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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Dec 2010 15:06:19 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/19/t1292771640168cftr5frnlbqz.htm/, Retrieved Sat, 04 May 2024 21:24:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112484, Retrieved Sat, 04 May 2024 21:24:10 +0000

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-       [(Partial) Autocorrelation Function] [] [2010-12-19 15:06:19] [020d6ac062bd52f65e15713212085515] [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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112484&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112484&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112484&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.577934	4.4767	1.7e-05
2	0.106341	0.8237	0.206683
3	-0.107026	-0.829	0.20519
4	-0.200542	-1.5534	0.062794
5	-0.343699	-2.6623	0.004974
6	-0.488825	-3.7864	0.000178
7	-0.479356	-3.7131	0.000225
8	-0.290255	-2.2483	0.014121
9	-0.116709	-0.904	0.184799
10	0.052106	0.4036	0.343966
11	0.365718	2.8328	0.003137
12	0.604241	4.6804	8e-06
13	0.456547	3.5364	0.000395
14	0.167304	1.2959	0.099982
15	-0.034474	-0.267	0.395179
16	-0.128089	-0.9922	0.162549
17	-0.188335	-1.4588	0.074913

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.577934 & 4.4767 & 1.7e-05 \tabularnewline
2 & 0.106341 & 0.8237 & 0.206683 \tabularnewline
3 & -0.107026 & -0.829 & 0.20519 \tabularnewline
4 & -0.200542 & -1.5534 & 0.062794 \tabularnewline
5 & -0.343699 & -2.6623 & 0.004974 \tabularnewline
6 & -0.488825 & -3.7864 & 0.000178 \tabularnewline
7 & -0.479356 & -3.7131 & 0.000225 \tabularnewline
8 & -0.290255 & -2.2483 & 0.014121 \tabularnewline
9 & -0.116709 & -0.904 & 0.184799 \tabularnewline
10 & 0.052106 & 0.4036 & 0.343966 \tabularnewline
11 & 0.365718 & 2.8328 & 0.003137 \tabularnewline
12 & 0.604241 & 4.6804 & 8e-06 \tabularnewline
13 & 0.456547 & 3.5364 & 0.000395 \tabularnewline
14 & 0.167304 & 1.2959 & 0.099982 \tabularnewline
15 & -0.034474 & -0.267 & 0.395179 \tabularnewline
16 & -0.128089 & -0.9922 & 0.162549 \tabularnewline
17 & -0.188335 & -1.4588 & 0.074913 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112484&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]0.577934[/C][C]4.4767[/C][C]1.7e-05[/C][/ROW]
[ROW][C]2[/C][C]0.106341[/C][C]0.8237[/C][C]0.206683[/C][/ROW]
[ROW][C]3[/C][C]-0.107026[/C][C]-0.829[/C][C]0.20519[/C][/ROW]
[ROW][C]4[/C][C]-0.200542[/C][C]-1.5534[/C][C]0.062794[/C][/ROW]
[ROW][C]5[/C][C]-0.343699[/C][C]-2.6623[/C][C]0.004974[/C][/ROW]
[ROW][C]6[/C][C]-0.488825[/C][C]-3.7864[/C][C]0.000178[/C][/ROW]
[ROW][C]7[/C][C]-0.479356[/C][C]-3.7131[/C][C]0.000225[/C][/ROW]
[ROW][C]8[/C][C]-0.290255[/C][C]-2.2483[/C][C]0.014121[/C][/ROW]
[ROW][C]9[/C][C]-0.116709[/C][C]-0.904[/C][C]0.184799[/C][/ROW]
[ROW][C]10[/C][C]0.052106[/C][C]0.4036[/C][C]0.343966[/C][/ROW]
[ROW][C]11[/C][C]0.365718[/C][C]2.8328[/C][C]0.003137[/C][/ROW]
[ROW][C]12[/C][C]0.604241[/C][C]4.6804[/C][C]8e-06[/C][/ROW]
[ROW][C]13[/C][C]0.456547[/C][C]3.5364[/C][C]0.000395[/C][/ROW]
[ROW][C]14[/C][C]0.167304[/C][C]1.2959[/C][C]0.099982[/C][/ROW]
[ROW][C]15[/C][C]-0.034474[/C][C]-0.267[/C][C]0.395179[/C][/ROW]
[ROW][C]16[/C][C]-0.128089[/C][C]-0.9922[/C][C]0.162549[/C][/ROW]
[ROW][C]17[/C][C]-0.188335[/C][C]-1.4588[/C][C]0.074913[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112484&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112484&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	0.577934	4.4767	1.7e-05
2	0.106341	0.8237	0.206683
3	-0.107026	-0.829	0.20519
4	-0.200542	-1.5534	0.062794
5	-0.343699	-2.6623	0.004974
6	-0.488825	-3.7864	0.000178
7	-0.479356	-3.7131	0.000225
8	-0.290255	-2.2483	0.014121
9	-0.116709	-0.904	0.184799
10	0.052106	0.4036	0.343966
11	0.365718	2.8328	0.003137
12	0.604241	4.6804	8e-06
13	0.456547	3.5364	0.000395
14	0.167304	1.2959	0.099982
15	-0.034474	-0.267	0.395179
16	-0.128089	-0.9922	0.162549
17	-0.188335	-1.4588	0.074913

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.577934	4.4767	1.7e-05
2	-0.341845	-2.6479	0.005166
3	0.013723	0.1063	0.457851
4	-0.148777	-1.1524	0.126859
5	-0.274739	-2.1281	0.018722
6	-0.290317	-2.2488	0.014105
7	-0.209018	-1.619	0.055341
8	-0.125874	-0.975	0.166734
9	-0.23558	-1.8248	0.036506
10	-0.089555	-0.6937	0.245276
11	0.246754	1.9113	0.03037
12	0.186325	1.4433	0.077073
13	-0.149518	-1.1582	0.125693
14	-0.036218	-0.2805	0.390012
15	-0.085081	-0.659	0.256197
16	-0.07273	-0.5634	0.287643
17	0.068673	0.5319	0.298367

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.577934 & 4.4767 & 1.7e-05 \tabularnewline
2 & -0.341845 & -2.6479 & 0.005166 \tabularnewline
3 & 0.013723 & 0.1063 & 0.457851 \tabularnewline
4 & -0.148777 & -1.1524 & 0.126859 \tabularnewline
5 & -0.274739 & -2.1281 & 0.018722 \tabularnewline
6 & -0.290317 & -2.2488 & 0.014105 \tabularnewline
7 & -0.209018 & -1.619 & 0.055341 \tabularnewline
8 & -0.125874 & -0.975 & 0.166734 \tabularnewline
9 & -0.23558 & -1.8248 & 0.036506 \tabularnewline
10 & -0.089555 & -0.6937 & 0.245276 \tabularnewline
11 & 0.246754 & 1.9113 & 0.03037 \tabularnewline
12 & 0.186325 & 1.4433 & 0.077073 \tabularnewline
13 & -0.149518 & -1.1582 & 0.125693 \tabularnewline
14 & -0.036218 & -0.2805 & 0.390012 \tabularnewline
15 & -0.085081 & -0.659 & 0.256197 \tabularnewline
16 & -0.07273 & -0.5634 & 0.287643 \tabularnewline
17 & 0.068673 & 0.5319 & 0.298367 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112484&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]0.577934[/C][C]4.4767[/C][C]1.7e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.341845[/C][C]-2.6479[/C][C]0.005166[/C][/ROW]
[ROW][C]3[/C][C]0.013723[/C][C]0.1063[/C][C]0.457851[/C][/ROW]
[ROW][C]4[/C][C]-0.148777[/C][C]-1.1524[/C][C]0.126859[/C][/ROW]
[ROW][C]5[/C][C]-0.274739[/C][C]-2.1281[/C][C]0.018722[/C][/ROW]
[ROW][C]6[/C][C]-0.290317[/C][C]-2.2488[/C][C]0.014105[/C][/ROW]
[ROW][C]7[/C][C]-0.209018[/C][C]-1.619[/C][C]0.055341[/C][/ROW]
[ROW][C]8[/C][C]-0.125874[/C][C]-0.975[/C][C]0.166734[/C][/ROW]
[ROW][C]9[/C][C]-0.23558[/C][C]-1.8248[/C][C]0.036506[/C][/ROW]
[ROW][C]10[/C][C]-0.089555[/C][C]-0.6937[/C][C]0.245276[/C][/ROW]
[ROW][C]11[/C][C]0.246754[/C][C]1.9113[/C][C]0.03037[/C][/ROW]
[ROW][C]12[/C][C]0.186325[/C][C]1.4433[/C][C]0.077073[/C][/ROW]
[ROW][C]13[/C][C]-0.149518[/C][C]-1.1582[/C][C]0.125693[/C][/ROW]
[ROW][C]14[/C][C]-0.036218[/C][C]-0.2805[/C][C]0.390012[/C][/ROW]
[ROW][C]15[/C][C]-0.085081[/C][C]-0.659[/C][C]0.256197[/C][/ROW]
[ROW][C]16[/C][C]-0.07273[/C][C]-0.5634[/C][C]0.287643[/C][/ROW]
[ROW][C]17[/C][C]0.068673[/C][C]0.5319[/C][C]0.298367[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112484&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112484&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	0.577934	4.4767	1.7e-05
2	-0.341845	-2.6479	0.005166
3	0.013723	0.1063	0.457851
4	-0.148777	-1.1524	0.126859
5	-0.274739	-2.1281	0.018722
6	-0.290317	-2.2488	0.014105
7	-0.209018	-1.619	0.055341
8	-0.125874	-0.975	0.166734
9	-0.23558	-1.8248	0.036506
10	-0.089555	-0.6937	0.245276
11	0.246754	1.9113	0.03037
12	0.186325	1.4433	0.077073
13	-0.149518	-1.1582	0.125693
14	-0.036218	-0.2805	0.390012
15	-0.085081	-0.659	0.256197
16	-0.07273	-0.5634	0.287643
17	0.068673	0.5319	0.298367

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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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Input Parameters & R Code