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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 26 May 2012 07:57:07 -0400

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/26/t13380334460ctakfzii4awxne.htm/, Retrieved Thu, 02 May 2024 15:48:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167588, Retrieved Thu, 02 May 2024 15:48:41 +0000

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No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

106

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

-       [(Partial) Autocorrelation Function] [autocorrelation f...] [2012-05-26 11:57:07] [a2709f7ab86902c8a6d752383a828f6c] [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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167588&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167588&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167588&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.171349	-1.3162	0.096606
2	-0.000798	-0.0061	0.497564
3	-0.14997	-1.1519	0.126996
4	-0.16362	-1.2568	0.106891
5	0.285182	2.1905	0.016225
6	-0.140068	-1.0759	0.14318
7	0.323712	2.4865	0.007876
8	-0.077866	-0.5981	0.276031
9	-0.182838	-1.4044	0.08272
10	-0.107182	-0.8233	0.206831
11	-0.051075	-0.3923	0.348119
12	0.373229	2.8668	0.00287
13	-0.017366	-0.1334	0.447168
14	0.056695	0.4355	0.332399
15	-0.068676	-0.5275	0.299909
16	-0.144879	-1.1128	0.135146
17	0.069387	0.533	0.298027

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.171349 & -1.3162 & 0.096606 \tabularnewline
2 & -0.000798 & -0.0061 & 0.497564 \tabularnewline
3 & -0.14997 & -1.1519 & 0.126996 \tabularnewline
4 & -0.16362 & -1.2568 & 0.106891 \tabularnewline
5 & 0.285182 & 2.1905 & 0.016225 \tabularnewline
6 & -0.140068 & -1.0759 & 0.14318 \tabularnewline
7 & 0.323712 & 2.4865 & 0.007876 \tabularnewline
8 & -0.077866 & -0.5981 & 0.276031 \tabularnewline
9 & -0.182838 & -1.4044 & 0.08272 \tabularnewline
10 & -0.107182 & -0.8233 & 0.206831 \tabularnewline
11 & -0.051075 & -0.3923 & 0.348119 \tabularnewline
12 & 0.373229 & 2.8668 & 0.00287 \tabularnewline
13 & -0.017366 & -0.1334 & 0.447168 \tabularnewline
14 & 0.056695 & 0.4355 & 0.332399 \tabularnewline
15 & -0.068676 & -0.5275 & 0.299909 \tabularnewline
16 & -0.144879 & -1.1128 & 0.135146 \tabularnewline
17 & 0.069387 & 0.533 & 0.298027 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167588&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]-0.171349[/C][C]-1.3162[/C][C]0.096606[/C][/ROW]
[ROW][C]2[/C][C]-0.000798[/C][C]-0.0061[/C][C]0.497564[/C][/ROW]
[ROW][C]3[/C][C]-0.14997[/C][C]-1.1519[/C][C]0.126996[/C][/ROW]
[ROW][C]4[/C][C]-0.16362[/C][C]-1.2568[/C][C]0.106891[/C][/ROW]
[ROW][C]5[/C][C]0.285182[/C][C]2.1905[/C][C]0.016225[/C][/ROW]
[ROW][C]6[/C][C]-0.140068[/C][C]-1.0759[/C][C]0.14318[/C][/ROW]
[ROW][C]7[/C][C]0.323712[/C][C]2.4865[/C][C]0.007876[/C][/ROW]
[ROW][C]8[/C][C]-0.077866[/C][C]-0.5981[/C][C]0.276031[/C][/ROW]
[ROW][C]9[/C][C]-0.182838[/C][C]-1.4044[/C][C]0.08272[/C][/ROW]
[ROW][C]10[/C][C]-0.107182[/C][C]-0.8233[/C][C]0.206831[/C][/ROW]
[ROW][C]11[/C][C]-0.051075[/C][C]-0.3923[/C][C]0.348119[/C][/ROW]
[ROW][C]12[/C][C]0.373229[/C][C]2.8668[/C][C]0.00287[/C][/ROW]
[ROW][C]13[/C][C]-0.017366[/C][C]-0.1334[/C][C]0.447168[/C][/ROW]
[ROW][C]14[/C][C]0.056695[/C][C]0.4355[/C][C]0.332399[/C][/ROW]
[ROW][C]15[/C][C]-0.068676[/C][C]-0.5275[/C][C]0.299909[/C][/ROW]
[ROW][C]16[/C][C]-0.144879[/C][C]-1.1128[/C][C]0.135146[/C][/ROW]
[ROW][C]17[/C][C]0.069387[/C][C]0.533[/C][C]0.298027[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167588&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167588&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	-0.171349	-1.3162	0.096606
2	-0.000798	-0.0061	0.497564
3	-0.14997	-1.1519	0.126996
4	-0.16362	-1.2568	0.106891
5	0.285182	2.1905	0.016225
6	-0.140068	-1.0759	0.14318
7	0.323712	2.4865	0.007876
8	-0.077866	-0.5981	0.276031
9	-0.182838	-1.4044	0.08272
10	-0.107182	-0.8233	0.206831
11	-0.051075	-0.3923	0.348119
12	0.373229	2.8668	0.00287
13	-0.017366	-0.1334	0.447168
14	0.056695	0.4355	0.332399
15	-0.068676	-0.5275	0.299909
16	-0.144879	-1.1128	0.135146
17	0.069387	0.533	0.298027

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.171349	-1.3162	0.096606
2	-0.031071	-0.2387	0.406098
3	-0.160292	-1.2312	0.111562
4	-0.231138	-1.7754	0.040495
5	0.222144	1.7063	0.046604
6	-0.102253	-0.7854	0.217676
7	0.283011	2.1738	0.01687
8	0.062989	0.4838	0.315149
9	-0.142287	-1.0929	0.139434
10	-0.193798	-1.4886	0.070961
11	0.028207	0.2167	0.41461
12	0.205493	1.5784	0.059908
13	0.066797	0.5131	0.304907
14	0.063218	0.4856	0.314529
15	0.07129	0.5476	0.293021
16	-0.031487	-0.2419	0.404865
17	0.000769	0.0059	0.497654

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.171349 & -1.3162 & 0.096606 \tabularnewline
2 & -0.031071 & -0.2387 & 0.406098 \tabularnewline
3 & -0.160292 & -1.2312 & 0.111562 \tabularnewline
4 & -0.231138 & -1.7754 & 0.040495 \tabularnewline
5 & 0.222144 & 1.7063 & 0.046604 \tabularnewline
6 & -0.102253 & -0.7854 & 0.217676 \tabularnewline
7 & 0.283011 & 2.1738 & 0.01687 \tabularnewline
8 & 0.062989 & 0.4838 & 0.315149 \tabularnewline
9 & -0.142287 & -1.0929 & 0.139434 \tabularnewline
10 & -0.193798 & -1.4886 & 0.070961 \tabularnewline
11 & 0.028207 & 0.2167 & 0.41461 \tabularnewline
12 & 0.205493 & 1.5784 & 0.059908 \tabularnewline
13 & 0.066797 & 0.5131 & 0.304907 \tabularnewline
14 & 0.063218 & 0.4856 & 0.314529 \tabularnewline
15 & 0.07129 & 0.5476 & 0.293021 \tabularnewline
16 & -0.031487 & -0.2419 & 0.404865 \tabularnewline
17 & 0.000769 & 0.0059 & 0.497654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167588&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]-0.171349[/C][C]-1.3162[/C][C]0.096606[/C][/ROW]
[ROW][C]2[/C][C]-0.031071[/C][C]-0.2387[/C][C]0.406098[/C][/ROW]
[ROW][C]3[/C][C]-0.160292[/C][C]-1.2312[/C][C]0.111562[/C][/ROW]
[ROW][C]4[/C][C]-0.231138[/C][C]-1.7754[/C][C]0.040495[/C][/ROW]
[ROW][C]5[/C][C]0.222144[/C][C]1.7063[/C][C]0.046604[/C][/ROW]
[ROW][C]6[/C][C]-0.102253[/C][C]-0.7854[/C][C]0.217676[/C][/ROW]
[ROW][C]7[/C][C]0.283011[/C][C]2.1738[/C][C]0.01687[/C][/ROW]
[ROW][C]8[/C][C]0.062989[/C][C]0.4838[/C][C]0.315149[/C][/ROW]
[ROW][C]9[/C][C]-0.142287[/C][C]-1.0929[/C][C]0.139434[/C][/ROW]
[ROW][C]10[/C][C]-0.193798[/C][C]-1.4886[/C][C]0.070961[/C][/ROW]
[ROW][C]11[/C][C]0.028207[/C][C]0.2167[/C][C]0.41461[/C][/ROW]
[ROW][C]12[/C][C]0.205493[/C][C]1.5784[/C][C]0.059908[/C][/ROW]
[ROW][C]13[/C][C]0.066797[/C][C]0.5131[/C][C]0.304907[/C][/ROW]
[ROW][C]14[/C][C]0.063218[/C][C]0.4856[/C][C]0.314529[/C][/ROW]
[ROW][C]15[/C][C]0.07129[/C][C]0.5476[/C][C]0.293021[/C][/ROW]
[ROW][C]16[/C][C]-0.031487[/C][C]-0.2419[/C][C]0.404865[/C][/ROW]
[ROW][C]17[/C][C]0.000769[/C][C]0.0059[/C][C]0.497654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167588&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167588&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	-0.171349	-1.3162	0.096606
2	-0.031071	-0.2387	0.406098
3	-0.160292	-1.2312	0.111562
4	-0.231138	-1.7754	0.040495
5	0.222144	1.7063	0.046604
6	-0.102253	-0.7854	0.217676
7	0.283011	2.1738	0.01687
8	0.062989	0.4838	0.315149
9	-0.142287	-1.0929	0.139434
10	-0.193798	-1.4886	0.070961
11	0.028207	0.2167	0.41461
12	0.205493	1.5784	0.059908
13	0.066797	0.5131	0.304907
14	0.063218	0.4856	0.314529
15	0.07129	0.5476	0.293021
16	-0.031487	-0.2419	0.404865
17	0.000769	0.0059	0.497654

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 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;

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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