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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 17 Aug 2010 23:54:42 +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/Aug/18/t12820892486vimw14xk8yi1q2.htm/, Retrieved Fri, 17 May 2024 00:00:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79165, Retrieved Fri, 17 May 2024 00:00:57 +0000

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Estimated Impact

140

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-       [(Partial) Autocorrelation Function] [] [2010-08-17 23:54:42] [ea4db07d8da34007b79212461ea6aa7b] [Current]

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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	3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79165&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]3 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=79165&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79165&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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.116684	-1.2729	0.102772
2	-0.062364	-0.6803	0.248814
3	-0.279593	-3.05	0.001411
4	0.248095	2.7064	0.003901
5	-0.32122	-3.5041	0.000323
6	0.125874	1.3731	0.086148
7	-0.247956	-2.7049	0.003918
8	0.252693	2.7566	0.003381
9	-0.2808	-3.0632	0.001354
10	-0.008401	-0.0916	0.463566
11	-0.079688	-0.8693	0.193218
12	0.800859	8.7363	0
13	-0.112015	-1.2219	0.112073
14	-0.098681	-1.0765	0.141945
15	-0.231451	-2.5248	0.006446
16	0.208243	2.2717	0.012452
17	-0.324377	-3.5385	0.000287
18	0.099888	1.0896	0.139035
19	-0.161743	-1.7644	0.040115
20	0.245875	2.6822	0.004177

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.116684 & -1.2729 & 0.102772 \tabularnewline
2 & -0.062364 & -0.6803 & 0.248814 \tabularnewline
3 & -0.279593 & -3.05 & 0.001411 \tabularnewline
4 & 0.248095 & 2.7064 & 0.003901 \tabularnewline
5 & -0.32122 & -3.5041 & 0.000323 \tabularnewline
6 & 0.125874 & 1.3731 & 0.086148 \tabularnewline
7 & -0.247956 & -2.7049 & 0.003918 \tabularnewline
8 & 0.252693 & 2.7566 & 0.003381 \tabularnewline
9 & -0.2808 & -3.0632 & 0.001354 \tabularnewline
10 & -0.008401 & -0.0916 & 0.463566 \tabularnewline
11 & -0.079688 & -0.8693 & 0.193218 \tabularnewline
12 & 0.800859 & 8.7363 & 0 \tabularnewline
13 & -0.112015 & -1.2219 & 0.112073 \tabularnewline
14 & -0.098681 & -1.0765 & 0.141945 \tabularnewline
15 & -0.231451 & -2.5248 & 0.006446 \tabularnewline
16 & 0.208243 & 2.2717 & 0.012452 \tabularnewline
17 & -0.324377 & -3.5385 & 0.000287 \tabularnewline
18 & 0.099888 & 1.0896 & 0.139035 \tabularnewline
19 & -0.161743 & -1.7644 & 0.040115 \tabularnewline
20 & 0.245875 & 2.6822 & 0.004177 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79165&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]-0.116684[/C][C]-1.2729[/C][C]0.102772[/C][/ROW]
[ROW][C]2[/C][C]-0.062364[/C][C]-0.6803[/C][C]0.248814[/C][/ROW]
[ROW][C]3[/C][C]-0.279593[/C][C]-3.05[/C][C]0.001411[/C][/ROW]
[ROW][C]4[/C][C]0.248095[/C][C]2.7064[/C][C]0.003901[/C][/ROW]
[ROW][C]5[/C][C]-0.32122[/C][C]-3.5041[/C][C]0.000323[/C][/ROW]
[ROW][C]6[/C][C]0.125874[/C][C]1.3731[/C][C]0.086148[/C][/ROW]
[ROW][C]7[/C][C]-0.247956[/C][C]-2.7049[/C][C]0.003918[/C][/ROW]
[ROW][C]8[/C][C]0.252693[/C][C]2.7566[/C][C]0.003381[/C][/ROW]
[ROW][C]9[/C][C]-0.2808[/C][C]-3.0632[/C][C]0.001354[/C][/ROW]
[ROW][C]10[/C][C]-0.008401[/C][C]-0.0916[/C][C]0.463566[/C][/ROW]
[ROW][C]11[/C][C]-0.079688[/C][C]-0.8693[/C][C]0.193218[/C][/ROW]
[ROW][C]12[/C][C]0.800859[/C][C]8.7363[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.112015[/C][C]-1.2219[/C][C]0.112073[/C][/ROW]
[ROW][C]14[/C][C]-0.098681[/C][C]-1.0765[/C][C]0.141945[/C][/ROW]
[ROW][C]15[/C][C]-0.231451[/C][C]-2.5248[/C][C]0.006446[/C][/ROW]
[ROW][C]16[/C][C]0.208243[/C][C]2.2717[/C][C]0.012452[/C][/ROW]
[ROW][C]17[/C][C]-0.324377[/C][C]-3.5385[/C][C]0.000287[/C][/ROW]
[ROW][C]18[/C][C]0.099888[/C][C]1.0896[/C][C]0.139035[/C][/ROW]
[ROW][C]19[/C][C]-0.161743[/C][C]-1.7644[/C][C]0.040115[/C][/ROW]
[ROW][C]20[/C][C]0.245875[/C][C]2.6822[/C][C]0.004177[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79165&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79165&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	-0.116684	-1.2729	0.102772
2	-0.062364	-0.6803	0.248814
3	-0.279593	-3.05	0.001411
4	0.248095	2.7064	0.003901
5	-0.32122	-3.5041	0.000323
6	0.125874	1.3731	0.086148
7	-0.247956	-2.7049	0.003918
8	0.252693	2.7566	0.003381
9	-0.2808	-3.0632	0.001354
10	-0.008401	-0.0916	0.463566
11	-0.079688	-0.8693	0.193218
12	0.800859	8.7363	0
13	-0.112015	-1.2219	0.112073
14	-0.098681	-1.0765	0.141945
15	-0.231451	-2.5248	0.006446
16	0.208243	2.2717	0.012452
17	-0.324377	-3.5385	0.000287
18	0.099888	1.0896	0.139035
19	-0.161743	-1.7644	0.040115
20	0.245875	2.6822	0.004177

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.116684	-1.2729	0.102772
2	-0.077028	-0.8403	0.201219
3	-0.302303	-3.2977	0.000643
4	0.184079	2.0081	0.023451
5	-0.371744	-4.0552	4.5e-05
6	0.061807	0.6742	0.250736
7	-0.287257	-3.1336	0.001087
8	0.071312	0.7779	0.219081
9	-0.299964	-3.2722	0.000698
10	-0.322434	-3.5173	0.000309
11	-0.018684	-0.2038	0.419422
12	0.654675	7.1417	0
13	0.112812	1.2306	0.110443
14	-0.077835	-0.8491	0.19877
15	0.107114	1.1685	0.122475
16	-0.077182	-0.842	0.200751
17	0.032937	0.3593	0.360002
18	-0.035067	-0.3825	0.351374
19	-0.017577	-0.1917	0.424133
20	0.051296	0.5596	0.288413

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.116684 & -1.2729 & 0.102772 \tabularnewline
2 & -0.077028 & -0.8403 & 0.201219 \tabularnewline
3 & -0.302303 & -3.2977 & 0.000643 \tabularnewline
4 & 0.184079 & 2.0081 & 0.023451 \tabularnewline
5 & -0.371744 & -4.0552 & 4.5e-05 \tabularnewline
6 & 0.061807 & 0.6742 & 0.250736 \tabularnewline
7 & -0.287257 & -3.1336 & 0.001087 \tabularnewline
8 & 0.071312 & 0.7779 & 0.219081 \tabularnewline
9 & -0.299964 & -3.2722 & 0.000698 \tabularnewline
10 & -0.322434 & -3.5173 & 0.000309 \tabularnewline
11 & -0.018684 & -0.2038 & 0.419422 \tabularnewline
12 & 0.654675 & 7.1417 & 0 \tabularnewline
13 & 0.112812 & 1.2306 & 0.110443 \tabularnewline
14 & -0.077835 & -0.8491 & 0.19877 \tabularnewline
15 & 0.107114 & 1.1685 & 0.122475 \tabularnewline
16 & -0.077182 & -0.842 & 0.200751 \tabularnewline
17 & 0.032937 & 0.3593 & 0.360002 \tabularnewline
18 & -0.035067 & -0.3825 & 0.351374 \tabularnewline
19 & -0.017577 & -0.1917 & 0.424133 \tabularnewline
20 & 0.051296 & 0.5596 & 0.288413 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79165&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]-0.116684[/C][C]-1.2729[/C][C]0.102772[/C][/ROW]
[ROW][C]2[/C][C]-0.077028[/C][C]-0.8403[/C][C]0.201219[/C][/ROW]
[ROW][C]3[/C][C]-0.302303[/C][C]-3.2977[/C][C]0.000643[/C][/ROW]
[ROW][C]4[/C][C]0.184079[/C][C]2.0081[/C][C]0.023451[/C][/ROW]
[ROW][C]5[/C][C]-0.371744[/C][C]-4.0552[/C][C]4.5e-05[/C][/ROW]
[ROW][C]6[/C][C]0.061807[/C][C]0.6742[/C][C]0.250736[/C][/ROW]
[ROW][C]7[/C][C]-0.287257[/C][C]-3.1336[/C][C]0.001087[/C][/ROW]
[ROW][C]8[/C][C]0.071312[/C][C]0.7779[/C][C]0.219081[/C][/ROW]
[ROW][C]9[/C][C]-0.299964[/C][C]-3.2722[/C][C]0.000698[/C][/ROW]
[ROW][C]10[/C][C]-0.322434[/C][C]-3.5173[/C][C]0.000309[/C][/ROW]
[ROW][C]11[/C][C]-0.018684[/C][C]-0.2038[/C][C]0.419422[/C][/ROW]
[ROW][C]12[/C][C]0.654675[/C][C]7.1417[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.112812[/C][C]1.2306[/C][C]0.110443[/C][/ROW]
[ROW][C]14[/C][C]-0.077835[/C][C]-0.8491[/C][C]0.19877[/C][/ROW]
[ROW][C]15[/C][C]0.107114[/C][C]1.1685[/C][C]0.122475[/C][/ROW]
[ROW][C]16[/C][C]-0.077182[/C][C]-0.842[/C][C]0.200751[/C][/ROW]
[ROW][C]17[/C][C]0.032937[/C][C]0.3593[/C][C]0.360002[/C][/ROW]
[ROW][C]18[/C][C]-0.035067[/C][C]-0.3825[/C][C]0.351374[/C][/ROW]
[ROW][C]19[/C][C]-0.017577[/C][C]-0.1917[/C][C]0.424133[/C][/ROW]
[ROW][C]20[/C][C]0.051296[/C][C]0.5596[/C][C]0.288413[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79165&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79165&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	-0.116684	-1.2729	0.102772
2	-0.077028	-0.8403	0.201219
3	-0.302303	-3.2977	0.000643
4	0.184079	2.0081	0.023451
5	-0.371744	-4.0552	4.5e-05
6	0.061807	0.6742	0.250736
7	-0.287257	-3.1336	0.001087
8	0.071312	0.7779	0.219081
9	-0.299964	-3.2722	0.000698
10	-0.322434	-3.5173	0.000309
11	-0.018684	-0.2038	0.419422
12	0.654675	7.1417	0
13	0.112812	1.2306	0.110443
14	-0.077835	-0.8491	0.19877
15	0.107114	1.1685	0.122475
16	-0.077182	-0.842	0.200751
17	0.032937	0.3593	0.360002
18	-0.035067	-0.3825	0.351374
19	-0.017577	-0.1917	0.424133
20	0.051296	0.5596	0.288413

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; 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