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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 14 Dec 2009 13:37:43 -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/Dec/14/t1260823131gmphs773fgeobzk.htm/, Retrieved Sun, 05 May 2024 12:58:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67669, Retrieved Sun, 05 May 2024 12:58:20 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

145

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

-     [Variance Reduction Matrix] [Variance reductio...] [2008-12-11 15:42:45] [12d343c4448a5f9e527bb31caeac580b]
- RMPD    [(Partial) Autocorrelation Function] [ACF] [2009-12-14 20:37:43] [244731fa3e7e6c85774b8c0902c58f85] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67669&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67669&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67669&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.406192	3.0935	0.001521
2	0.448204	3.4134	0.000588
3	0.419234	3.1928	0.001139
4	0.246401	1.8765	0.032808
5	0.179463	1.3668	0.088489
6	0.149436	1.1381	0.129884
7	0.110567	0.8421	0.201608
8	0.192356	1.4649	0.074169
9	0.184893	1.4081	0.08222
10	0.057293	0.4363	0.332109
11	0.046069	0.3508	0.363487
12	0.10698	0.8147	0.209279
13	-0.004489	-0.0342	0.486423
14	0.022927	0.1746	0.431
15	0.015424	0.1175	0.453447
16	-0.018583	-0.1415	0.443974
17	0.063345	0.4824	0.315661

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.406192 & 3.0935 & 0.001521 \tabularnewline
2 & 0.448204 & 3.4134 & 0.000588 \tabularnewline
3 & 0.419234 & 3.1928 & 0.001139 \tabularnewline
4 & 0.246401 & 1.8765 & 0.032808 \tabularnewline
5 & 0.179463 & 1.3668 & 0.088489 \tabularnewline
6 & 0.149436 & 1.1381 & 0.129884 \tabularnewline
7 & 0.110567 & 0.8421 & 0.201608 \tabularnewline
8 & 0.192356 & 1.4649 & 0.074169 \tabularnewline
9 & 0.184893 & 1.4081 & 0.08222 \tabularnewline
10 & 0.057293 & 0.4363 & 0.332109 \tabularnewline
11 & 0.046069 & 0.3508 & 0.363487 \tabularnewline
12 & 0.10698 & 0.8147 & 0.209279 \tabularnewline
13 & -0.004489 & -0.0342 & 0.486423 \tabularnewline
14 & 0.022927 & 0.1746 & 0.431 \tabularnewline
15 & 0.015424 & 0.1175 & 0.453447 \tabularnewline
16 & -0.018583 & -0.1415 & 0.443974 \tabularnewline
17 & 0.063345 & 0.4824 & 0.315661 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67669&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]0.406192[/C][C]3.0935[/C][C]0.001521[/C][/ROW]
[ROW][C]2[/C][C]0.448204[/C][C]3.4134[/C][C]0.000588[/C][/ROW]
[ROW][C]3[/C][C]0.419234[/C][C]3.1928[/C][C]0.001139[/C][/ROW]
[ROW][C]4[/C][C]0.246401[/C][C]1.8765[/C][C]0.032808[/C][/ROW]
[ROW][C]5[/C][C]0.179463[/C][C]1.3668[/C][C]0.088489[/C][/ROW]
[ROW][C]6[/C][C]0.149436[/C][C]1.1381[/C][C]0.129884[/C][/ROW]
[ROW][C]7[/C][C]0.110567[/C][C]0.8421[/C][C]0.201608[/C][/ROW]
[ROW][C]8[/C][C]0.192356[/C][C]1.4649[/C][C]0.074169[/C][/ROW]
[ROW][C]9[/C][C]0.184893[/C][C]1.4081[/C][C]0.08222[/C][/ROW]
[ROW][C]10[/C][C]0.057293[/C][C]0.4363[/C][C]0.332109[/C][/ROW]
[ROW][C]11[/C][C]0.046069[/C][C]0.3508[/C][C]0.363487[/C][/ROW]
[ROW][C]12[/C][C]0.10698[/C][C]0.8147[/C][C]0.209279[/C][/ROW]
[ROW][C]13[/C][C]-0.004489[/C][C]-0.0342[/C][C]0.486423[/C][/ROW]
[ROW][C]14[/C][C]0.022927[/C][C]0.1746[/C][C]0.431[/C][/ROW]
[ROW][C]15[/C][C]0.015424[/C][C]0.1175[/C][C]0.453447[/C][/ROW]
[ROW][C]16[/C][C]-0.018583[/C][C]-0.1415[/C][C]0.443974[/C][/ROW]
[ROW][C]17[/C][C]0.063345[/C][C]0.4824[/C][C]0.315661[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67669&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67669&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	0.406192	3.0935	0.001521
2	0.448204	3.4134	0.000588
3	0.419234	3.1928	0.001139
4	0.246401	1.8765	0.032808
5	0.179463	1.3668	0.088489
6	0.149436	1.1381	0.129884
7	0.110567	0.8421	0.201608
8	0.192356	1.4649	0.074169
9	0.184893	1.4081	0.08222
10	0.057293	0.4363	0.332109
11	0.046069	0.3508	0.363487
12	0.10698	0.8147	0.209279
13	-0.004489	-0.0342	0.486423
14	0.022927	0.1746	0.431
15	0.015424	0.1175	0.453447
16	-0.018583	-0.1415	0.443974
17	0.063345	0.4824	0.315661

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.406192	3.0935	0.001521
2	0.339173	2.5831	0.006168
3	0.218089	1.6609	0.051064
4	-0.070314	-0.5355	0.297177
5	-0.104906	-0.7989	0.213793
6	-0.018769	-0.1429	0.443416
7	0.03908	0.2976	0.383527
8	0.187228	1.4259	0.079631
9	0.113426	0.8638	0.19562
10	-0.174267	-1.3272	0.094826
11	-0.194369	-1.4803	0.072106
12	0.0826	0.6291	0.26589
13	0.064131	0.4884	0.313552
14	0.072452	0.5518	0.29161
15	-0.032996	-0.2513	0.40124
16	-0.126837	-0.966	0.169036
17	0.028302	0.2155	0.41505

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.406192 & 3.0935 & 0.001521 \tabularnewline
2 & 0.339173 & 2.5831 & 0.006168 \tabularnewline
3 & 0.218089 & 1.6609 & 0.051064 \tabularnewline
4 & -0.070314 & -0.5355 & 0.297177 \tabularnewline
5 & -0.104906 & -0.7989 & 0.213793 \tabularnewline
6 & -0.018769 & -0.1429 & 0.443416 \tabularnewline
7 & 0.03908 & 0.2976 & 0.383527 \tabularnewline
8 & 0.187228 & 1.4259 & 0.079631 \tabularnewline
9 & 0.113426 & 0.8638 & 0.19562 \tabularnewline
10 & -0.174267 & -1.3272 & 0.094826 \tabularnewline
11 & -0.194369 & -1.4803 & 0.072106 \tabularnewline
12 & 0.0826 & 0.6291 & 0.26589 \tabularnewline
13 & 0.064131 & 0.4884 & 0.313552 \tabularnewline
14 & 0.072452 & 0.5518 & 0.29161 \tabularnewline
15 & -0.032996 & -0.2513 & 0.40124 \tabularnewline
16 & -0.126837 & -0.966 & 0.169036 \tabularnewline
17 & 0.028302 & 0.2155 & 0.41505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67669&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]0.406192[/C][C]3.0935[/C][C]0.001521[/C][/ROW]
[ROW][C]2[/C][C]0.339173[/C][C]2.5831[/C][C]0.006168[/C][/ROW]
[ROW][C]3[/C][C]0.218089[/C][C]1.6609[/C][C]0.051064[/C][/ROW]
[ROW][C]4[/C][C]-0.070314[/C][C]-0.5355[/C][C]0.297177[/C][/ROW]
[ROW][C]5[/C][C]-0.104906[/C][C]-0.7989[/C][C]0.213793[/C][/ROW]
[ROW][C]6[/C][C]-0.018769[/C][C]-0.1429[/C][C]0.443416[/C][/ROW]
[ROW][C]7[/C][C]0.03908[/C][C]0.2976[/C][C]0.383527[/C][/ROW]
[ROW][C]8[/C][C]0.187228[/C][C]1.4259[/C][C]0.079631[/C][/ROW]
[ROW][C]9[/C][C]0.113426[/C][C]0.8638[/C][C]0.19562[/C][/ROW]
[ROW][C]10[/C][C]-0.174267[/C][C]-1.3272[/C][C]0.094826[/C][/ROW]
[ROW][C]11[/C][C]-0.194369[/C][C]-1.4803[/C][C]0.072106[/C][/ROW]
[ROW][C]12[/C][C]0.0826[/C][C]0.6291[/C][C]0.26589[/C][/ROW]
[ROW][C]13[/C][C]0.064131[/C][C]0.4884[/C][C]0.313552[/C][/ROW]
[ROW][C]14[/C][C]0.072452[/C][C]0.5518[/C][C]0.29161[/C][/ROW]
[ROW][C]15[/C][C]-0.032996[/C][C]-0.2513[/C][C]0.40124[/C][/ROW]
[ROW][C]16[/C][C]-0.126837[/C][C]-0.966[/C][C]0.169036[/C][/ROW]
[ROW][C]17[/C][C]0.028302[/C][C]0.2155[/C][C]0.41505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67669&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67669&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	0.406192	3.0935	0.001521
2	0.339173	2.5831	0.006168
3	0.218089	1.6609	0.051064
4	-0.070314	-0.5355	0.297177
5	-0.104906	-0.7989	0.213793
6	-0.018769	-0.1429	0.443416
7	0.03908	0.2976	0.383527
8	0.187228	1.4259	0.079631
9	0.113426	0.8638	0.19562
10	-0.174267	-1.3272	0.094826
11	-0.194369	-1.4803	0.072106
12	0.0826	0.6291	0.26589
13	0.064131	0.4884	0.313552
14	0.072452	0.5518	0.29161
15	-0.032996	-0.2513	0.40124
16	-0.126837	-0.966	0.169036
17	0.028302	0.2155	0.41505

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Industri�le omzetcijfers volgens BTW ; par2 = ADSEI ; par3 = maandelijkse industri�le omzet volgens BTW in Belgi� ;

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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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code