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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 13 Nov 2013 04:15:56 -0500

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/2013/Nov/13/t1384334169gced8gn4i4lvx5e.htm/, Retrieved Sun, 28 Apr 2024 19:27:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=224672, Retrieved Sun, 28 Apr 2024 19:27:05 +0000

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

-       [(Partial) Autocorrelation Function] [] [2013-11-13 09:15:56] [2ad58ca14453c04e73fc838d0bf536d8] [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' @ 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224672&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224672&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224672&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' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.411029	3.7447	0.000166
2	0.105176	0.9582	0.170372
3	-0.092799	-0.8454	0.200149
4	0.060515	0.5513	0.291448
5	0.164552	1.4991	0.068815
6	0.303461	2.7647	0.00351
7	0.196103	1.7866	0.038828
8	0.108062	0.9845	0.163867
9	-0.159923	-1.457	0.074449
10	-0.030843	-0.281	0.389707
11	0.153456	1.3981	0.082911
12	0.324505	2.9564	0.002026
13	0.167538	1.5263	0.065363
14	0.022197	0.2022	0.420119
15	-0.067537	-0.6153	0.270023
16	-9.8e-05	-9e-04	0.499646
17	0.04879	0.4445	0.32892
18	0.129152	1.1766	0.121353
19	0.085305	0.7772	0.219635

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.411029 & 3.7447 & 0.000166 \tabularnewline
2 & 0.105176 & 0.9582 & 0.170372 \tabularnewline
3 & -0.092799 & -0.8454 & 0.200149 \tabularnewline
4 & 0.060515 & 0.5513 & 0.291448 \tabularnewline
5 & 0.164552 & 1.4991 & 0.068815 \tabularnewline
6 & 0.303461 & 2.7647 & 0.00351 \tabularnewline
7 & 0.196103 & 1.7866 & 0.038828 \tabularnewline
8 & 0.108062 & 0.9845 & 0.163867 \tabularnewline
9 & -0.159923 & -1.457 & 0.074449 \tabularnewline
10 & -0.030843 & -0.281 & 0.389707 \tabularnewline
11 & 0.153456 & 1.3981 & 0.082911 \tabularnewline
12 & 0.324505 & 2.9564 & 0.002026 \tabularnewline
13 & 0.167538 & 1.5263 & 0.065363 \tabularnewline
14 & 0.022197 & 0.2022 & 0.420119 \tabularnewline
15 & -0.067537 & -0.6153 & 0.270023 \tabularnewline
16 & -9.8e-05 & -9e-04 & 0.499646 \tabularnewline
17 & 0.04879 & 0.4445 & 0.32892 \tabularnewline
18 & 0.129152 & 1.1766 & 0.121353 \tabularnewline
19 & 0.085305 & 0.7772 & 0.219635 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224672&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]0.411029[/C][C]3.7447[/C][C]0.000166[/C][/ROW]
[ROW][C]2[/C][C]0.105176[/C][C]0.9582[/C][C]0.170372[/C][/ROW]
[ROW][C]3[/C][C]-0.092799[/C][C]-0.8454[/C][C]0.200149[/C][/ROW]
[ROW][C]4[/C][C]0.060515[/C][C]0.5513[/C][C]0.291448[/C][/ROW]
[ROW][C]5[/C][C]0.164552[/C][C]1.4991[/C][C]0.068815[/C][/ROW]
[ROW][C]6[/C][C]0.303461[/C][C]2.7647[/C][C]0.00351[/C][/ROW]
[ROW][C]7[/C][C]0.196103[/C][C]1.7866[/C][C]0.038828[/C][/ROW]
[ROW][C]8[/C][C]0.108062[/C][C]0.9845[/C][C]0.163867[/C][/ROW]
[ROW][C]9[/C][C]-0.159923[/C][C]-1.457[/C][C]0.074449[/C][/ROW]
[ROW][C]10[/C][C]-0.030843[/C][C]-0.281[/C][C]0.389707[/C][/ROW]
[ROW][C]11[/C][C]0.153456[/C][C]1.3981[/C][C]0.082911[/C][/ROW]
[ROW][C]12[/C][C]0.324505[/C][C]2.9564[/C][C]0.002026[/C][/ROW]
[ROW][C]13[/C][C]0.167538[/C][C]1.5263[/C][C]0.065363[/C][/ROW]
[ROW][C]14[/C][C]0.022197[/C][C]0.2022[/C][C]0.420119[/C][/ROW]
[ROW][C]15[/C][C]-0.067537[/C][C]-0.6153[/C][C]0.270023[/C][/ROW]
[ROW][C]16[/C][C]-9.8e-05[/C][C]-9e-04[/C][C]0.499646[/C][/ROW]
[ROW][C]17[/C][C]0.04879[/C][C]0.4445[/C][C]0.32892[/C][/ROW]
[ROW][C]18[/C][C]0.129152[/C][C]1.1766[/C][C]0.121353[/C][/ROW]
[ROW][C]19[/C][C]0.085305[/C][C]0.7772[/C][C]0.219635[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224672&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224672&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	0.411029	3.7447	0.000166
2	0.105176	0.9582	0.170372
3	-0.092799	-0.8454	0.200149
4	0.060515	0.5513	0.291448
5	0.164552	1.4991	0.068815
6	0.303461	2.7647	0.00351
7	0.196103	1.7866	0.038828
8	0.108062	0.9845	0.163867
9	-0.159923	-1.457	0.074449
10	-0.030843	-0.281	0.389707
11	0.153456	1.3981	0.082911
12	0.324505	2.9564	0.002026
13	0.167538	1.5263	0.065363
14	0.022197	0.2022	0.420119
15	-0.067537	-0.6153	0.270023
16	-9.8e-05	-9e-04	0.499646
17	0.04879	0.4445	0.32892
18	0.129152	1.1766	0.121353
19	0.085305	0.7772	0.219635

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.411029	3.7447	0.000166
2	-0.076732	-0.6991	0.243234
3	-0.130492	-1.1888	0.118947
4	0.192451	1.7533	0.04162
5	0.10078	0.9181	0.180601
6	0.199543	1.8179	0.036342
7	0.01791	0.1632	0.43539
8	0.03625	0.3303	0.371021
9	-0.226748	-2.0658	0.020985
10	0.116118	1.0579	0.146588
11	0.151442	1.3797	0.085692
12	0.112295	1.0231	0.154626
13	-0.049977	-0.4553	0.325036
14	-0.030635	-0.2791	0.390431
15	0.039995	0.3644	0.358254
16	-0.004973	-0.0453	0.481986
17	-0.011054	-0.1007	0.460011
18	-0.044731	-0.4075	0.34234
19	-0.015652	-0.1426	0.443479

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.411029 & 3.7447 & 0.000166 \tabularnewline
2 & -0.076732 & -0.6991 & 0.243234 \tabularnewline
3 & -0.130492 & -1.1888 & 0.118947 \tabularnewline
4 & 0.192451 & 1.7533 & 0.04162 \tabularnewline
5 & 0.10078 & 0.9181 & 0.180601 \tabularnewline
6 & 0.199543 & 1.8179 & 0.036342 \tabularnewline
7 & 0.01791 & 0.1632 & 0.43539 \tabularnewline
8 & 0.03625 & 0.3303 & 0.371021 \tabularnewline
9 & -0.226748 & -2.0658 & 0.020985 \tabularnewline
10 & 0.116118 & 1.0579 & 0.146588 \tabularnewline
11 & 0.151442 & 1.3797 & 0.085692 \tabularnewline
12 & 0.112295 & 1.0231 & 0.154626 \tabularnewline
13 & -0.049977 & -0.4553 & 0.325036 \tabularnewline
14 & -0.030635 & -0.2791 & 0.390431 \tabularnewline
15 & 0.039995 & 0.3644 & 0.358254 \tabularnewline
16 & -0.004973 & -0.0453 & 0.481986 \tabularnewline
17 & -0.011054 & -0.1007 & 0.460011 \tabularnewline
18 & -0.044731 & -0.4075 & 0.34234 \tabularnewline
19 & -0.015652 & -0.1426 & 0.443479 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=224672&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]0.411029[/C][C]3.7447[/C][C]0.000166[/C][/ROW]
[ROW][C]2[/C][C]-0.076732[/C][C]-0.6991[/C][C]0.243234[/C][/ROW]
[ROW][C]3[/C][C]-0.130492[/C][C]-1.1888[/C][C]0.118947[/C][/ROW]
[ROW][C]4[/C][C]0.192451[/C][C]1.7533[/C][C]0.04162[/C][/ROW]
[ROW][C]5[/C][C]0.10078[/C][C]0.9181[/C][C]0.180601[/C][/ROW]
[ROW][C]6[/C][C]0.199543[/C][C]1.8179[/C][C]0.036342[/C][/ROW]
[ROW][C]7[/C][C]0.01791[/C][C]0.1632[/C][C]0.43539[/C][/ROW]
[ROW][C]8[/C][C]0.03625[/C][C]0.3303[/C][C]0.371021[/C][/ROW]
[ROW][C]9[/C][C]-0.226748[/C][C]-2.0658[/C][C]0.020985[/C][/ROW]
[ROW][C]10[/C][C]0.116118[/C][C]1.0579[/C][C]0.146588[/C][/ROW]
[ROW][C]11[/C][C]0.151442[/C][C]1.3797[/C][C]0.085692[/C][/ROW]
[ROW][C]12[/C][C]0.112295[/C][C]1.0231[/C][C]0.154626[/C][/ROW]
[ROW][C]13[/C][C]-0.049977[/C][C]-0.4553[/C][C]0.325036[/C][/ROW]
[ROW][C]14[/C][C]-0.030635[/C][C]-0.2791[/C][C]0.390431[/C][/ROW]
[ROW][C]15[/C][C]0.039995[/C][C]0.3644[/C][C]0.358254[/C][/ROW]
[ROW][C]16[/C][C]-0.004973[/C][C]-0.0453[/C][C]0.481986[/C][/ROW]
[ROW][C]17[/C][C]-0.011054[/C][C]-0.1007[/C][C]0.460011[/C][/ROW]
[ROW][C]18[/C][C]-0.044731[/C][C]-0.4075[/C][C]0.34234[/C][/ROW]
[ROW][C]19[/C][C]-0.015652[/C][C]-0.1426[/C][C]0.443479[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=224672&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=224672&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	0.411029	3.7447	0.000166
2	-0.076732	-0.6991	0.243234
3	-0.130492	-1.1888	0.118947
4	0.192451	1.7533	0.04162
5	0.10078	0.9181	0.180601
6	0.199543	1.8179	0.036342
7	0.01791	0.1632	0.43539
8	0.03625	0.3303	0.371021
9	-0.226748	-2.0658	0.020985
10	0.116118	1.0579	0.146588
11	0.151442	1.3797	0.085692
12	0.112295	1.0231	0.154626
13	-0.049977	-0.4553	0.325036
14	-0.030635	-0.2791	0.390431
15	0.039995	0.3644	0.358254
16	-0.004973	-0.0453	0.481986
17	-0.011054	-0.1007	0.460011
18	-0.044731	-0.4075	0.34234
19	-0.015652	-0.1426	0.443479

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