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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 07 Dec 2009 12:20:58 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/07/t126021368366m3v0l7oqyyq26.htm/, Retrieved Sun, 05 May 2024 02:19:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64613, Retrieved Sun, 05 May 2024 02:19:10 +0000

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Estimated Impact

137

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-    D        [(Partial) Autocorrelation Function] [WS 8: Methode 1 ACF] [2009-11-27 12:58:46] [8cf9233b7464ea02e32be3b30fdac052]
-   PD            [(Partial) Autocorrelation Function] [] [2009-12-07 19:20:58] [a7903eee767dfd0f468efdd2f9e43d36] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64613&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]1 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=64613&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64613&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.742189	5.9375	0
2	0.329889	2.6391	0.005214
3	0.070328	0.5626	0.287829
4	-0.002153	-0.0172	0.493155
5	0.076971	0.6158	0.270116
6	0.145741	1.1659	0.123985
7	0.117722	0.9418	0.174925
8	0.044371	0.355	0.36189
9	0.047513	0.3801	0.352563
10	0.147684	1.1815	0.120893
11	0.309489	2.4759	0.007973
12	0.401596	3.2128	0.00103
13	0.226903	1.8152	0.037087
14	0.000301	0.0024	0.499042
15	-0.111802	-0.8944	0.187226
16	-0.166003	-1.328	0.094444
17	-0.16946	-1.3557	0.089983
18	-0.176356	-1.4108	0.081566

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.742189 & 5.9375 & 0 \tabularnewline
2 & 0.329889 & 2.6391 & 0.005214 \tabularnewline
3 & 0.070328 & 0.5626 & 0.287829 \tabularnewline
4 & -0.002153 & -0.0172 & 0.493155 \tabularnewline
5 & 0.076971 & 0.6158 & 0.270116 \tabularnewline
6 & 0.145741 & 1.1659 & 0.123985 \tabularnewline
7 & 0.117722 & 0.9418 & 0.174925 \tabularnewline
8 & 0.044371 & 0.355 & 0.36189 \tabularnewline
9 & 0.047513 & 0.3801 & 0.352563 \tabularnewline
10 & 0.147684 & 1.1815 & 0.120893 \tabularnewline
11 & 0.309489 & 2.4759 & 0.007973 \tabularnewline
12 & 0.401596 & 3.2128 & 0.00103 \tabularnewline
13 & 0.226903 & 1.8152 & 0.037087 \tabularnewline
14 & 0.000301 & 0.0024 & 0.499042 \tabularnewline
15 & -0.111802 & -0.8944 & 0.187226 \tabularnewline
16 & -0.166003 & -1.328 & 0.094444 \tabularnewline
17 & -0.16946 & -1.3557 & 0.089983 \tabularnewline
18 & -0.176356 & -1.4108 & 0.081566 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64613&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]0.742189[/C][C]5.9375[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.329889[/C][C]2.6391[/C][C]0.005214[/C][/ROW]
[ROW][C]3[/C][C]0.070328[/C][C]0.5626[/C][C]0.287829[/C][/ROW]
[ROW][C]4[/C][C]-0.002153[/C][C]-0.0172[/C][C]0.493155[/C][/ROW]
[ROW][C]5[/C][C]0.076971[/C][C]0.6158[/C][C]0.270116[/C][/ROW]
[ROW][C]6[/C][C]0.145741[/C][C]1.1659[/C][C]0.123985[/C][/ROW]
[ROW][C]7[/C][C]0.117722[/C][C]0.9418[/C][C]0.174925[/C][/ROW]
[ROW][C]8[/C][C]0.044371[/C][C]0.355[/C][C]0.36189[/C][/ROW]
[ROW][C]9[/C][C]0.047513[/C][C]0.3801[/C][C]0.352563[/C][/ROW]
[ROW][C]10[/C][C]0.147684[/C][C]1.1815[/C][C]0.120893[/C][/ROW]
[ROW][C]11[/C][C]0.309489[/C][C]2.4759[/C][C]0.007973[/C][/ROW]
[ROW][C]12[/C][C]0.401596[/C][C]3.2128[/C][C]0.00103[/C][/ROW]
[ROW][C]13[/C][C]0.226903[/C][C]1.8152[/C][C]0.037087[/C][/ROW]
[ROW][C]14[/C][C]0.000301[/C][C]0.0024[/C][C]0.499042[/C][/ROW]
[ROW][C]15[/C][C]-0.111802[/C][C]-0.8944[/C][C]0.187226[/C][/ROW]
[ROW][C]16[/C][C]-0.166003[/C][C]-1.328[/C][C]0.094444[/C][/ROW]
[ROW][C]17[/C][C]-0.16946[/C][C]-1.3557[/C][C]0.089983[/C][/ROW]
[ROW][C]18[/C][C]-0.176356[/C][C]-1.4108[/C][C]0.081566[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64613&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64613&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	0.742189	5.9375	0
2	0.329889	2.6391	0.005214
3	0.070328	0.5626	0.287829
4	-0.002153	-0.0172	0.493155
5	0.076971	0.6158	0.270116
6	0.145741	1.1659	0.123985
7	0.117722	0.9418	0.174925
8	0.044371	0.355	0.36189
9	0.047513	0.3801	0.352563
10	0.147684	1.1815	0.120893
11	0.309489	2.4759	0.007973
12	0.401596	3.2128	0.00103
13	0.226903	1.8152	0.037087
14	0.000301	0.0024	0.499042
15	-0.111802	-0.8944	0.187226
16	-0.166003	-1.328	0.094444
17	-0.16946	-1.3557	0.089983
18	-0.176356	-1.4108	0.081566

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.742189	5.9375	0
2	-0.491935	-3.9355	0.000104
3	0.206048	1.6484	0.052088
4	-0.007766	-0.0621	0.475328
5	0.200337	1.6027	0.056963
6	-0.130091	-1.0407	0.150959
7	0.009634	0.0771	0.469402
8	-0.008552	-0.0684	0.472835
9	0.212899	1.7032	0.046692
10	0.065599	0.5248	0.300772
11	0.257513	2.0601	0.02173
12	-0.060976	-0.4878	0.313676
13	-0.359024	-2.8722	0.002761
14	0.28644	2.2915	0.012617
15	-0.207483	-1.6599	0.050918
16	-0.161882	-1.2951	0.099977
17	-0.115223	-0.9218	0.180051
18	-0.068354	-0.5468	0.293197

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.742189 & 5.9375 & 0 \tabularnewline
2 & -0.491935 & -3.9355 & 0.000104 \tabularnewline
3 & 0.206048 & 1.6484 & 0.052088 \tabularnewline
4 & -0.007766 & -0.0621 & 0.475328 \tabularnewline
5 & 0.200337 & 1.6027 & 0.056963 \tabularnewline
6 & -0.130091 & -1.0407 & 0.150959 \tabularnewline
7 & 0.009634 & 0.0771 & 0.469402 \tabularnewline
8 & -0.008552 & -0.0684 & 0.472835 \tabularnewline
9 & 0.212899 & 1.7032 & 0.046692 \tabularnewline
10 & 0.065599 & 0.5248 & 0.300772 \tabularnewline
11 & 0.257513 & 2.0601 & 0.02173 \tabularnewline
12 & -0.060976 & -0.4878 & 0.313676 \tabularnewline
13 & -0.359024 & -2.8722 & 0.002761 \tabularnewline
14 & 0.28644 & 2.2915 & 0.012617 \tabularnewline
15 & -0.207483 & -1.6599 & 0.050918 \tabularnewline
16 & -0.161882 & -1.2951 & 0.099977 \tabularnewline
17 & -0.115223 & -0.9218 & 0.180051 \tabularnewline
18 & -0.068354 & -0.5468 & 0.293197 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64613&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]0.742189[/C][C]5.9375[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.491935[/C][C]-3.9355[/C][C]0.000104[/C][/ROW]
[ROW][C]3[/C][C]0.206048[/C][C]1.6484[/C][C]0.052088[/C][/ROW]
[ROW][C]4[/C][C]-0.007766[/C][C]-0.0621[/C][C]0.475328[/C][/ROW]
[ROW][C]5[/C][C]0.200337[/C][C]1.6027[/C][C]0.056963[/C][/ROW]
[ROW][C]6[/C][C]-0.130091[/C][C]-1.0407[/C][C]0.150959[/C][/ROW]
[ROW][C]7[/C][C]0.009634[/C][C]0.0771[/C][C]0.469402[/C][/ROW]
[ROW][C]8[/C][C]-0.008552[/C][C]-0.0684[/C][C]0.472835[/C][/ROW]
[ROW][C]9[/C][C]0.212899[/C][C]1.7032[/C][C]0.046692[/C][/ROW]
[ROW][C]10[/C][C]0.065599[/C][C]0.5248[/C][C]0.300772[/C][/ROW]
[ROW][C]11[/C][C]0.257513[/C][C]2.0601[/C][C]0.02173[/C][/ROW]
[ROW][C]12[/C][C]-0.060976[/C][C]-0.4878[/C][C]0.313676[/C][/ROW]
[ROW][C]13[/C][C]-0.359024[/C][C]-2.8722[/C][C]0.002761[/C][/ROW]
[ROW][C]14[/C][C]0.28644[/C][C]2.2915[/C][C]0.012617[/C][/ROW]
[ROW][C]15[/C][C]-0.207483[/C][C]-1.6599[/C][C]0.050918[/C][/ROW]
[ROW][C]16[/C][C]-0.161882[/C][C]-1.2951[/C][C]0.099977[/C][/ROW]
[ROW][C]17[/C][C]-0.115223[/C][C]-0.9218[/C][C]0.180051[/C][/ROW]
[ROW][C]18[/C][C]-0.068354[/C][C]-0.5468[/C][C]0.293197[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64613&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64613&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	0.742189	5.9375	0
2	-0.491935	-3.9355	0.000104
3	0.206048	1.6484	0.052088
4	-0.007766	-0.0621	0.475328
5	0.200337	1.6027	0.056963
6	-0.130091	-1.0407	0.150959
7	0.009634	0.0771	0.469402
8	-0.008552	-0.0684	0.472835
9	0.212899	1.7032	0.046692
10	0.065599	0.5248	0.300772
11	0.257513	2.0601	0.02173
12	-0.060976	-0.4878	0.313676
13	-0.359024	-2.8722	0.002761
14	0.28644	2.2915	0.012617
15	-0.207483	-1.6599	0.050918
16	-0.161882	-1.2951	0.099977
17	-0.115223	-0.9218	0.180051
18	-0.068354	-0.5468	0.293197

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