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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 27 Nov 2009 10:38:04 -0700

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/2009/Nov/27/t1259343578qfd7mi72ccftw4n.htm/, Retrieved Sun, 28 Apr 2024 20:11:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61046, Retrieved Sun, 28 Apr 2024 20:11:58 +0000

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Estimated Impact

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]
-   PD          [(Partial) Autocorrelation Function] [ws8 methode 1] [2009-11-27 17:38:04] [d41d8cd98f00b204e9800998ecf8427e] [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=61046&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=61046&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61046&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	0.348414	2.4139	0.009824
2	0.447695	3.1017	0.001609
3	0.458803	3.1787	0.001295
4	0.280148	1.9409	0.029076
5	0.22131	1.5333	0.065886
6	0.151655	1.0507	0.149329
7	-0.011999	-0.0831	0.467046
8	0.051215	0.3548	0.362136
9	0.039766	0.2755	0.392054
10	-0.048471	-0.3358	0.369235
11	-0.041966	-0.2907	0.386248
12	0.076325	0.5288	0.299692
13	0.004385	0.0304	0.487945
14	0.070379	0.4876	0.314027
15	0.04361	0.3021	0.381925
16	-0.006747	-0.0467	0.481456

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.348414 & 2.4139 & 0.009824 \tabularnewline
2 & 0.447695 & 3.1017 & 0.001609 \tabularnewline
3 & 0.458803 & 3.1787 & 0.001295 \tabularnewline
4 & 0.280148 & 1.9409 & 0.029076 \tabularnewline
5 & 0.22131 & 1.5333 & 0.065886 \tabularnewline
6 & 0.151655 & 1.0507 & 0.149329 \tabularnewline
7 & -0.011999 & -0.0831 & 0.467046 \tabularnewline
8 & 0.051215 & 0.3548 & 0.362136 \tabularnewline
9 & 0.039766 & 0.2755 & 0.392054 \tabularnewline
10 & -0.048471 & -0.3358 & 0.369235 \tabularnewline
11 & -0.041966 & -0.2907 & 0.386248 \tabularnewline
12 & 0.076325 & 0.5288 & 0.299692 \tabularnewline
13 & 0.004385 & 0.0304 & 0.487945 \tabularnewline
14 & 0.070379 & 0.4876 & 0.314027 \tabularnewline
15 & 0.04361 & 0.3021 & 0.381925 \tabularnewline
16 & -0.006747 & -0.0467 & 0.481456 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61046&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]0.348414[/C][C]2.4139[/C][C]0.009824[/C][/ROW]
[ROW][C]2[/C][C]0.447695[/C][C]3.1017[/C][C]0.001609[/C][/ROW]
[ROW][C]3[/C][C]0.458803[/C][C]3.1787[/C][C]0.001295[/C][/ROW]
[ROW][C]4[/C][C]0.280148[/C][C]1.9409[/C][C]0.029076[/C][/ROW]
[ROW][C]5[/C][C]0.22131[/C][C]1.5333[/C][C]0.065886[/C][/ROW]
[ROW][C]6[/C][C]0.151655[/C][C]1.0507[/C][C]0.149329[/C][/ROW]
[ROW][C]7[/C][C]-0.011999[/C][C]-0.0831[/C][C]0.467046[/C][/ROW]
[ROW][C]8[/C][C]0.051215[/C][C]0.3548[/C][C]0.362136[/C][/ROW]
[ROW][C]9[/C][C]0.039766[/C][C]0.2755[/C][C]0.392054[/C][/ROW]
[ROW][C]10[/C][C]-0.048471[/C][C]-0.3358[/C][C]0.369235[/C][/ROW]
[ROW][C]11[/C][C]-0.041966[/C][C]-0.2907[/C][C]0.386248[/C][/ROW]
[ROW][C]12[/C][C]0.076325[/C][C]0.5288[/C][C]0.299692[/C][/ROW]
[ROW][C]13[/C][C]0.004385[/C][C]0.0304[/C][C]0.487945[/C][/ROW]
[ROW][C]14[/C][C]0.070379[/C][C]0.4876[/C][C]0.314027[/C][/ROW]
[ROW][C]15[/C][C]0.04361[/C][C]0.3021[/C][C]0.381925[/C][/ROW]
[ROW][C]16[/C][C]-0.006747[/C][C]-0.0467[/C][C]0.481456[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61046&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61046&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	0.348414	2.4139	0.009824
2	0.447695	3.1017	0.001609
3	0.458803	3.1787	0.001295
4	0.280148	1.9409	0.029076
5	0.22131	1.5333	0.065886
6	0.151655	1.0507	0.149329
7	-0.011999	-0.0831	0.467046
8	0.051215	0.3548	0.362136
9	0.039766	0.2755	0.392054
10	-0.048471	-0.3358	0.369235
11	-0.041966	-0.2907	0.386248
12	0.076325	0.5288	0.299692
13	0.004385	0.0304	0.487945
14	0.070379	0.4876	0.314027
15	0.04361	0.3021	0.381925
16	-0.006747	-0.0467	0.481456

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.348414	2.4139	0.009824
2	0.371386	2.573	0.006614
3	0.305448	2.1162	0.01977
4	-0.016064	-0.1113	0.455924
5	-0.121612	-0.8426	0.201828
6	-0.124379	-0.8617	0.196563
7	-0.207625	-1.4385	0.078395
8	0.027142	0.188	0.425817
9	0.162293	1.1244	0.133218
10	0.06112	0.4234	0.336929
11	-0.05124	-0.355	0.362072
12	0.109132	0.7561	0.226646
13	0.018538	0.1284	0.449172
14	0.022894	0.1586	0.43732
15	-0.056217	-0.3895	0.349321
16	-0.120514	-0.8349	0.203943

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.348414 & 2.4139 & 0.009824 \tabularnewline
2 & 0.371386 & 2.573 & 0.006614 \tabularnewline
3 & 0.305448 & 2.1162 & 0.01977 \tabularnewline
4 & -0.016064 & -0.1113 & 0.455924 \tabularnewline
5 & -0.121612 & -0.8426 & 0.201828 \tabularnewline
6 & -0.124379 & -0.8617 & 0.196563 \tabularnewline
7 & -0.207625 & -1.4385 & 0.078395 \tabularnewline
8 & 0.027142 & 0.188 & 0.425817 \tabularnewline
9 & 0.162293 & 1.1244 & 0.133218 \tabularnewline
10 & 0.06112 & 0.4234 & 0.336929 \tabularnewline
11 & -0.05124 & -0.355 & 0.362072 \tabularnewline
12 & 0.109132 & 0.7561 & 0.226646 \tabularnewline
13 & 0.018538 & 0.1284 & 0.449172 \tabularnewline
14 & 0.022894 & 0.1586 & 0.43732 \tabularnewline
15 & -0.056217 & -0.3895 & 0.349321 \tabularnewline
16 & -0.120514 & -0.8349 & 0.203943 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61046&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]0.348414[/C][C]2.4139[/C][C]0.009824[/C][/ROW]
[ROW][C]2[/C][C]0.371386[/C][C]2.573[/C][C]0.006614[/C][/ROW]
[ROW][C]3[/C][C]0.305448[/C][C]2.1162[/C][C]0.01977[/C][/ROW]
[ROW][C]4[/C][C]-0.016064[/C][C]-0.1113[/C][C]0.455924[/C][/ROW]
[ROW][C]5[/C][C]-0.121612[/C][C]-0.8426[/C][C]0.201828[/C][/ROW]
[ROW][C]6[/C][C]-0.124379[/C][C]-0.8617[/C][C]0.196563[/C][/ROW]
[ROW][C]7[/C][C]-0.207625[/C][C]-1.4385[/C][C]0.078395[/C][/ROW]
[ROW][C]8[/C][C]0.027142[/C][C]0.188[/C][C]0.425817[/C][/ROW]
[ROW][C]9[/C][C]0.162293[/C][C]1.1244[/C][C]0.133218[/C][/ROW]
[ROW][C]10[/C][C]0.06112[/C][C]0.4234[/C][C]0.336929[/C][/ROW]
[ROW][C]11[/C][C]-0.05124[/C][C]-0.355[/C][C]0.362072[/C][/ROW]
[ROW][C]12[/C][C]0.109132[/C][C]0.7561[/C][C]0.226646[/C][/ROW]
[ROW][C]13[/C][C]0.018538[/C][C]0.1284[/C][C]0.449172[/C][/ROW]
[ROW][C]14[/C][C]0.022894[/C][C]0.1586[/C][C]0.43732[/C][/ROW]
[ROW][C]15[/C][C]-0.056217[/C][C]-0.3895[/C][C]0.349321[/C][/ROW]
[ROW][C]16[/C][C]-0.120514[/C][C]-0.8349[/C][C]0.203943[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=61046&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61046&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	0.348414	2.4139	0.009824
2	0.371386	2.573	0.006614
3	0.305448	2.1162	0.01977
4	-0.016064	-0.1113	0.455924
5	-0.121612	-0.8426	0.201828
6	-0.124379	-0.8617	0.196563
7	-0.207625	-1.4385	0.078395
8	0.027142	0.188	0.425817
9	0.162293	1.1244	0.133218
10	0.06112	0.4234	0.336929
11	-0.05124	-0.355	0.362072
12	0.109132	0.7561	0.226646
13	0.018538	0.1284	0.449172
14	0.022894	0.1586	0.43732
15	-0.056217	-0.3895	0.349321
16	-0.120514	-0.8349	0.203943

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 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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