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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 05 Dec 2010 13:32:17 +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/05/t12915561423sm5k1wzy61ceo0.htm/, Retrieved Wed, 01 May 2024 22:22:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105390, Retrieved Wed, 01 May 2024 22:22:06 +0000

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User-defined keywords

Estimated Impact

142

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D      [(Partial) Autocorrelation Function] [Ws 9 - ACF] [2010-12-05 13:32:17] [0829c729852d8a4b1b0c41cf0848af95] [Current]
-   P         [(Partial) Autocorrelation Function] [Ws 9 - ACF (d = 1)] [2010-12-05 13:40:03] [603e2f5305d3a2a4e062624458fa1155] 
-   P           [(Partial) Autocorrelation Function] [Ws 9 - ACF (d = 1)] [2010-12-05 14:08:10] [603e2f5305d3a2a4e062624458fa1155] 
-   P         [(Partial) Autocorrelation Function] [Ws 9 - ACF (d = D...] [2010-12-05 13:43:06] [603e2f5305d3a2a4e062624458fa1155] 
-   P           [(Partial) Autocorrelation Function] [Ws 9 - ACF (d = D...] [2010-12-05 14:15:47] [603e2f5305d3a2a4e062624458fa1155] 
-   PD        [(Partial) Autocorrelation Function] [PAPER - ACF] [2010-12-19 10:56:45] [603e2f5305d3a2a4e062624458fa1155] 
-   P           [(Partial) Autocorrelation Function] [PAPER - ACF (2)] [2010-12-21 13:48:18] [603e2f5305d3a2a4e062624458fa1155] 

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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=105390&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=105390&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105390&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	0.921406	7.0172	0
2	0.813384	6.1946	0
3	0.712794	5.4285	1e-06
4	0.610464	4.6492	1e-05
5	0.523526	3.9871	9.5e-05
6	0.404002	3.0768	0.001596
7	0.25953	1.9765	0.026429
8	0.146123	1.1128	0.135185
9	0.058554	0.4459	0.328652
10	-0.022793	-0.1736	0.431397
11	-0.095603	-0.7281	0.234744
12	-0.174787	-1.3311	0.094177
13	-0.233689	-1.7797	0.04018
14	-0.249493	-1.9001	0.031198
15	-0.264299	-2.0128	0.024391
16	-0.298059	-2.27	0.013472
17	-0.351634	-2.678	0.00481

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.921406 & 7.0172 & 0 \tabularnewline
2 & 0.813384 & 6.1946 & 0 \tabularnewline
3 & 0.712794 & 5.4285 & 1e-06 \tabularnewline
4 & 0.610464 & 4.6492 & 1e-05 \tabularnewline
5 & 0.523526 & 3.9871 & 9.5e-05 \tabularnewline
6 & 0.404002 & 3.0768 & 0.001596 \tabularnewline
7 & 0.25953 & 1.9765 & 0.026429 \tabularnewline
8 & 0.146123 & 1.1128 & 0.135185 \tabularnewline
9 & 0.058554 & 0.4459 & 0.328652 \tabularnewline
10 & -0.022793 & -0.1736 & 0.431397 \tabularnewline
11 & -0.095603 & -0.7281 & 0.234744 \tabularnewline
12 & -0.174787 & -1.3311 & 0.094177 \tabularnewline
13 & -0.233689 & -1.7797 & 0.04018 \tabularnewline
14 & -0.249493 & -1.9001 & 0.031198 \tabularnewline
15 & -0.264299 & -2.0128 & 0.024391 \tabularnewline
16 & -0.298059 & -2.27 & 0.013472 \tabularnewline
17 & -0.351634 & -2.678 & 0.00481 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105390&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]0.921406[/C][C]7.0172[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.813384[/C][C]6.1946[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.712794[/C][C]5.4285[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]0.610464[/C][C]4.6492[/C][C]1e-05[/C][/ROW]
[ROW][C]5[/C][C]0.523526[/C][C]3.9871[/C][C]9.5e-05[/C][/ROW]
[ROW][C]6[/C][C]0.404002[/C][C]3.0768[/C][C]0.001596[/C][/ROW]
[ROW][C]7[/C][C]0.25953[/C][C]1.9765[/C][C]0.026429[/C][/ROW]
[ROW][C]8[/C][C]0.146123[/C][C]1.1128[/C][C]0.135185[/C][/ROW]
[ROW][C]9[/C][C]0.058554[/C][C]0.4459[/C][C]0.328652[/C][/ROW]
[ROW][C]10[/C][C]-0.022793[/C][C]-0.1736[/C][C]0.431397[/C][/ROW]
[ROW][C]11[/C][C]-0.095603[/C][C]-0.7281[/C][C]0.234744[/C][/ROW]
[ROW][C]12[/C][C]-0.174787[/C][C]-1.3311[/C][C]0.094177[/C][/ROW]
[ROW][C]13[/C][C]-0.233689[/C][C]-1.7797[/C][C]0.04018[/C][/ROW]
[ROW][C]14[/C][C]-0.249493[/C][C]-1.9001[/C][C]0.031198[/C][/ROW]
[ROW][C]15[/C][C]-0.264299[/C][C]-2.0128[/C][C]0.024391[/C][/ROW]
[ROW][C]16[/C][C]-0.298059[/C][C]-2.27[/C][C]0.013472[/C][/ROW]
[ROW][C]17[/C][C]-0.351634[/C][C]-2.678[/C][C]0.00481[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105390&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105390&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	0.921406	7.0172	0
2	0.813384	6.1946	0
3	0.712794	5.4285	1e-06
4	0.610464	4.6492	1e-05
5	0.523526	3.9871	9.5e-05
6	0.404002	3.0768	0.001596
7	0.25953	1.9765	0.026429
8	0.146123	1.1128	0.135185
9	0.058554	0.4459	0.328652
10	-0.022793	-0.1736	0.431397
11	-0.095603	-0.7281	0.234744
12	-0.174787	-1.3311	0.094177
13	-0.233689	-1.7797	0.04018
14	-0.249493	-1.9001	0.031198
15	-0.264299	-2.0128	0.024391
16	-0.298059	-2.27	0.013472
17	-0.351634	-2.678	0.00481

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.921406	7.0172	0
2	-0.23577	-1.7956	0.038886
3	0.027187	0.207	0.418348
4	-0.097003	-0.7388	0.231518
5	0.059392	0.4523	0.326365
6	-0.337982	-2.574	0.006315
7	-0.150724	-1.1479	0.127865
8	0.125557	0.9562	0.171466
9	0.028637	0.2181	0.414061
10	-0.13228	-1.0074	0.15896
11	-0.004931	-0.0376	0.485086
12	-0.045627	-0.3475	0.364742
13	0.041013	0.3123	0.377948
14	0.068094	0.5186	0.30301
15	-0.115585	-0.8803	0.191173
16	-0.180935	-1.378	0.086754
17	-0.181791	-1.3845	0.085757

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.921406 & 7.0172 & 0 \tabularnewline
2 & -0.23577 & -1.7956 & 0.038886 \tabularnewline
3 & 0.027187 & 0.207 & 0.418348 \tabularnewline
4 & -0.097003 & -0.7388 & 0.231518 \tabularnewline
5 & 0.059392 & 0.4523 & 0.326365 \tabularnewline
6 & -0.337982 & -2.574 & 0.006315 \tabularnewline
7 & -0.150724 & -1.1479 & 0.127865 \tabularnewline
8 & 0.125557 & 0.9562 & 0.171466 \tabularnewline
9 & 0.028637 & 0.2181 & 0.414061 \tabularnewline
10 & -0.13228 & -1.0074 & 0.15896 \tabularnewline
11 & -0.004931 & -0.0376 & 0.485086 \tabularnewline
12 & -0.045627 & -0.3475 & 0.364742 \tabularnewline
13 & 0.041013 & 0.3123 & 0.377948 \tabularnewline
14 & 0.068094 & 0.5186 & 0.30301 \tabularnewline
15 & -0.115585 & -0.8803 & 0.191173 \tabularnewline
16 & -0.180935 & -1.378 & 0.086754 \tabularnewline
17 & -0.181791 & -1.3845 & 0.085757 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105390&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]0.921406[/C][C]7.0172[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.23577[/C][C]-1.7956[/C][C]0.038886[/C][/ROW]
[ROW][C]3[/C][C]0.027187[/C][C]0.207[/C][C]0.418348[/C][/ROW]
[ROW][C]4[/C][C]-0.097003[/C][C]-0.7388[/C][C]0.231518[/C][/ROW]
[ROW][C]5[/C][C]0.059392[/C][C]0.4523[/C][C]0.326365[/C][/ROW]
[ROW][C]6[/C][C]-0.337982[/C][C]-2.574[/C][C]0.006315[/C][/ROW]
[ROW][C]7[/C][C]-0.150724[/C][C]-1.1479[/C][C]0.127865[/C][/ROW]
[ROW][C]8[/C][C]0.125557[/C][C]0.9562[/C][C]0.171466[/C][/ROW]
[ROW][C]9[/C][C]0.028637[/C][C]0.2181[/C][C]0.414061[/C][/ROW]
[ROW][C]10[/C][C]-0.13228[/C][C]-1.0074[/C][C]0.15896[/C][/ROW]
[ROW][C]11[/C][C]-0.004931[/C][C]-0.0376[/C][C]0.485086[/C][/ROW]
[ROW][C]12[/C][C]-0.045627[/C][C]-0.3475[/C][C]0.364742[/C][/ROW]
[ROW][C]13[/C][C]0.041013[/C][C]0.3123[/C][C]0.377948[/C][/ROW]
[ROW][C]14[/C][C]0.068094[/C][C]0.5186[/C][C]0.30301[/C][/ROW]
[ROW][C]15[/C][C]-0.115585[/C][C]-0.8803[/C][C]0.191173[/C][/ROW]
[ROW][C]16[/C][C]-0.180935[/C][C]-1.378[/C][C]0.086754[/C][/ROW]
[ROW][C]17[/C][C]-0.181791[/C][C]-1.3845[/C][C]0.085757[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105390&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105390&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	0.921406	7.0172	0
2	-0.23577	-1.7956	0.038886
3	0.027187	0.207	0.418348
4	-0.097003	-0.7388	0.231518
5	0.059392	0.4523	0.326365
6	-0.337982	-2.574	0.006315
7	-0.150724	-1.1479	0.127865
8	0.125557	0.9562	0.171466
9	0.028637	0.2181	0.414061
10	-0.13228	-1.0074	0.15896
11	-0.004931	-0.0376	0.485086
12	-0.045627	-0.3475	0.364742
13	0.041013	0.3123	0.377948
14	0.068094	0.5186	0.30301
15	-0.115585	-0.8803	0.191173
16	-0.180935	-1.378	0.086754
17	-0.181791	-1.3845	0.085757

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code