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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 25 Nov 2009 01:10:24 -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/Nov/25/t1259136726jhfzhteqwr60jnk.htm/, Retrieved Tue, 07 May 2024 13:32:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59298, Retrieved Tue, 07 May 2024 13:32:33 +0000

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Estimated Impact

165

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] [] [2009-11-25 08:10:24] [ed082d38031561faed979d8cebfeba4d] [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=59298&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=59298&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59298&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	0.593088	4.594	1.1e-05
2	0.261158	2.0229	0.023772
3	-0.002495	-0.0193	0.492324
4	-0.198831	-1.5401	0.064393
5	-0.327391	-2.536	0.006918
6	-0.387485	-3.0014	0.001956
7	-0.377334	-2.9228	0.002443
8	-0.296572	-2.2972	0.012555
9	-0.141731	-1.0978	0.138329
10	0.087696	0.6793	0.249783
11	0.396128	3.0684	0.001614
12	0.791641	6.132	0
13	0.473905	3.6708	0.000258
14	0.212969	1.6497	0.05212
15	0.003842	0.0298	0.48818
16	-0.15379	-1.1913	0.119122
17	-0.260239	-2.0158	0.024153

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.593088 & 4.594 & 1.1e-05 \tabularnewline
2 & 0.261158 & 2.0229 & 0.023772 \tabularnewline
3 & -0.002495 & -0.0193 & 0.492324 \tabularnewline
4 & -0.198831 & -1.5401 & 0.064393 \tabularnewline
5 & -0.327391 & -2.536 & 0.006918 \tabularnewline
6 & -0.387485 & -3.0014 & 0.001956 \tabularnewline
7 & -0.377334 & -2.9228 & 0.002443 \tabularnewline
8 & -0.296572 & -2.2972 & 0.012555 \tabularnewline
9 & -0.141731 & -1.0978 & 0.138329 \tabularnewline
10 & 0.087696 & 0.6793 & 0.249783 \tabularnewline
11 & 0.396128 & 3.0684 & 0.001614 \tabularnewline
12 & 0.791641 & 6.132 & 0 \tabularnewline
13 & 0.473905 & 3.6708 & 0.000258 \tabularnewline
14 & 0.212969 & 1.6497 & 0.05212 \tabularnewline
15 & 0.003842 & 0.0298 & 0.48818 \tabularnewline
16 & -0.15379 & -1.1913 & 0.119122 \tabularnewline
17 & -0.260239 & -2.0158 & 0.024153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59298&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]0.593088[/C][C]4.594[/C][C]1.1e-05[/C][/ROW]
[ROW][C]2[/C][C]0.261158[/C][C]2.0229[/C][C]0.023772[/C][/ROW]
[ROW][C]3[/C][C]-0.002495[/C][C]-0.0193[/C][C]0.492324[/C][/ROW]
[ROW][C]4[/C][C]-0.198831[/C][C]-1.5401[/C][C]0.064393[/C][/ROW]
[ROW][C]5[/C][C]-0.327391[/C][C]-2.536[/C][C]0.006918[/C][/ROW]
[ROW][C]6[/C][C]-0.387485[/C][C]-3.0014[/C][C]0.001956[/C][/ROW]
[ROW][C]7[/C][C]-0.377334[/C][C]-2.9228[/C][C]0.002443[/C][/ROW]
[ROW][C]8[/C][C]-0.296572[/C][C]-2.2972[/C][C]0.012555[/C][/ROW]
[ROW][C]9[/C][C]-0.141731[/C][C]-1.0978[/C][C]0.138329[/C][/ROW]
[ROW][C]10[/C][C]0.087696[/C][C]0.6793[/C][C]0.249783[/C][/ROW]
[ROW][C]11[/C][C]0.396128[/C][C]3.0684[/C][C]0.001614[/C][/ROW]
[ROW][C]12[/C][C]0.791641[/C][C]6.132[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.473905[/C][C]3.6708[/C][C]0.000258[/C][/ROW]
[ROW][C]14[/C][C]0.212969[/C][C]1.6497[/C][C]0.05212[/C][/ROW]
[ROW][C]15[/C][C]0.003842[/C][C]0.0298[/C][C]0.48818[/C][/ROW]
[ROW][C]16[/C][C]-0.15379[/C][C]-1.1913[/C][C]0.119122[/C][/ROW]
[ROW][C]17[/C][C]-0.260239[/C][C]-2.0158[/C][C]0.024153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59298&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59298&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	0.593088	4.594	1.1e-05
2	0.261158	2.0229	0.023772
3	-0.002495	-0.0193	0.492324
4	-0.198831	-1.5401	0.064393
5	-0.327391	-2.536	0.006918
6	-0.387485	-3.0014	0.001956
7	-0.377334	-2.9228	0.002443
8	-0.296572	-2.2972	0.012555
9	-0.141731	-1.0978	0.138329
10	0.087696	0.6793	0.249783
11	0.396128	3.0684	0.001614
12	0.791641	6.132	0
13	0.473905	3.6708	0.000258
14	0.212969	1.6497	0.05212
15	0.003842	0.0298	0.48818
16	-0.15379	-1.1913	0.119122
17	-0.260239	-2.0158	0.024153

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.593088	4.594	1.1e-05
2	-0.139754	-1.0825	0.141674
3	-0.151269	-1.1717	0.122969
4	-0.157296	-1.2184	0.113918
5	-0.158721	-1.2294	0.111852
6	-0.152934	-1.1846	0.12042
7	-0.132378	-1.0254	0.154646
8	-0.090559	-0.7015	0.242863
9	-0.0092	-0.0713	0.471713
10	0.117582	0.9108	0.183026
11	0.314144	2.4334	0.008978
12	0.668784	5.1804	1e-06
13	-0.662187	-5.1293	2e-06
14	0.038199	0.2959	0.38417
15	0.056718	0.4393	0.330998
16	0.061417	0.4757	0.317997
17	0.065091	0.5042	0.307987

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.593088 & 4.594 & 1.1e-05 \tabularnewline
2 & -0.139754 & -1.0825 & 0.141674 \tabularnewline
3 & -0.151269 & -1.1717 & 0.122969 \tabularnewline
4 & -0.157296 & -1.2184 & 0.113918 \tabularnewline
5 & -0.158721 & -1.2294 & 0.111852 \tabularnewline
6 & -0.152934 & -1.1846 & 0.12042 \tabularnewline
7 & -0.132378 & -1.0254 & 0.154646 \tabularnewline
8 & -0.090559 & -0.7015 & 0.242863 \tabularnewline
9 & -0.0092 & -0.0713 & 0.471713 \tabularnewline
10 & 0.117582 & 0.9108 & 0.183026 \tabularnewline
11 & 0.314144 & 2.4334 & 0.008978 \tabularnewline
12 & 0.668784 & 5.1804 & 1e-06 \tabularnewline
13 & -0.662187 & -5.1293 & 2e-06 \tabularnewline
14 & 0.038199 & 0.2959 & 0.38417 \tabularnewline
15 & 0.056718 & 0.4393 & 0.330998 \tabularnewline
16 & 0.061417 & 0.4757 & 0.317997 \tabularnewline
17 & 0.065091 & 0.5042 & 0.307987 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59298&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]0.593088[/C][C]4.594[/C][C]1.1e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.139754[/C][C]-1.0825[/C][C]0.141674[/C][/ROW]
[ROW][C]3[/C][C]-0.151269[/C][C]-1.1717[/C][C]0.122969[/C][/ROW]
[ROW][C]4[/C][C]-0.157296[/C][C]-1.2184[/C][C]0.113918[/C][/ROW]
[ROW][C]5[/C][C]-0.158721[/C][C]-1.2294[/C][C]0.111852[/C][/ROW]
[ROW][C]6[/C][C]-0.152934[/C][C]-1.1846[/C][C]0.12042[/C][/ROW]
[ROW][C]7[/C][C]-0.132378[/C][C]-1.0254[/C][C]0.154646[/C][/ROW]
[ROW][C]8[/C][C]-0.090559[/C][C]-0.7015[/C][C]0.242863[/C][/ROW]
[ROW][C]9[/C][C]-0.0092[/C][C]-0.0713[/C][C]0.471713[/C][/ROW]
[ROW][C]10[/C][C]0.117582[/C][C]0.9108[/C][C]0.183026[/C][/ROW]
[ROW][C]11[/C][C]0.314144[/C][C]2.4334[/C][C]0.008978[/C][/ROW]
[ROW][C]12[/C][C]0.668784[/C][C]5.1804[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.662187[/C][C]-5.1293[/C][C]2e-06[/C][/ROW]
[ROW][C]14[/C][C]0.038199[/C][C]0.2959[/C][C]0.38417[/C][/ROW]
[ROW][C]15[/C][C]0.056718[/C][C]0.4393[/C][C]0.330998[/C][/ROW]
[ROW][C]16[/C][C]0.061417[/C][C]0.4757[/C][C]0.317997[/C][/ROW]
[ROW][C]17[/C][C]0.065091[/C][C]0.5042[/C][C]0.307987[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59298&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59298&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	0.593088	4.594	1.1e-05
2	-0.139754	-1.0825	0.141674
3	-0.151269	-1.1717	0.122969
4	-0.157296	-1.2184	0.113918
5	-0.158721	-1.2294	0.111852
6	-0.152934	-1.1846	0.12042
7	-0.132378	-1.0254	0.154646
8	-0.090559	-0.7015	0.242863
9	-0.0092	-0.0713	0.471713
10	0.117582	0.9108	0.183026
11	0.314144	2.4334	0.008978
12	0.668784	5.1804	1e-06
13	-0.662187	-5.1293	2e-06
14	0.038199	0.2959	0.38417
15	0.056718	0.4393	0.330998
16	0.061417	0.4757	0.317997
17	0.065091	0.5042	0.307987

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