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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 15 Dec 2011 03:27:20 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/15/t1323937665s9bnlhomf9g0x0r.htm/, Retrieved Wed, 08 May 2024 13:32:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=155292, Retrieved Wed, 08 May 2024 13:32:25 +0000

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Estimated Impact

122

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-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2011-12-15 08:27:20] [51aabe75794be7f34bed5d3096a085df] [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' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155292&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155292&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155292&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' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.048594	-0.2834	0.389313
2	-0.262267	-1.5293	0.067725
3	0.153064	0.8925	0.189196
4	-0.10604	-0.6183	0.270243
5	-0.252797	-1.474	0.074834
6	0.147143	0.858	0.198454
7	0.207635	1.2107	0.117178
8	-0.062003	-0.3615	0.359968
9	-0.110661	-0.6453	0.261545
10	0.033869	0.1975	0.42231
11	0.110362	0.6435	0.262103
12	-0.169954	-0.991	0.164344
13	-0.053458	-0.3117	0.378583
14	0.054706	0.319	0.375843
15	-0.089582	-0.5223	0.302407
16	-0.060866	-0.3549	0.362427

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.048594 & -0.2834 & 0.389313 \tabularnewline
2 & -0.262267 & -1.5293 & 0.067725 \tabularnewline
3 & 0.153064 & 0.8925 & 0.189196 \tabularnewline
4 & -0.10604 & -0.6183 & 0.270243 \tabularnewline
5 & -0.252797 & -1.474 & 0.074834 \tabularnewline
6 & 0.147143 & 0.858 & 0.198454 \tabularnewline
7 & 0.207635 & 1.2107 & 0.117178 \tabularnewline
8 & -0.062003 & -0.3615 & 0.359968 \tabularnewline
9 & -0.110661 & -0.6453 & 0.261545 \tabularnewline
10 & 0.033869 & 0.1975 & 0.42231 \tabularnewline
11 & 0.110362 & 0.6435 & 0.262103 \tabularnewline
12 & -0.169954 & -0.991 & 0.164344 \tabularnewline
13 & -0.053458 & -0.3117 & 0.378583 \tabularnewline
14 & 0.054706 & 0.319 & 0.375843 \tabularnewline
15 & -0.089582 & -0.5223 & 0.302407 \tabularnewline
16 & -0.060866 & -0.3549 & 0.362427 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155292&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]-0.048594[/C][C]-0.2834[/C][C]0.389313[/C][/ROW]
[ROW][C]2[/C][C]-0.262267[/C][C]-1.5293[/C][C]0.067725[/C][/ROW]
[ROW][C]3[/C][C]0.153064[/C][C]0.8925[/C][C]0.189196[/C][/ROW]
[ROW][C]4[/C][C]-0.10604[/C][C]-0.6183[/C][C]0.270243[/C][/ROW]
[ROW][C]5[/C][C]-0.252797[/C][C]-1.474[/C][C]0.074834[/C][/ROW]
[ROW][C]6[/C][C]0.147143[/C][C]0.858[/C][C]0.198454[/C][/ROW]
[ROW][C]7[/C][C]0.207635[/C][C]1.2107[/C][C]0.117178[/C][/ROW]
[ROW][C]8[/C][C]-0.062003[/C][C]-0.3615[/C][C]0.359968[/C][/ROW]
[ROW][C]9[/C][C]-0.110661[/C][C]-0.6453[/C][C]0.261545[/C][/ROW]
[ROW][C]10[/C][C]0.033869[/C][C]0.1975[/C][C]0.42231[/C][/ROW]
[ROW][C]11[/C][C]0.110362[/C][C]0.6435[/C][C]0.262103[/C][/ROW]
[ROW][C]12[/C][C]-0.169954[/C][C]-0.991[/C][C]0.164344[/C][/ROW]
[ROW][C]13[/C][C]-0.053458[/C][C]-0.3117[/C][C]0.378583[/C][/ROW]
[ROW][C]14[/C][C]0.054706[/C][C]0.319[/C][C]0.375843[/C][/ROW]
[ROW][C]15[/C][C]-0.089582[/C][C]-0.5223[/C][C]0.302407[/C][/ROW]
[ROW][C]16[/C][C]-0.060866[/C][C]-0.3549[/C][C]0.362427[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155292&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155292&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	-0.048594	-0.2834	0.389313
2	-0.262267	-1.5293	0.067725
3	0.153064	0.8925	0.189196
4	-0.10604	-0.6183	0.270243
5	-0.252797	-1.474	0.074834
6	0.147143	0.858	0.198454
7	0.207635	1.2107	0.117178
8	-0.062003	-0.3615	0.359968
9	-0.110661	-0.6453	0.261545
10	0.033869	0.1975	0.42231
11	0.110362	0.6435	0.262103
12	-0.169954	-0.991	0.164344
13	-0.053458	-0.3117	0.378583
14	0.054706	0.319	0.375843
15	-0.089582	-0.5223	0.302407
16	-0.060866	-0.3549	0.362427

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.048594	-0.2834	0.389313
2	-0.265255	-1.5467	0.065599
3	0.133754	0.7799	0.220419
4	-0.178921	-1.0433	0.15209
5	-0.205821	-1.2001	0.119192
6	0.048252	0.2814	0.390071
7	0.148629	0.8667	0.196104
8	0.036739	0.2142	0.415826
9	-0.129012	-0.7523	0.228536
10	-0.041187	-0.2402	0.405825
11	0.1884	1.0985	0.139842
12	-0.10076	-0.5875	0.280366
13	-0.101124	-0.5897	0.279662
14	-0.138027	-0.8048	0.213256
15	-0.019229	-0.1121	0.455693
16	-0.002546	-0.0148	0.494122

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.048594 & -0.2834 & 0.389313 \tabularnewline
2 & -0.265255 & -1.5467 & 0.065599 \tabularnewline
3 & 0.133754 & 0.7799 & 0.220419 \tabularnewline
4 & -0.178921 & -1.0433 & 0.15209 \tabularnewline
5 & -0.205821 & -1.2001 & 0.119192 \tabularnewline
6 & 0.048252 & 0.2814 & 0.390071 \tabularnewline
7 & 0.148629 & 0.8667 & 0.196104 \tabularnewline
8 & 0.036739 & 0.2142 & 0.415826 \tabularnewline
9 & -0.129012 & -0.7523 & 0.228536 \tabularnewline
10 & -0.041187 & -0.2402 & 0.405825 \tabularnewline
11 & 0.1884 & 1.0985 & 0.139842 \tabularnewline
12 & -0.10076 & -0.5875 & 0.280366 \tabularnewline
13 & -0.101124 & -0.5897 & 0.279662 \tabularnewline
14 & -0.138027 & -0.8048 & 0.213256 \tabularnewline
15 & -0.019229 & -0.1121 & 0.455693 \tabularnewline
16 & -0.002546 & -0.0148 & 0.494122 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155292&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]-0.048594[/C][C]-0.2834[/C][C]0.389313[/C][/ROW]
[ROW][C]2[/C][C]-0.265255[/C][C]-1.5467[/C][C]0.065599[/C][/ROW]
[ROW][C]3[/C][C]0.133754[/C][C]0.7799[/C][C]0.220419[/C][/ROW]
[ROW][C]4[/C][C]-0.178921[/C][C]-1.0433[/C][C]0.15209[/C][/ROW]
[ROW][C]5[/C][C]-0.205821[/C][C]-1.2001[/C][C]0.119192[/C][/ROW]
[ROW][C]6[/C][C]0.048252[/C][C]0.2814[/C][C]0.390071[/C][/ROW]
[ROW][C]7[/C][C]0.148629[/C][C]0.8667[/C][C]0.196104[/C][/ROW]
[ROW][C]8[/C][C]0.036739[/C][C]0.2142[/C][C]0.415826[/C][/ROW]
[ROW][C]9[/C][C]-0.129012[/C][C]-0.7523[/C][C]0.228536[/C][/ROW]
[ROW][C]10[/C][C]-0.041187[/C][C]-0.2402[/C][C]0.405825[/C][/ROW]
[ROW][C]11[/C][C]0.1884[/C][C]1.0985[/C][C]0.139842[/C][/ROW]
[ROW][C]12[/C][C]-0.10076[/C][C]-0.5875[/C][C]0.280366[/C][/ROW]
[ROW][C]13[/C][C]-0.101124[/C][C]-0.5897[/C][C]0.279662[/C][/ROW]
[ROW][C]14[/C][C]-0.138027[/C][C]-0.8048[/C][C]0.213256[/C][/ROW]
[ROW][C]15[/C][C]-0.019229[/C][C]-0.1121[/C][C]0.455693[/C][/ROW]
[ROW][C]16[/C][C]-0.002546[/C][C]-0.0148[/C][C]0.494122[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155292&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155292&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	-0.048594	-0.2834	0.389313
2	-0.265255	-1.5467	0.065599
3	0.133754	0.7799	0.220419
4	-0.178921	-1.0433	0.15209
5	-0.205821	-1.2001	0.119192
6	0.048252	0.2814	0.390071
7	0.148629	0.8667	0.196104
8	0.036739	0.2142	0.415826
9	-0.129012	-0.7523	0.228536
10	-0.041187	-0.2402	0.405825
11	0.1884	1.0985	0.139842
12	-0.10076	-0.5875	0.280366
13	-0.101124	-0.5897	0.279662
14	-0.138027	-0.8048	0.213256
15	-0.019229	-0.1121	0.455693
16	-0.002546	-0.0148	0.494122

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 = 2 ; par4 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 4 ; 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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Input Parameters & R Code