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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 26 Nov 2009 02:16:46 -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/26/t12592270659x8jtdku2tqzdma.htm/, Retrieved Sun, 28 Apr 2024 22:32:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59721, Retrieved Sun, 28 Apr 2024 22:32:22 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Basisjaar 2000 = 100

Estimated Impact

183

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] [Grondstofprijsind...] [2009-11-26 09:16:46] [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=59721&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=59721&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59721&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	0.492511	2.9551	0.002742
2	0.271004	1.626	0.056334
3	0.202898	1.2174	0.115689
4	0.123898	0.7434	0.231035
5	-0.120624	-0.7237	0.236949
6	-0.074371	-0.4462	0.329052
7	0.060108	0.3606	0.360235
8	-0.12679	-0.7607	0.225884
9	-0.180054	-1.0803	0.143591
10	-0.046633	-0.2798	0.390617
11	-0.006101	-0.0366	0.4855
12	-0.345079	-2.0705	0.022819
13	-0.220699	-1.3242	0.096892
14	-0.11927	-0.7156	0.239421
15	-0.072616	-0.4357	0.332829
16	-0.08924	-0.5354	0.297819
17	0.005862	0.0352	0.486068

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.492511 & 2.9551 & 0.002742 \tabularnewline
2 & 0.271004 & 1.626 & 0.056334 \tabularnewline
3 & 0.202898 & 1.2174 & 0.115689 \tabularnewline
4 & 0.123898 & 0.7434 & 0.231035 \tabularnewline
5 & -0.120624 & -0.7237 & 0.236949 \tabularnewline
6 & -0.074371 & -0.4462 & 0.329052 \tabularnewline
7 & 0.060108 & 0.3606 & 0.360235 \tabularnewline
8 & -0.12679 & -0.7607 & 0.225884 \tabularnewline
9 & -0.180054 & -1.0803 & 0.143591 \tabularnewline
10 & -0.046633 & -0.2798 & 0.390617 \tabularnewline
11 & -0.006101 & -0.0366 & 0.4855 \tabularnewline
12 & -0.345079 & -2.0705 & 0.022819 \tabularnewline
13 & -0.220699 & -1.3242 & 0.096892 \tabularnewline
14 & -0.11927 & -0.7156 & 0.239421 \tabularnewline
15 & -0.072616 & -0.4357 & 0.332829 \tabularnewline
16 & -0.08924 & -0.5354 & 0.297819 \tabularnewline
17 & 0.005862 & 0.0352 & 0.486068 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59721&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]0.492511[/C][C]2.9551[/C][C]0.002742[/C][/ROW]
[ROW][C]2[/C][C]0.271004[/C][C]1.626[/C][C]0.056334[/C][/ROW]
[ROW][C]3[/C][C]0.202898[/C][C]1.2174[/C][C]0.115689[/C][/ROW]
[ROW][C]4[/C][C]0.123898[/C][C]0.7434[/C][C]0.231035[/C][/ROW]
[ROW][C]5[/C][C]-0.120624[/C][C]-0.7237[/C][C]0.236949[/C][/ROW]
[ROW][C]6[/C][C]-0.074371[/C][C]-0.4462[/C][C]0.329052[/C][/ROW]
[ROW][C]7[/C][C]0.060108[/C][C]0.3606[/C][C]0.360235[/C][/ROW]
[ROW][C]8[/C][C]-0.12679[/C][C]-0.7607[/C][C]0.225884[/C][/ROW]
[ROW][C]9[/C][C]-0.180054[/C][C]-1.0803[/C][C]0.143591[/C][/ROW]
[ROW][C]10[/C][C]-0.046633[/C][C]-0.2798[/C][C]0.390617[/C][/ROW]
[ROW][C]11[/C][C]-0.006101[/C][C]-0.0366[/C][C]0.4855[/C][/ROW]
[ROW][C]12[/C][C]-0.345079[/C][C]-2.0705[/C][C]0.022819[/C][/ROW]
[ROW][C]13[/C][C]-0.220699[/C][C]-1.3242[/C][C]0.096892[/C][/ROW]
[ROW][C]14[/C][C]-0.11927[/C][C]-0.7156[/C][C]0.239421[/C][/ROW]
[ROW][C]15[/C][C]-0.072616[/C][C]-0.4357[/C][C]0.332829[/C][/ROW]
[ROW][C]16[/C][C]-0.08924[/C][C]-0.5354[/C][C]0.297819[/C][/ROW]
[ROW][C]17[/C][C]0.005862[/C][C]0.0352[/C][C]0.486068[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59721&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59721&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	0.492511	2.9551	0.002742
2	0.271004	1.626	0.056334
3	0.202898	1.2174	0.115689
4	0.123898	0.7434	0.231035
5	-0.120624	-0.7237	0.236949
6	-0.074371	-0.4462	0.329052
7	0.060108	0.3606	0.360235
8	-0.12679	-0.7607	0.225884
9	-0.180054	-1.0803	0.143591
10	-0.046633	-0.2798	0.390617
11	-0.006101	-0.0366	0.4855
12	-0.345079	-2.0705	0.022819
13	-0.220699	-1.3242	0.096892
14	-0.11927	-0.7156	0.239421
15	-0.072616	-0.4357	0.332829
16	-0.08924	-0.5354	0.297819
17	0.005862	0.0352	0.486068

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.492511	2.9551	0.002742
2	0.037545	0.2253	0.411522
3	0.073966	0.4438	0.329923
4	-0.011722	-0.0703	0.472158
5	-0.259793	-1.5588	0.063902
6	0.086927	0.5216	0.302586
7	0.151971	0.9118	0.183963
8	-0.254691	-1.5281	0.067608
9	-0.037035	-0.2222	0.412703
10	0.081906	0.4914	0.31305
11	0.000913	0.0055	0.49783
12	-0.408256	-2.4495	0.00965
13	0.106327	0.638	0.263769
14	-0.00126	-0.0076	0.497005
15	0.121615	0.7297	0.235151
16	-0.003336	-0.02	0.49207
17	-0.213605	-1.2816	0.104083

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.492511 & 2.9551 & 0.002742 \tabularnewline
2 & 0.037545 & 0.2253 & 0.411522 \tabularnewline
3 & 0.073966 & 0.4438 & 0.329923 \tabularnewline
4 & -0.011722 & -0.0703 & 0.472158 \tabularnewline
5 & -0.259793 & -1.5588 & 0.063902 \tabularnewline
6 & 0.086927 & 0.5216 & 0.302586 \tabularnewline
7 & 0.151971 & 0.9118 & 0.183963 \tabularnewline
8 & -0.254691 & -1.5281 & 0.067608 \tabularnewline
9 & -0.037035 & -0.2222 & 0.412703 \tabularnewline
10 & 0.081906 & 0.4914 & 0.31305 \tabularnewline
11 & 0.000913 & 0.0055 & 0.49783 \tabularnewline
12 & -0.408256 & -2.4495 & 0.00965 \tabularnewline
13 & 0.106327 & 0.638 & 0.263769 \tabularnewline
14 & -0.00126 & -0.0076 & 0.497005 \tabularnewline
15 & 0.121615 & 0.7297 & 0.235151 \tabularnewline
16 & -0.003336 & -0.02 & 0.49207 \tabularnewline
17 & -0.213605 & -1.2816 & 0.104083 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59721&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]0.492511[/C][C]2.9551[/C][C]0.002742[/C][/ROW]
[ROW][C]2[/C][C]0.037545[/C][C]0.2253[/C][C]0.411522[/C][/ROW]
[ROW][C]3[/C][C]0.073966[/C][C]0.4438[/C][C]0.329923[/C][/ROW]
[ROW][C]4[/C][C]-0.011722[/C][C]-0.0703[/C][C]0.472158[/C][/ROW]
[ROW][C]5[/C][C]-0.259793[/C][C]-1.5588[/C][C]0.063902[/C][/ROW]
[ROW][C]6[/C][C]0.086927[/C][C]0.5216[/C][C]0.302586[/C][/ROW]
[ROW][C]7[/C][C]0.151971[/C][C]0.9118[/C][C]0.183963[/C][/ROW]
[ROW][C]8[/C][C]-0.254691[/C][C]-1.5281[/C][C]0.067608[/C][/ROW]
[ROW][C]9[/C][C]-0.037035[/C][C]-0.2222[/C][C]0.412703[/C][/ROW]
[ROW][C]10[/C][C]0.081906[/C][C]0.4914[/C][C]0.31305[/C][/ROW]
[ROW][C]11[/C][C]0.000913[/C][C]0.0055[/C][C]0.49783[/C][/ROW]
[ROW][C]12[/C][C]-0.408256[/C][C]-2.4495[/C][C]0.00965[/C][/ROW]
[ROW][C]13[/C][C]0.106327[/C][C]0.638[/C][C]0.263769[/C][/ROW]
[ROW][C]14[/C][C]-0.00126[/C][C]-0.0076[/C][C]0.497005[/C][/ROW]
[ROW][C]15[/C][C]0.121615[/C][C]0.7297[/C][C]0.235151[/C][/ROW]
[ROW][C]16[/C][C]-0.003336[/C][C]-0.02[/C][C]0.49207[/C][/ROW]
[ROW][C]17[/C][C]-0.213605[/C][C]-1.2816[/C][C]0.104083[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59721&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59721&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	0.492511	2.9551	0.002742
2	0.037545	0.2253	0.411522
3	0.073966	0.4438	0.329923
4	-0.011722	-0.0703	0.472158
5	-0.259793	-1.5588	0.063902
6	0.086927	0.5216	0.302586
7	0.151971	0.9118	0.183963
8	-0.254691	-1.5281	0.067608
9	-0.037035	-0.2222	0.412703
10	0.081906	0.4914	0.31305
11	0.000913	0.0055	0.49783
12	-0.408256	-2.4495	0.00965
13	0.106327	0.638	0.263769
14	-0.00126	-0.0076	0.497005
15	0.121615	0.7297	0.235151
16	-0.003336	-0.02	0.49207
17	-0.213605	-1.2816	0.104083

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 2 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code