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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 18 Dec 2010 11:12:52 +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/18/t12926706497u0osj2gm36hr2m.htm/, Retrieved Tue, 30 Apr 2024 05:52:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111844, Retrieved Tue, 30 Apr 2024 05:52:14 +0000

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155

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

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [(Partial) Autocorrelation Function] [autocorrelatie ru...] [2010-12-14 18:37:20] [d6e648f00513dd750579ba7880c5fbf5]
F R  D    [(Partial) Autocorrelation Function] [] [2010-12-16 10:12:12] [58af523ef9b33032fd2497c80088399b]
-    D        [(Partial) Autocorrelation Function] [] [2010-12-18 11:12:52] [7c1b7ddc8e9000e55b944088fdfb52dc] [Current]
-    D          [(Partial) Autocorrelation Function] [] [2010-12-29 09:42:31] [126c9e58bb659a0bfb4675d843c2c69e] 

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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=111844&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=111844&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111844&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	0.952914	7.131	0
2	0.909914	6.8092	0
3	0.863627	6.4628	0
4	0.818503	6.1251	0
5	0.773535	5.7886	0
6	0.724342	5.4205	1e-06
7	0.67371	5.0416	3e-06
8	0.613671	4.5923	1.3e-05
9	0.554955	4.1529	5.7e-05
10	0.501365	3.7519	0.000209
11	0.450756	3.3731	0.000677
12	0.406961	3.0454	0.001769
13	0.356879	2.6706	0.004946
14	0.302734	2.2655	0.013686
15	0.246279	1.843	0.035313
16	0.190902	1.4286	0.07934
17	0.140839	1.0539	0.148218

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.952914 & 7.131 & 0 \tabularnewline
2 & 0.909914 & 6.8092 & 0 \tabularnewline
3 & 0.863627 & 6.4628 & 0 \tabularnewline
4 & 0.818503 & 6.1251 & 0 \tabularnewline
5 & 0.773535 & 5.7886 & 0 \tabularnewline
6 & 0.724342 & 5.4205 & 1e-06 \tabularnewline
7 & 0.67371 & 5.0416 & 3e-06 \tabularnewline
8 & 0.613671 & 4.5923 & 1.3e-05 \tabularnewline
9 & 0.554955 & 4.1529 & 5.7e-05 \tabularnewline
10 & 0.501365 & 3.7519 & 0.000209 \tabularnewline
11 & 0.450756 & 3.3731 & 0.000677 \tabularnewline
12 & 0.406961 & 3.0454 & 0.001769 \tabularnewline
13 & 0.356879 & 2.6706 & 0.004946 \tabularnewline
14 & 0.302734 & 2.2655 & 0.013686 \tabularnewline
15 & 0.246279 & 1.843 & 0.035313 \tabularnewline
16 & 0.190902 & 1.4286 & 0.07934 \tabularnewline
17 & 0.140839 & 1.0539 & 0.148218 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111844&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]0.952914[/C][C]7.131[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.909914[/C][C]6.8092[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.863627[/C][C]6.4628[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.818503[/C][C]6.1251[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.773535[/C][C]5.7886[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.724342[/C][C]5.4205[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.67371[/C][C]5.0416[/C][C]3e-06[/C][/ROW]
[ROW][C]8[/C][C]0.613671[/C][C]4.5923[/C][C]1.3e-05[/C][/ROW]
[ROW][C]9[/C][C]0.554955[/C][C]4.1529[/C][C]5.7e-05[/C][/ROW]
[ROW][C]10[/C][C]0.501365[/C][C]3.7519[/C][C]0.000209[/C][/ROW]
[ROW][C]11[/C][C]0.450756[/C][C]3.3731[/C][C]0.000677[/C][/ROW]
[ROW][C]12[/C][C]0.406961[/C][C]3.0454[/C][C]0.001769[/C][/ROW]
[ROW][C]13[/C][C]0.356879[/C][C]2.6706[/C][C]0.004946[/C][/ROW]
[ROW][C]14[/C][C]0.302734[/C][C]2.2655[/C][C]0.013686[/C][/ROW]
[ROW][C]15[/C][C]0.246279[/C][C]1.843[/C][C]0.035313[/C][/ROW]
[ROW][C]16[/C][C]0.190902[/C][C]1.4286[/C][C]0.07934[/C][/ROW]
[ROW][C]17[/C][C]0.140839[/C][C]1.0539[/C][C]0.148218[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111844&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111844&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	0.952914	7.131	0
2	0.909914	6.8092	0
3	0.863627	6.4628	0
4	0.818503	6.1251	0
5	0.773535	5.7886	0
6	0.724342	5.4205	1e-06
7	0.67371	5.0416	3e-06
8	0.613671	4.5923	1.3e-05
9	0.554955	4.1529	5.7e-05
10	0.501365	3.7519	0.000209
11	0.450756	3.3731	0.000677
12	0.406961	3.0454	0.001769
13	0.356879	2.6706	0.004946
14	0.302734	2.2655	0.013686
15	0.246279	1.843	0.035313
16	0.190902	1.4286	0.07934
17	0.140839	1.0539	0.148218

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.952914	7.131	0
2	0.020317	0.152	0.439851
3	-0.056431	-0.4223	0.337215
4	-0.01504	-0.1125	0.455396
5	-0.021058	-0.1576	0.437675
6	-0.071994	-0.5388	0.296096
7	-0.048295	-0.3614	0.359577
8	-0.13233	-0.9903	0.163152
9	-0.032809	-0.2455	0.403476
10	0.024654	0.1845	0.427147
11	0.001318	0.0099	0.496081
12	0.042307	0.3166	0.376363
13	-0.085998	-0.6436	0.261246
14	-0.08927	-0.668	0.253427
15	-0.062579	-0.4683	0.320694
16	-0.041209	-0.3084	0.379469
17	-0.003458	-0.0259	0.489724

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.952914 & 7.131 & 0 \tabularnewline
2 & 0.020317 & 0.152 & 0.439851 \tabularnewline
3 & -0.056431 & -0.4223 & 0.337215 \tabularnewline
4 & -0.01504 & -0.1125 & 0.455396 \tabularnewline
5 & -0.021058 & -0.1576 & 0.437675 \tabularnewline
6 & -0.071994 & -0.5388 & 0.296096 \tabularnewline
7 & -0.048295 & -0.3614 & 0.359577 \tabularnewline
8 & -0.13233 & -0.9903 & 0.163152 \tabularnewline
9 & -0.032809 & -0.2455 & 0.403476 \tabularnewline
10 & 0.024654 & 0.1845 & 0.427147 \tabularnewline
11 & 0.001318 & 0.0099 & 0.496081 \tabularnewline
12 & 0.042307 & 0.3166 & 0.376363 \tabularnewline
13 & -0.085998 & -0.6436 & 0.261246 \tabularnewline
14 & -0.08927 & -0.668 & 0.253427 \tabularnewline
15 & -0.062579 & -0.4683 & 0.320694 \tabularnewline
16 & -0.041209 & -0.3084 & 0.379469 \tabularnewline
17 & -0.003458 & -0.0259 & 0.489724 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111844&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]0.952914[/C][C]7.131[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.020317[/C][C]0.152[/C][C]0.439851[/C][/ROW]
[ROW][C]3[/C][C]-0.056431[/C][C]-0.4223[/C][C]0.337215[/C][/ROW]
[ROW][C]4[/C][C]-0.01504[/C][C]-0.1125[/C][C]0.455396[/C][/ROW]
[ROW][C]5[/C][C]-0.021058[/C][C]-0.1576[/C][C]0.437675[/C][/ROW]
[ROW][C]6[/C][C]-0.071994[/C][C]-0.5388[/C][C]0.296096[/C][/ROW]
[ROW][C]7[/C][C]-0.048295[/C][C]-0.3614[/C][C]0.359577[/C][/ROW]
[ROW][C]8[/C][C]-0.13233[/C][C]-0.9903[/C][C]0.163152[/C][/ROW]
[ROW][C]9[/C][C]-0.032809[/C][C]-0.2455[/C][C]0.403476[/C][/ROW]
[ROW][C]10[/C][C]0.024654[/C][C]0.1845[/C][C]0.427147[/C][/ROW]
[ROW][C]11[/C][C]0.001318[/C][C]0.0099[/C][C]0.496081[/C][/ROW]
[ROW][C]12[/C][C]0.042307[/C][C]0.3166[/C][C]0.376363[/C][/ROW]
[ROW][C]13[/C][C]-0.085998[/C][C]-0.6436[/C][C]0.261246[/C][/ROW]
[ROW][C]14[/C][C]-0.08927[/C][C]-0.668[/C][C]0.253427[/C][/ROW]
[ROW][C]15[/C][C]-0.062579[/C][C]-0.4683[/C][C]0.320694[/C][/ROW]
[ROW][C]16[/C][C]-0.041209[/C][C]-0.3084[/C][C]0.379469[/C][/ROW]
[ROW][C]17[/C][C]-0.003458[/C][C]-0.0259[/C][C]0.489724[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111844&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111844&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	0.952914	7.131	0
2	0.020317	0.152	0.439851
3	-0.056431	-0.4223	0.337215
4	-0.01504	-0.1125	0.455396
5	-0.021058	-0.1576	0.437675
6	-0.071994	-0.5388	0.296096
7	-0.048295	-0.3614	0.359577
8	-0.13233	-0.9903	0.163152
9	-0.032809	-0.2455	0.403476
10	0.024654	0.1845	0.427147
11	0.001318	0.0099	0.496081
12	0.042307	0.3166	0.376363
13	-0.085998	-0.6436	0.261246
14	-0.08927	-0.668	0.253427
15	-0.062579	-0.4683	0.320694
16	-0.041209	-0.3084	0.379469
17	-0.003458	-0.0259	0.489724

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code