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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 16 Oct 2014 18:19:34 +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/2014/Oct/16/t1413480013i94ifeicurh0e84.htm/, Retrieved Mon, 13 May 2024 19:14:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=242811, Retrieved Mon, 13 May 2024 19:14:55 +0000

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-       [(Partial) Autocorrelation Function] [] [2014-10-16 17:19:34] [d67845bcf6d8dd3cd224f69460cf281c] [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=242811&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=242811&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=242811&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	-0.633147	-5.7682	0
2	0.206577	1.882	0.03167
3	-0.113932	-1.038	0.15115
4	0.067335	0.6135	0.270627
5	0.085331	0.7774	0.219567
6	-0.186493	-1.699	0.04653
7	0.077357	0.7048	0.241468
8	0.083618	0.7618	0.22417
9	-0.129441	-1.1793	0.120832
10	0.199117	1.814	0.036643
11	-0.509982	-4.6462	6e-06
12	0.739677	6.7388	0
13	-0.515084	-4.6926	5e-06
14	0.193685	1.7646	0.040659
15	-0.097116	-0.8848	0.189418
16	0.049094	0.4473	0.327925
17	0.053231	0.485	0.314491
18	-0.111495	-1.0158	0.156347
19	0.031846	0.2901	0.386221

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.633147 & -5.7682 & 0 \tabularnewline
2 & 0.206577 & 1.882 & 0.03167 \tabularnewline
3 & -0.113932 & -1.038 & 0.15115 \tabularnewline
4 & 0.067335 & 0.6135 & 0.270627 \tabularnewline
5 & 0.085331 & 0.7774 & 0.219567 \tabularnewline
6 & -0.186493 & -1.699 & 0.04653 \tabularnewline
7 & 0.077357 & 0.7048 & 0.241468 \tabularnewline
8 & 0.083618 & 0.7618 & 0.22417 \tabularnewline
9 & -0.129441 & -1.1793 & 0.120832 \tabularnewline
10 & 0.199117 & 1.814 & 0.036643 \tabularnewline
11 & -0.509982 & -4.6462 & 6e-06 \tabularnewline
12 & 0.739677 & 6.7388 & 0 \tabularnewline
13 & -0.515084 & -4.6926 & 5e-06 \tabularnewline
14 & 0.193685 & 1.7646 & 0.040659 \tabularnewline
15 & -0.097116 & -0.8848 & 0.189418 \tabularnewline
16 & 0.049094 & 0.4473 & 0.327925 \tabularnewline
17 & 0.053231 & 0.485 & 0.314491 \tabularnewline
18 & -0.111495 & -1.0158 & 0.156347 \tabularnewline
19 & 0.031846 & 0.2901 & 0.386221 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=242811&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]-0.633147[/C][C]-5.7682[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.206577[/C][C]1.882[/C][C]0.03167[/C][/ROW]
[ROW][C]3[/C][C]-0.113932[/C][C]-1.038[/C][C]0.15115[/C][/ROW]
[ROW][C]4[/C][C]0.067335[/C][C]0.6135[/C][C]0.270627[/C][/ROW]
[ROW][C]5[/C][C]0.085331[/C][C]0.7774[/C][C]0.219567[/C][/ROW]
[ROW][C]6[/C][C]-0.186493[/C][C]-1.699[/C][C]0.04653[/C][/ROW]
[ROW][C]7[/C][C]0.077357[/C][C]0.7048[/C][C]0.241468[/C][/ROW]
[ROW][C]8[/C][C]0.083618[/C][C]0.7618[/C][C]0.22417[/C][/ROW]
[ROW][C]9[/C][C]-0.129441[/C][C]-1.1793[/C][C]0.120832[/C][/ROW]
[ROW][C]10[/C][C]0.199117[/C][C]1.814[/C][C]0.036643[/C][/ROW]
[ROW][C]11[/C][C]-0.509982[/C][C]-4.6462[/C][C]6e-06[/C][/ROW]
[ROW][C]12[/C][C]0.739677[/C][C]6.7388[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.515084[/C][C]-4.6926[/C][C]5e-06[/C][/ROW]
[ROW][C]14[/C][C]0.193685[/C][C]1.7646[/C][C]0.040659[/C][/ROW]
[ROW][C]15[/C][C]-0.097116[/C][C]-0.8848[/C][C]0.189418[/C][/ROW]
[ROW][C]16[/C][C]0.049094[/C][C]0.4473[/C][C]0.327925[/C][/ROW]
[ROW][C]17[/C][C]0.053231[/C][C]0.485[/C][C]0.314491[/C][/ROW]
[ROW][C]18[/C][C]-0.111495[/C][C]-1.0158[/C][C]0.156347[/C][/ROW]
[ROW][C]19[/C][C]0.031846[/C][C]0.2901[/C][C]0.386221[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=242811&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=242811&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	-0.633147	-5.7682	0
2	0.206577	1.882	0.03167
3	-0.113932	-1.038	0.15115
4	0.067335	0.6135	0.270627
5	0.085331	0.7774	0.219567
6	-0.186493	-1.699	0.04653
7	0.077357	0.7048	0.241468
8	0.083618	0.7618	0.22417
9	-0.129441	-1.1793	0.120832
10	0.199117	1.814	0.036643
11	-0.509982	-4.6462	6e-06
12	0.739677	6.7388	0
13	-0.515084	-4.6926	5e-06
14	0.193685	1.7646	0.040659
15	-0.097116	-0.8848	0.189418
16	0.049094	0.4473	0.327925
17	0.053231	0.485	0.314491
18	-0.111495	-1.0158	0.156347
19	0.031846	0.2901	0.386221

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.633147	-5.7682	0
2	-0.324303	-2.9545	0.002037
3	-0.272428	-2.4819	0.007542
4	-0.194562	-1.7725	0.039987
5	0.097217	0.8857	0.189172
6	-0.053284	-0.4854	0.314322
7	-0.166604	-1.5178	0.066428
8	0.05649	0.5146	0.304085
9	-0.056456	-0.5143	0.30419
10	0.196322	1.7886	0.038666
11	-0.531205	-4.8395	3e-06
12	0.283749	2.5851	0.005742
13	0.101411	0.9239	0.179108
14	0.022156	0.2018	0.420265
15	-0.006456	-0.0588	0.476618
16	-0.020304	-0.185	0.426848
17	-0.125248	-1.1411	0.128562
18	0.029994	0.2733	0.392668
19	-0.003866	-0.0352	0.485995

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.633147 & -5.7682 & 0 \tabularnewline
2 & -0.324303 & -2.9545 & 0.002037 \tabularnewline
3 & -0.272428 & -2.4819 & 0.007542 \tabularnewline
4 & -0.194562 & -1.7725 & 0.039987 \tabularnewline
5 & 0.097217 & 0.8857 & 0.189172 \tabularnewline
6 & -0.053284 & -0.4854 & 0.314322 \tabularnewline
7 & -0.166604 & -1.5178 & 0.066428 \tabularnewline
8 & 0.05649 & 0.5146 & 0.304085 \tabularnewline
9 & -0.056456 & -0.5143 & 0.30419 \tabularnewline
10 & 0.196322 & 1.7886 & 0.038666 \tabularnewline
11 & -0.531205 & -4.8395 & 3e-06 \tabularnewline
12 & 0.283749 & 2.5851 & 0.005742 \tabularnewline
13 & 0.101411 & 0.9239 & 0.179108 \tabularnewline
14 & 0.022156 & 0.2018 & 0.420265 \tabularnewline
15 & -0.006456 & -0.0588 & 0.476618 \tabularnewline
16 & -0.020304 & -0.185 & 0.426848 \tabularnewline
17 & -0.125248 & -1.1411 & 0.128562 \tabularnewline
18 & 0.029994 & 0.2733 & 0.392668 \tabularnewline
19 & -0.003866 & -0.0352 & 0.485995 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=242811&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]-0.633147[/C][C]-5.7682[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.324303[/C][C]-2.9545[/C][C]0.002037[/C][/ROW]
[ROW][C]3[/C][C]-0.272428[/C][C]-2.4819[/C][C]0.007542[/C][/ROW]
[ROW][C]4[/C][C]-0.194562[/C][C]-1.7725[/C][C]0.039987[/C][/ROW]
[ROW][C]5[/C][C]0.097217[/C][C]0.8857[/C][C]0.189172[/C][/ROW]
[ROW][C]6[/C][C]-0.053284[/C][C]-0.4854[/C][C]0.314322[/C][/ROW]
[ROW][C]7[/C][C]-0.166604[/C][C]-1.5178[/C][C]0.066428[/C][/ROW]
[ROW][C]8[/C][C]0.05649[/C][C]0.5146[/C][C]0.304085[/C][/ROW]
[ROW][C]9[/C][C]-0.056456[/C][C]-0.5143[/C][C]0.30419[/C][/ROW]
[ROW][C]10[/C][C]0.196322[/C][C]1.7886[/C][C]0.038666[/C][/ROW]
[ROW][C]11[/C][C]-0.531205[/C][C]-4.8395[/C][C]3e-06[/C][/ROW]
[ROW][C]12[/C][C]0.283749[/C][C]2.5851[/C][C]0.005742[/C][/ROW]
[ROW][C]13[/C][C]0.101411[/C][C]0.9239[/C][C]0.179108[/C][/ROW]
[ROW][C]14[/C][C]0.022156[/C][C]0.2018[/C][C]0.420265[/C][/ROW]
[ROW][C]15[/C][C]-0.006456[/C][C]-0.0588[/C][C]0.476618[/C][/ROW]
[ROW][C]16[/C][C]-0.020304[/C][C]-0.185[/C][C]0.426848[/C][/ROW]
[ROW][C]17[/C][C]-0.125248[/C][C]-1.1411[/C][C]0.128562[/C][/ROW]
[ROW][C]18[/C][C]0.029994[/C][C]0.2733[/C][C]0.392668[/C][/ROW]
[ROW][C]19[/C][C]-0.003866[/C][C]-0.0352[/C][C]0.485995[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=242811&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=242811&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	-0.633147	-5.7682	0
2	-0.324303	-2.9545	0.002037
3	-0.272428	-2.4819	0.007542
4	-0.194562	-1.7725	0.039987
5	0.097217	0.8857	0.189172
6	-0.053284	-0.4854	0.314322
7	-0.166604	-1.5178	0.066428
8	0.05649	0.5146	0.304085
9	-0.056456	-0.5143	0.30419
10	0.196322	1.7886	0.038666
11	-0.531205	-4.8395	3e-06
12	0.283749	2.5851	0.005742
13	0.101411	0.9239	0.179108
14	0.022156	0.2018	0.420265
15	-0.006456	-0.0588	0.476618
16	-0.020304	-0.185	0.426848
17	-0.125248	-1.1411	0.128562
18	0.029994	0.2733	0.392668
19	-0.003866	-0.0352	0.485995

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
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