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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

Tue, 14 Dec 2010 13:53:45 +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/14/t1292334783fz3qihy7j7s7zni.htm/, Retrieved Thu, 02 May 2024 19:42:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109653, Retrieved Thu, 02 May 2024 19:42:28 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Workshop 6

Estimated Impact

155

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

-       [(Partial) Autocorrelation Function] [Workshop 6: ACF 2 ] [2010-12-14 13:53:45] [f76239c595e4d455b3b05a43389f68d5] [Current]
- R PD    [(Partial) Autocorrelation Function] [ACF] [2011-12-22 13:01:36] [74be16979710d4c4e7c6647856088456] 
- R  D    [(Partial) Autocorrelation Function] [ACF] [2011-12-22 15:17:24] [74be16979710d4c4e7c6647856088456] 
- R  D    [(Partial) Autocorrelation Function] [Berekening 11] [2012-08-11 14:08:21] [eb6e95800005ec22b7fd76eead8d8a59] 

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-5
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0

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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109653&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109653&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109653&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.16484	-1.2662	0.105216
2	-0.074458	-0.5719	0.284774
3	0.079203	0.6084	0.27264
4	0.043926	0.3374	0.368507
5	0.065702	0.5047	0.307837
6	-0.110665	-0.85	0.199371
7	0.106537	0.8183	0.208232
8	0.026261	0.2017	0.420417
9	-0.097985	-0.7526	0.22733
10	-0.091244	-0.7009	0.243074
11	0.142048	1.0911	0.139834
12	0.017248	0.1325	0.447525
13	0.03243	0.2491	0.402074
14	-0.051486	-0.3955	0.346961
15	0.114756	0.8815	0.190823
16	-0.028798	-0.2212	0.41285
17	-0.022452	-0.1725	0.431834

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.16484 & -1.2662 & 0.105216 \tabularnewline
2 & -0.074458 & -0.5719 & 0.284774 \tabularnewline
3 & 0.079203 & 0.6084 & 0.27264 \tabularnewline
4 & 0.043926 & 0.3374 & 0.368507 \tabularnewline
5 & 0.065702 & 0.5047 & 0.307837 \tabularnewline
6 & -0.110665 & -0.85 & 0.199371 \tabularnewline
7 & 0.106537 & 0.8183 & 0.208232 \tabularnewline
8 & 0.026261 & 0.2017 & 0.420417 \tabularnewline
9 & -0.097985 & -0.7526 & 0.22733 \tabularnewline
10 & -0.091244 & -0.7009 & 0.243074 \tabularnewline
11 & 0.142048 & 1.0911 & 0.139834 \tabularnewline
12 & 0.017248 & 0.1325 & 0.447525 \tabularnewline
13 & 0.03243 & 0.2491 & 0.402074 \tabularnewline
14 & -0.051486 & -0.3955 & 0.346961 \tabularnewline
15 & 0.114756 & 0.8815 & 0.190823 \tabularnewline
16 & -0.028798 & -0.2212 & 0.41285 \tabularnewline
17 & -0.022452 & -0.1725 & 0.431834 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109653&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]-0.16484[/C][C]-1.2662[/C][C]0.105216[/C][/ROW]
[ROW][C]2[/C][C]-0.074458[/C][C]-0.5719[/C][C]0.284774[/C][/ROW]
[ROW][C]3[/C][C]0.079203[/C][C]0.6084[/C][C]0.27264[/C][/ROW]
[ROW][C]4[/C][C]0.043926[/C][C]0.3374[/C][C]0.368507[/C][/ROW]
[ROW][C]5[/C][C]0.065702[/C][C]0.5047[/C][C]0.307837[/C][/ROW]
[ROW][C]6[/C][C]-0.110665[/C][C]-0.85[/C][C]0.199371[/C][/ROW]
[ROW][C]7[/C][C]0.106537[/C][C]0.8183[/C][C]0.208232[/C][/ROW]
[ROW][C]8[/C][C]0.026261[/C][C]0.2017[/C][C]0.420417[/C][/ROW]
[ROW][C]9[/C][C]-0.097985[/C][C]-0.7526[/C][C]0.22733[/C][/ROW]
[ROW][C]10[/C][C]-0.091244[/C][C]-0.7009[/C][C]0.243074[/C][/ROW]
[ROW][C]11[/C][C]0.142048[/C][C]1.0911[/C][C]0.139834[/C][/ROW]
[ROW][C]12[/C][C]0.017248[/C][C]0.1325[/C][C]0.447525[/C][/ROW]
[ROW][C]13[/C][C]0.03243[/C][C]0.2491[/C][C]0.402074[/C][/ROW]
[ROW][C]14[/C][C]-0.051486[/C][C]-0.3955[/C][C]0.346961[/C][/ROW]
[ROW][C]15[/C][C]0.114756[/C][C]0.8815[/C][C]0.190823[/C][/ROW]
[ROW][C]16[/C][C]-0.028798[/C][C]-0.2212[/C][C]0.41285[/C][/ROW]
[ROW][C]17[/C][C]-0.022452[/C][C]-0.1725[/C][C]0.431834[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109653&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109653&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	-0.16484	-1.2662	0.105216
2	-0.074458	-0.5719	0.284774
3	0.079203	0.6084	0.27264
4	0.043926	0.3374	0.368507
5	0.065702	0.5047	0.307837
6	-0.110665	-0.85	0.199371
7	0.106537	0.8183	0.208232
8	0.026261	0.2017	0.420417
9	-0.097985	-0.7526	0.22733
10	-0.091244	-0.7009	0.243074
11	0.142048	1.0911	0.139834
12	0.017248	0.1325	0.447525
13	0.03243	0.2491	0.402074
14	-0.051486	-0.3955	0.346961
15	0.114756	0.8815	0.190823
16	-0.028798	-0.2212	0.41285
17	-0.022452	-0.1725	0.431834

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.16484	-1.2662	0.105216
2	-0.104469	-0.8024	0.212759
3	0.050328	0.3866	0.35023
4	0.061607	0.4732	0.318904
5	0.099778	0.7664	0.223244
6	-0.081796	-0.6283	0.26612
7	0.081357	0.6249	0.267218
8	0.029478	0.2264	0.410826
9	-0.07253	-0.5571	0.289779
10	-0.134911	-1.0363	0.152153
11	0.098869	0.7594	0.22531
12	0.03376	0.2593	0.398147
13	0.106944	0.8215	0.207347
14	-0.028151	-0.2162	0.414777
15	0.104389	0.8018	0.212936
16	-0.042445	-0.326	0.37278
17	0.023918	0.1837	0.427434

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.16484 & -1.2662 & 0.105216 \tabularnewline
2 & -0.104469 & -0.8024 & 0.212759 \tabularnewline
3 & 0.050328 & 0.3866 & 0.35023 \tabularnewline
4 & 0.061607 & 0.4732 & 0.318904 \tabularnewline
5 & 0.099778 & 0.7664 & 0.223244 \tabularnewline
6 & -0.081796 & -0.6283 & 0.26612 \tabularnewline
7 & 0.081357 & 0.6249 & 0.267218 \tabularnewline
8 & 0.029478 & 0.2264 & 0.410826 \tabularnewline
9 & -0.07253 & -0.5571 & 0.289779 \tabularnewline
10 & -0.134911 & -1.0363 & 0.152153 \tabularnewline
11 & 0.098869 & 0.7594 & 0.22531 \tabularnewline
12 & 0.03376 & 0.2593 & 0.398147 \tabularnewline
13 & 0.106944 & 0.8215 & 0.207347 \tabularnewline
14 & -0.028151 & -0.2162 & 0.414777 \tabularnewline
15 & 0.104389 & 0.8018 & 0.212936 \tabularnewline
16 & -0.042445 & -0.326 & 0.37278 \tabularnewline
17 & 0.023918 & 0.1837 & 0.427434 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109653&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]-0.16484[/C][C]-1.2662[/C][C]0.105216[/C][/ROW]
[ROW][C]2[/C][C]-0.104469[/C][C]-0.8024[/C][C]0.212759[/C][/ROW]
[ROW][C]3[/C][C]0.050328[/C][C]0.3866[/C][C]0.35023[/C][/ROW]
[ROW][C]4[/C][C]0.061607[/C][C]0.4732[/C][C]0.318904[/C][/ROW]
[ROW][C]5[/C][C]0.099778[/C][C]0.7664[/C][C]0.223244[/C][/ROW]
[ROW][C]6[/C][C]-0.081796[/C][C]-0.6283[/C][C]0.26612[/C][/ROW]
[ROW][C]7[/C][C]0.081357[/C][C]0.6249[/C][C]0.267218[/C][/ROW]
[ROW][C]8[/C][C]0.029478[/C][C]0.2264[/C][C]0.410826[/C][/ROW]
[ROW][C]9[/C][C]-0.07253[/C][C]-0.5571[/C][C]0.289779[/C][/ROW]
[ROW][C]10[/C][C]-0.134911[/C][C]-1.0363[/C][C]0.152153[/C][/ROW]
[ROW][C]11[/C][C]0.098869[/C][C]0.7594[/C][C]0.22531[/C][/ROW]
[ROW][C]12[/C][C]0.03376[/C][C]0.2593[/C][C]0.398147[/C][/ROW]
[ROW][C]13[/C][C]0.106944[/C][C]0.8215[/C][C]0.207347[/C][/ROW]
[ROW][C]14[/C][C]-0.028151[/C][C]-0.2162[/C][C]0.414777[/C][/ROW]
[ROW][C]15[/C][C]0.104389[/C][C]0.8018[/C][C]0.212936[/C][/ROW]
[ROW][C]16[/C][C]-0.042445[/C][C]-0.326[/C][C]0.37278[/C][/ROW]
[ROW][C]17[/C][C]0.023918[/C][C]0.1837[/C][C]0.427434[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109653&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109653&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	-0.16484	-1.2662	0.105216
2	-0.104469	-0.8024	0.212759
3	0.050328	0.3866	0.35023
4	0.061607	0.4732	0.318904
5	0.099778	0.7664	0.223244
6	-0.081796	-0.6283	0.26612
7	0.081357	0.6249	0.267218
8	0.029478	0.2264	0.410826
9	-0.07253	-0.5571	0.289779
10	-0.134911	-1.0363	0.152153
11	0.098869	0.7594	0.22531
12	0.03376	0.2593	0.398147
13	0.106944	0.8215	0.207347
14	-0.028151	-0.2162	0.414777
15	0.104389	0.8018	0.212936
16	-0.042445	-0.326	0.37278
17	0.023918	0.1837	0.427434

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