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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 07 Dec 2010 08:47:05 +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/07/t1291711501qv4h0m49p0nycar.htm/, Retrieved Sat, 04 May 2024 04:10:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106013, Retrieved Sat, 04 May 2024 04:10:13 +0000

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Estimated Impact

155

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] [WS9 ACF 1] [2010-12-07 08:47:05] [67e3c2d70de1dbb070b545ca6c893d5e] [Current]
-   P         [(Partial) Autocorrelation Function] [WS9 ACF 2 d=1 D=0] [2010-12-07 08:50:58] [07a238a5afc23eb944f8545182f29d5a] 
-   P         [(Partial) Autocorrelation Function] [WS9 ACF 3 d=1 D=0...] [2010-12-07 08:52:55] [07a238a5afc23eb944f8545182f29d5a] 
-   P           [(Partial) Autocorrelation Function] [WS9 ACF 4 d=D=1 (...] [2010-12-07 08:56:39] [07a238a5afc23eb944f8545182f29d5a] 

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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=106013&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=106013&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106013&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	0.890217	7.5537	0
2	0.725751	6.1582	0
3	0.611695	5.1904	1e-06
4	0.564166	4.7871	4e-06
5	0.561599	4.7653	5e-06
6	0.538003	4.5651	1e-05
7	0.47865	4.0615	6.1e-05
8	0.407094	3.4543	0.000464
9	0.377579	3.2039	0.001011
10	0.404766	3.4346	0.000494
11	0.47634	4.0419	6.6e-05
12	0.492163	4.1761	4.1e-05
13	0.343838	2.9176	0.002351
14	0.166186	1.4101	0.081402
15	0.040327	0.3422	0.366603
16	-0.017739	-0.1505	0.440388
17	-0.032873	-0.2789	0.390546
18	-0.064908	-0.5508	0.291752

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.890217 & 7.5537 & 0 \tabularnewline
2 & 0.725751 & 6.1582 & 0 \tabularnewline
3 & 0.611695 & 5.1904 & 1e-06 \tabularnewline
4 & 0.564166 & 4.7871 & 4e-06 \tabularnewline
5 & 0.561599 & 4.7653 & 5e-06 \tabularnewline
6 & 0.538003 & 4.5651 & 1e-05 \tabularnewline
7 & 0.47865 & 4.0615 & 6.1e-05 \tabularnewline
8 & 0.407094 & 3.4543 & 0.000464 \tabularnewline
9 & 0.377579 & 3.2039 & 0.001011 \tabularnewline
10 & 0.404766 & 3.4346 & 0.000494 \tabularnewline
11 & 0.47634 & 4.0419 & 6.6e-05 \tabularnewline
12 & 0.492163 & 4.1761 & 4.1e-05 \tabularnewline
13 & 0.343838 & 2.9176 & 0.002351 \tabularnewline
14 & 0.166186 & 1.4101 & 0.081402 \tabularnewline
15 & 0.040327 & 0.3422 & 0.366603 \tabularnewline
16 & -0.017739 & -0.1505 & 0.440388 \tabularnewline
17 & -0.032873 & -0.2789 & 0.390546 \tabularnewline
18 & -0.064908 & -0.5508 & 0.291752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106013&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]0.890217[/C][C]7.5537[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.725751[/C][C]6.1582[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.611695[/C][C]5.1904[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]0.564166[/C][C]4.7871[/C][C]4e-06[/C][/ROW]
[ROW][C]5[/C][C]0.561599[/C][C]4.7653[/C][C]5e-06[/C][/ROW]
[ROW][C]6[/C][C]0.538003[/C][C]4.5651[/C][C]1e-05[/C][/ROW]
[ROW][C]7[/C][C]0.47865[/C][C]4.0615[/C][C]6.1e-05[/C][/ROW]
[ROW][C]8[/C][C]0.407094[/C][C]3.4543[/C][C]0.000464[/C][/ROW]
[ROW][C]9[/C][C]0.377579[/C][C]3.2039[/C][C]0.001011[/C][/ROW]
[ROW][C]10[/C][C]0.404766[/C][C]3.4346[/C][C]0.000494[/C][/ROW]
[ROW][C]11[/C][C]0.47634[/C][C]4.0419[/C][C]6.6e-05[/C][/ROW]
[ROW][C]12[/C][C]0.492163[/C][C]4.1761[/C][C]4.1e-05[/C][/ROW]
[ROW][C]13[/C][C]0.343838[/C][C]2.9176[/C][C]0.002351[/C][/ROW]
[ROW][C]14[/C][C]0.166186[/C][C]1.4101[/C][C]0.081402[/C][/ROW]
[ROW][C]15[/C][C]0.040327[/C][C]0.3422[/C][C]0.366603[/C][/ROW]
[ROW][C]16[/C][C]-0.017739[/C][C]-0.1505[/C][C]0.440388[/C][/ROW]
[ROW][C]17[/C][C]-0.032873[/C][C]-0.2789[/C][C]0.390546[/C][/ROW]
[ROW][C]18[/C][C]-0.064908[/C][C]-0.5508[/C][C]0.291752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106013&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106013&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	0.890217	7.5537	0
2	0.725751	6.1582	0
3	0.611695	5.1904	1e-06
4	0.564166	4.7871	4e-06
5	0.561599	4.7653	5e-06
6	0.538003	4.5651	1e-05
7	0.47865	4.0615	6.1e-05
8	0.407094	3.4543	0.000464
9	0.377579	3.2039	0.001011
10	0.404766	3.4346	0.000494
11	0.47634	4.0419	6.6e-05
12	0.492163	4.1761	4.1e-05
13	0.343838	2.9176	0.002351
14	0.166186	1.4101	0.081402
15	0.040327	0.3422	0.366603
16	-0.017739	-0.1505	0.440388
17	-0.032873	-0.2789	0.390546
18	-0.064908	-0.5508	0.291752

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.890217	7.5537	0
2	-0.321591	-2.7288	0.003992
3	0.237203	2.0127	0.023941
4	0.128785	1.0928	0.139067
5	0.130028	1.1033	0.13678
6	-0.118461	-1.0052	0.159089
7	-0.018215	-0.1546	0.438799
8	-0.020776	-0.1763	0.430281
9	0.173085	1.4687	0.073138
10	0.117782	0.9994	0.160472
11	0.229397	1.9465	0.027749
12	-0.261443	-2.2184	0.01484
13	-0.656797	-5.5731	0
14	0.127629	1.083	0.141219
15	-0.105395	-0.8943	0.18707
16	-0.060416	-0.5126	0.304885
17	-0.026518	-0.225	0.411304
18	0.052518	0.4456	0.328601

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.890217 & 7.5537 & 0 \tabularnewline
2 & -0.321591 & -2.7288 & 0.003992 \tabularnewline
3 & 0.237203 & 2.0127 & 0.023941 \tabularnewline
4 & 0.128785 & 1.0928 & 0.139067 \tabularnewline
5 & 0.130028 & 1.1033 & 0.13678 \tabularnewline
6 & -0.118461 & -1.0052 & 0.159089 \tabularnewline
7 & -0.018215 & -0.1546 & 0.438799 \tabularnewline
8 & -0.020776 & -0.1763 & 0.430281 \tabularnewline
9 & 0.173085 & 1.4687 & 0.073138 \tabularnewline
10 & 0.117782 & 0.9994 & 0.160472 \tabularnewline
11 & 0.229397 & 1.9465 & 0.027749 \tabularnewline
12 & -0.261443 & -2.2184 & 0.01484 \tabularnewline
13 & -0.656797 & -5.5731 & 0 \tabularnewline
14 & 0.127629 & 1.083 & 0.141219 \tabularnewline
15 & -0.105395 & -0.8943 & 0.18707 \tabularnewline
16 & -0.060416 & -0.5126 & 0.304885 \tabularnewline
17 & -0.026518 & -0.225 & 0.411304 \tabularnewline
18 & 0.052518 & 0.4456 & 0.328601 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106013&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]0.890217[/C][C]7.5537[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.321591[/C][C]-2.7288[/C][C]0.003992[/C][/ROW]
[ROW][C]3[/C][C]0.237203[/C][C]2.0127[/C][C]0.023941[/C][/ROW]
[ROW][C]4[/C][C]0.128785[/C][C]1.0928[/C][C]0.139067[/C][/ROW]
[ROW][C]5[/C][C]0.130028[/C][C]1.1033[/C][C]0.13678[/C][/ROW]
[ROW][C]6[/C][C]-0.118461[/C][C]-1.0052[/C][C]0.159089[/C][/ROW]
[ROW][C]7[/C][C]-0.018215[/C][C]-0.1546[/C][C]0.438799[/C][/ROW]
[ROW][C]8[/C][C]-0.020776[/C][C]-0.1763[/C][C]0.430281[/C][/ROW]
[ROW][C]9[/C][C]0.173085[/C][C]1.4687[/C][C]0.073138[/C][/ROW]
[ROW][C]10[/C][C]0.117782[/C][C]0.9994[/C][C]0.160472[/C][/ROW]
[ROW][C]11[/C][C]0.229397[/C][C]1.9465[/C][C]0.027749[/C][/ROW]
[ROW][C]12[/C][C]-0.261443[/C][C]-2.2184[/C][C]0.01484[/C][/ROW]
[ROW][C]13[/C][C]-0.656797[/C][C]-5.5731[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.127629[/C][C]1.083[/C][C]0.141219[/C][/ROW]
[ROW][C]15[/C][C]-0.105395[/C][C]-0.8943[/C][C]0.18707[/C][/ROW]
[ROW][C]16[/C][C]-0.060416[/C][C]-0.5126[/C][C]0.304885[/C][/ROW]
[ROW][C]17[/C][C]-0.026518[/C][C]-0.225[/C][C]0.411304[/C][/ROW]
[ROW][C]18[/C][C]0.052518[/C][C]0.4456[/C][C]0.328601[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106013&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106013&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	0.890217	7.5537	0
2	-0.321591	-2.7288	0.003992
3	0.237203	2.0127	0.023941
4	0.128785	1.0928	0.139067
5	0.130028	1.1033	0.13678
6	-0.118461	-1.0052	0.159089
7	-0.018215	-0.1546	0.438799
8	-0.020776	-0.1763	0.430281
9	0.173085	1.4687	0.073138
10	0.117782	0.9994	0.160472
11	0.229397	1.9465	0.027749
12	-0.261443	-2.2184	0.01484
13	-0.656797	-5.5731	0
14	0.127629	1.083	0.141219
15	-0.105395	-0.8943	0.18707
16	-0.060416	-0.5126	0.304885
17	-0.026518	-0.225	0.411304
18	0.052518	0.4456	0.328601

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