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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 24 Oct 2015 13:47:25 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/24/t1445690886zyqsrzz2t43uhpz.htm/, Retrieved Wed, 15 May 2024 03:54:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283030, Retrieved Wed, 15 May 2024 03:54:11 +0000

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Estimated Impact

106

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-       [(Partial) Autocorrelation Function] [] [2015-10-24 12:47:25] [88f551c1d3f4ff2d65b8ab6790c1e3d2] [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	'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283030&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283030&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283030&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.157526	1.3273	0.094324
2	0.033179	0.2796	0.390309
3	-0.249187	-2.0997	0.019656
4	-0.25807	-2.1745	0.016499
5	-0.086009	-0.7247	0.235501
6	-0.103648	-0.8733	0.192708
7	-0.020528	-0.173	0.431582
8	-0.13657	-1.1508	0.126846
9	0.114372	0.9637	0.16923
10	0.058246	0.4908	0.312546
11	0.164697	1.3878	0.084774
12	0.265605	2.238	0.014179
13	0.083119	0.7004	0.242991
14	-0.08755	-0.7377	0.23156
15	-0.181736	-1.5313	0.065065
16	-0.196999	-1.6599	0.050668
17	-0.022262	-0.1876	0.425869
18	-0.006015	-0.0507	0.47986

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.157526 & 1.3273 & 0.094324 \tabularnewline
2 & 0.033179 & 0.2796 & 0.390309 \tabularnewline
3 & -0.249187 & -2.0997 & 0.019656 \tabularnewline
4 & -0.25807 & -2.1745 & 0.016499 \tabularnewline
5 & -0.086009 & -0.7247 & 0.235501 \tabularnewline
6 & -0.103648 & -0.8733 & 0.192708 \tabularnewline
7 & -0.020528 & -0.173 & 0.431582 \tabularnewline
8 & -0.13657 & -1.1508 & 0.126846 \tabularnewline
9 & 0.114372 & 0.9637 & 0.16923 \tabularnewline
10 & 0.058246 & 0.4908 & 0.312546 \tabularnewline
11 & 0.164697 & 1.3878 & 0.084774 \tabularnewline
12 & 0.265605 & 2.238 & 0.014179 \tabularnewline
13 & 0.083119 & 0.7004 & 0.242991 \tabularnewline
14 & -0.08755 & -0.7377 & 0.23156 \tabularnewline
15 & -0.181736 & -1.5313 & 0.065065 \tabularnewline
16 & -0.196999 & -1.6599 & 0.050668 \tabularnewline
17 & -0.022262 & -0.1876 & 0.425869 \tabularnewline
18 & -0.006015 & -0.0507 & 0.47986 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283030&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]0.157526[/C][C]1.3273[/C][C]0.094324[/C][/ROW]
[ROW][C]2[/C][C]0.033179[/C][C]0.2796[/C][C]0.390309[/C][/ROW]
[ROW][C]3[/C][C]-0.249187[/C][C]-2.0997[/C][C]0.019656[/C][/ROW]
[ROW][C]4[/C][C]-0.25807[/C][C]-2.1745[/C][C]0.016499[/C][/ROW]
[ROW][C]5[/C][C]-0.086009[/C][C]-0.7247[/C][C]0.235501[/C][/ROW]
[ROW][C]6[/C][C]-0.103648[/C][C]-0.8733[/C][C]0.192708[/C][/ROW]
[ROW][C]7[/C][C]-0.020528[/C][C]-0.173[/C][C]0.431582[/C][/ROW]
[ROW][C]8[/C][C]-0.13657[/C][C]-1.1508[/C][C]0.126846[/C][/ROW]
[ROW][C]9[/C][C]0.114372[/C][C]0.9637[/C][C]0.16923[/C][/ROW]
[ROW][C]10[/C][C]0.058246[/C][C]0.4908[/C][C]0.312546[/C][/ROW]
[ROW][C]11[/C][C]0.164697[/C][C]1.3878[/C][C]0.084774[/C][/ROW]
[ROW][C]12[/C][C]0.265605[/C][C]2.238[/C][C]0.014179[/C][/ROW]
[ROW][C]13[/C][C]0.083119[/C][C]0.7004[/C][C]0.242991[/C][/ROW]
[ROW][C]14[/C][C]-0.08755[/C][C]-0.7377[/C][C]0.23156[/C][/ROW]
[ROW][C]15[/C][C]-0.181736[/C][C]-1.5313[/C][C]0.065065[/C][/ROW]
[ROW][C]16[/C][C]-0.196999[/C][C]-1.6599[/C][C]0.050668[/C][/ROW]
[ROW][C]17[/C][C]-0.022262[/C][C]-0.1876[/C][C]0.425869[/C][/ROW]
[ROW][C]18[/C][C]-0.006015[/C][C]-0.0507[/C][C]0.47986[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283030&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283030&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	0.157526	1.3273	0.094324
2	0.033179	0.2796	0.390309
3	-0.249187	-2.0997	0.019656
4	-0.25807	-2.1745	0.016499
5	-0.086009	-0.7247	0.235501
6	-0.103648	-0.8733	0.192708
7	-0.020528	-0.173	0.431582
8	-0.13657	-1.1508	0.126846
9	0.114372	0.9637	0.16923
10	0.058246	0.4908	0.312546
11	0.164697	1.3878	0.084774
12	0.265605	2.238	0.014179
13	0.083119	0.7004	0.242991
14	-0.08755	-0.7377	0.23156
15	-0.181736	-1.5313	0.065065
16	-0.196999	-1.6599	0.050668
17	-0.022262	-0.1876	0.425869
18	-0.006015	-0.0507	0.47986

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.157526	1.3273	0.094324
2	0.008578	0.0723	0.471293
3	-0.262246	-2.2097	0.015175
4	-0.197043	-1.6603	0.050631
5	-0.005705	-0.0481	0.480896
6	-0.148573	-1.2519	0.107358
7	-0.116346	-0.9803	0.165122
8	-0.221615	-1.8674	0.03299
9	0.078983	0.6655	0.253935
10	-0.052765	-0.4446	0.328978
11	0.029803	0.2511	0.401222
12	0.235467	1.9841	0.025557
13	0.086153	0.7259	0.235132
14	-0.10185	-0.8582	0.196834
15	0.008672	0.0731	0.470979
16	-0.035457	-0.2988	0.382995
17	0.085581	0.7211	0.236602
18	-0.060843	-0.5127	0.304887

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.157526 & 1.3273 & 0.094324 \tabularnewline
2 & 0.008578 & 0.0723 & 0.471293 \tabularnewline
3 & -0.262246 & -2.2097 & 0.015175 \tabularnewline
4 & -0.197043 & -1.6603 & 0.050631 \tabularnewline
5 & -0.005705 & -0.0481 & 0.480896 \tabularnewline
6 & -0.148573 & -1.2519 & 0.107358 \tabularnewline
7 & -0.116346 & -0.9803 & 0.165122 \tabularnewline
8 & -0.221615 & -1.8674 & 0.03299 \tabularnewline
9 & 0.078983 & 0.6655 & 0.253935 \tabularnewline
10 & -0.052765 & -0.4446 & 0.328978 \tabularnewline
11 & 0.029803 & 0.2511 & 0.401222 \tabularnewline
12 & 0.235467 & 1.9841 & 0.025557 \tabularnewline
13 & 0.086153 & 0.7259 & 0.235132 \tabularnewline
14 & -0.10185 & -0.8582 & 0.196834 \tabularnewline
15 & 0.008672 & 0.0731 & 0.470979 \tabularnewline
16 & -0.035457 & -0.2988 & 0.382995 \tabularnewline
17 & 0.085581 & 0.7211 & 0.236602 \tabularnewline
18 & -0.060843 & -0.5127 & 0.304887 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283030&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]0.157526[/C][C]1.3273[/C][C]0.094324[/C][/ROW]
[ROW][C]2[/C][C]0.008578[/C][C]0.0723[/C][C]0.471293[/C][/ROW]
[ROW][C]3[/C][C]-0.262246[/C][C]-2.2097[/C][C]0.015175[/C][/ROW]
[ROW][C]4[/C][C]-0.197043[/C][C]-1.6603[/C][C]0.050631[/C][/ROW]
[ROW][C]5[/C][C]-0.005705[/C][C]-0.0481[/C][C]0.480896[/C][/ROW]
[ROW][C]6[/C][C]-0.148573[/C][C]-1.2519[/C][C]0.107358[/C][/ROW]
[ROW][C]7[/C][C]-0.116346[/C][C]-0.9803[/C][C]0.165122[/C][/ROW]
[ROW][C]8[/C][C]-0.221615[/C][C]-1.8674[/C][C]0.03299[/C][/ROW]
[ROW][C]9[/C][C]0.078983[/C][C]0.6655[/C][C]0.253935[/C][/ROW]
[ROW][C]10[/C][C]-0.052765[/C][C]-0.4446[/C][C]0.328978[/C][/ROW]
[ROW][C]11[/C][C]0.029803[/C][C]0.2511[/C][C]0.401222[/C][/ROW]
[ROW][C]12[/C][C]0.235467[/C][C]1.9841[/C][C]0.025557[/C][/ROW]
[ROW][C]13[/C][C]0.086153[/C][C]0.7259[/C][C]0.235132[/C][/ROW]
[ROW][C]14[/C][C]-0.10185[/C][C]-0.8582[/C][C]0.196834[/C][/ROW]
[ROW][C]15[/C][C]0.008672[/C][C]0.0731[/C][C]0.470979[/C][/ROW]
[ROW][C]16[/C][C]-0.035457[/C][C]-0.2988[/C][C]0.382995[/C][/ROW]
[ROW][C]17[/C][C]0.085581[/C][C]0.7211[/C][C]0.236602[/C][/ROW]
[ROW][C]18[/C][C]-0.060843[/C][C]-0.5127[/C][C]0.304887[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283030&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283030&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	0.157526	1.3273	0.094324
2	0.008578	0.0723	0.471293
3	-0.262246	-2.2097	0.015175
4	-0.197043	-1.6603	0.050631
5	-0.005705	-0.0481	0.480896
6	-0.148573	-1.2519	0.107358
7	-0.116346	-0.9803	0.165122
8	-0.221615	-1.8674	0.03299
9	0.078983	0.6655	0.253935
10	-0.052765	-0.4446	0.328978
11	0.029803	0.2511	0.401222
12	0.235467	1.9841	0.025557
13	0.086153	0.7259	0.235132
14	-0.10185	-0.8582	0.196834
15	0.008672	0.0731	0.470979
16	-0.035457	-0.2988	0.382995
17	0.085581	0.7211	0.236602
18	-0.060843	-0.5127	0.304887

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code