733 \tabularnewline
14 & -0.035796 & -0.2401 & 0.405661 \tabularnewline
15 & -0.037297 & -0.2502 & 0.401787 \tabularnewline
16 & -0.105714 & -0.7092 & 0.240945 \tabularnewline
17 & -0.074201 & -0.4978 & 0.31054 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104644&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]-0.243728[/C][C]-1.635[/C][C]0.054515[/C][/ROW]
[ROW][C]2[/C][C]0.084325[/C][C]0.5657[/C][C]0.287213[/C][/ROW]
[ROW][C]3[/C][C]0.064119[/C][C]0.4301[/C][C]0.334579[/C][/ROW]
[ROW][C]4[/C][C]0.317081[/C][C]2.127[/C][C]0.019466[/C][/ROW]
[ROW][C]5[/C][C]0.032316[/C][C]0.2168[/C][C]0.41468[/C][/ROW]
[ROW][C]6[/C][C]-0.306899[/C][C]-2.0587[/C][C]0.022668[/C][/ROW]
[ROW][C]7[/C][C]0.140553[/C][C]0.9429[/C][C]0.175395[/C][/ROW]
[ROW][C]8[/C][C]-0.284631[/C][C]-1.9094[/C][C]0.031302[/C][/ROW]
[ROW][C]9[/C][C]0.309142[/C][C]2.0738[/C][C]0.021926[/C][/ROW]
[ROW][C]10[/C][C]-0.02482[/C][C]-0.1665[/C][C]0.434257[/C][/ROW]
[ROW][C]11[/C][C]0.136938[/C][C]0.9186[/C][C]0.1816[/C][/ROW]
[ROW][C]12[/C][C]-0.210219[/C][C]-1.4102[/C][C]0.082679[/C][/ROW]
[ROW][C]13[/C][C]-0.108258[/C][C]-0.7262[/C][C]0.235733[/C][/ROW]
[ROW][C]14[/C][C]-0.035796[/C][C]-0.2401[/C][C]0.405661[/C][/ROW]
[ROW][C]15[/C][C]-0.037297[/C][C]-0.2502[/C][C]0.401787[/C][/ROW]
[ROW][C]16[/C][C]-0.105714[/C][C]-0.7092[/C][C]0.240945[/C][/ROW]
[ROW][C]17[/C][C]-0.074201[/C][C]-0.4978[/C][C]0.31054[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104644&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104644&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	-0.243728	-1.635	0.054515
2	0.084325	0.5657	0.287213
3	0.064119	0.4301	0.334579
4	0.317081	2.127	0.019466
5	0.032316	0.2168	0.41468
6	-0.306899	-2.0587	0.022668
7	0.140553	0.9429	0.175395
8	-0.284631	-1.9094	0.031302
9	0.309142	2.0738	0.021926
10	-0.02482	-0.1665	0.434257
11	0.136938	0.9186	0.1816
12	-0.210219	-1.4102	0.082679
13	-0.108258	-0.7262	0.235733
14	-0.035796	-0.2401	0.405661
15	-0.037297	-0.2502	0.401787
16	-0.105714	-0.7092	0.240945
17	-0.074201	-0.4978	0.31054

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code