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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 17 Dec 2010 20:39:23 +0000

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/2010/Dec/17/t1292618258udc9zg40goki42g.htm/, Retrieved Sat, 04 May 2024 02:47:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111727, Retrieved Sat, 04 May 2024 02:47:01 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

149

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

-     [Univariate Data Series] [Bouwvergunningen] [2009-11-02 16:57:06] [11ac052cc87d77b9933b02bea117068e]
-   P   [Univariate Data Series] [Bouwvergunningen ...] [2009-11-11 14:29:30] [11ac052cc87d77b9933b02bea117068e]
- RMPD    [Variance Reduction Matrix] [Workshop 6] [2010-12-16 20:00:53] [29e492448d11757ae0fad5ef6e7f8e86]
- RMPD        [(Partial) Autocorrelation Function] [] [2010-12-17 20:39:23] [0956ee981dded61b2e7128dae94e5715] [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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111727&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111727&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111727&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.279509	2.054	0.022417
2	0.047875	0.3518	0.363177
3	0.096586	0.7098	0.240454
4	0.317913	2.3362	0.011612
5	0.306247	2.2504	0.014258
6	0.145346	1.0681	0.14512
7	-0.161168	-1.1843	0.120733
8	-0.046902	-0.3447	0.365845
9	0.091307	0.671	0.252551
10	0.031688	0.2329	0.408376
11	9.4e-05	7e-04	0.499726
12	-0.392368	-2.8833	0.00282
13	-0.185443	-1.3627	0.089314
14	0.065422	0.4808	0.316317
15	-0.03479	-0.2557	0.399594
16	-0.19849	-1.4586	0.075234
17	-0.220274	-1.6187	0.055672
18	-0.193864	-1.4246	0.080013

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.279509 & 2.054 & 0.022417 \tabularnewline
2 & 0.047875 & 0.3518 & 0.363177 \tabularnewline
3 & 0.096586 & 0.7098 & 0.240454 \tabularnewline
4 & 0.317913 & 2.3362 & 0.011612 \tabularnewline
5 & 0.306247 & 2.2504 & 0.014258 \tabularnewline
6 & 0.145346 & 1.0681 & 0.14512 \tabularnewline
7 & -0.161168 & -1.1843 & 0.120733 \tabularnewline
8 & -0.046902 & -0.3447 & 0.365845 \tabularnewline
9 & 0.091307 & 0.671 & 0.252551 \tabularnewline
10 & 0.031688 & 0.2329 & 0.408376 \tabularnewline
11 & 9.4e-05 & 7e-04 & 0.499726 \tabularnewline
12 & -0.392368 & -2.8833 & 0.00282 \tabularnewline
13 & -0.185443 & -1.3627 & 0.089314 \tabularnewline
14 & 0.065422 & 0.4808 & 0.316317 \tabularnewline
15 & -0.03479 & -0.2557 & 0.399594 \tabularnewline
16 & -0.19849 & -1.4586 & 0.075234 \tabularnewline
17 & -0.220274 & -1.6187 & 0.055672 \tabularnewline
18 & -0.193864 & -1.4246 & 0.080013 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111727&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]0.279509[/C][C]2.054[/C][C]0.022417[/C][/ROW]
[ROW][C]2[/C][C]0.047875[/C][C]0.3518[/C][C]0.363177[/C][/ROW]
[ROW][C]3[/C][C]0.096586[/C][C]0.7098[/C][C]0.240454[/C][/ROW]
[ROW][C]4[/C][C]0.317913[/C][C]2.3362[/C][C]0.011612[/C][/ROW]
[ROW][C]5[/C][C]0.306247[/C][C]2.2504[/C][C]0.014258[/C][/ROW]
[ROW][C]6[/C][C]0.145346[/C][C]1.0681[/C][C]0.14512[/C][/ROW]
[ROW][C]7[/C][C]-0.161168[/C][C]-1.1843[/C][C]0.120733[/C][/ROW]
[ROW][C]8[/C][C]-0.046902[/C][C]-0.3447[/C][C]0.365845[/C][/ROW]
[ROW][C]9[/C][C]0.091307[/C][C]0.671[/C][C]0.252551[/C][/ROW]
[ROW][C]10[/C][C]0.031688[/C][C]0.2329[/C][C]0.408376[/C][/ROW]
[ROW][C]11[/C][C]9.4e-05[/C][C]7e-04[/C][C]0.499726[/C][/ROW]
[ROW][C]12[/C][C]-0.392368[/C][C]-2.8833[/C][C]0.00282[/C][/ROW]
[ROW][C]13[/C][C]-0.185443[/C][C]-1.3627[/C][C]0.089314[/C][/ROW]
[ROW][C]14[/C][C]0.065422[/C][C]0.4808[/C][C]0.316317[/C][/ROW]
[ROW][C]15[/C][C]-0.03479[/C][C]-0.2557[/C][C]0.399594[/C][/ROW]
[ROW][C]16[/C][C]-0.19849[/C][C]-1.4586[/C][C]0.075234[/C][/ROW]
[ROW][C]17[/C][C]-0.220274[/C][C]-1.6187[/C][C]0.055672[/C][/ROW]
[ROW][C]18[/C][C]-0.193864[/C][C]-1.4246[/C][C]0.080013[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111727&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111727&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	0.279509	2.054	0.022417
2	0.047875	0.3518	0.363177
3	0.096586	0.7098	0.240454
4	0.317913	2.3362	0.011612
5	0.306247	2.2504	0.014258
6	0.145346	1.0681	0.14512
7	-0.161168	-1.1843	0.120733
8	-0.046902	-0.3447	0.365845
9	0.091307	0.671	0.252551
10	0.031688	0.2329	0.408376
11	9.4e-05	7e-04	0.499726
12	-0.392368	-2.8833	0.00282
13	-0.185443	-1.3627	0.089314
14	0.065422	0.4808	0.316317
15	-0.03479	-0.2557	0.399594
16	-0.19849	-1.4586	0.075234
17	-0.220274	-1.6187	0.055672
18	-0.193864	-1.4246	0.080013

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.279509	2.054	0.022417
2	-0.032815	-0.2411	0.405181
3	0.099836	0.7336	0.23317
4	0.290401	2.134	0.0187
5	0.173668	1.2762	0.103674
6	0.040202	0.2954	0.384402
7	-0.276751	-2.0337	0.023454
8	-0.080467	-0.5913	0.278391
9	-0.030562	-0.2246	0.411574
10	-0.07395	-0.5434	0.294539
11	0.124518	0.915	0.182126
12	-0.396048	-2.9103	0.002618
13	0.051474	0.3783	0.353362
14	0.096162	0.7066	0.241414
15	-0.097579	-0.7171	0.238216
16	0.088568	0.6508	0.258954
17	-0.09034	-0.6639	0.254803
18	-0.052876	-0.3886	0.349566

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.279509 & 2.054 & 0.022417 \tabularnewline
2 & -0.032815 & -0.2411 & 0.405181 \tabularnewline
3 & 0.099836 & 0.7336 & 0.23317 \tabularnewline
4 & 0.290401 & 2.134 & 0.0187 \tabularnewline
5 & 0.173668 & 1.2762 & 0.103674 \tabularnewline
6 & 0.040202 & 0.2954 & 0.384402 \tabularnewline
7 & -0.276751 & -2.0337 & 0.023454 \tabularnewline
8 & -0.080467 & -0.5913 & 0.278391 \tabularnewline
9 & -0.030562 & -0.2246 & 0.411574 \tabularnewline
10 & -0.07395 & -0.5434 & 0.294539 \tabularnewline
11 & 0.124518 & 0.915 & 0.182126 \tabularnewline
12 & -0.396048 & -2.9103 & 0.002618 \tabularnewline
13 & 0.051474 & 0.3783 & 0.353362 \tabularnewline
14 & 0.096162 & 0.7066 & 0.241414 \tabularnewline
15 & -0.097579 & -0.7171 & 0.238216 \tabularnewline
16 & 0.088568 & 0.6508 & 0.258954 \tabularnewline
17 & -0.09034 & -0.6639 & 0.254803 \tabularnewline
18 & -0.052876 & -0.3886 & 0.349566 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111727&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]0.279509[/C][C]2.054[/C][C]0.022417[/C][/ROW]
[ROW][C]2[/C][C]-0.032815[/C][C]-0.2411[/C][C]0.405181[/C][/ROW]
[ROW][C]3[/C][C]0.099836[/C][C]0.7336[/C][C]0.23317[/C][/ROW]
[ROW][C]4[/C][C]0.290401[/C][C]2.134[/C][C]0.0187[/C][/ROW]
[ROW][C]5[/C][C]0.173668[/C][C]1.2762[/C][C]0.103674[/C][/ROW]
[ROW][C]6[/C][C]0.040202[/C][C]0.2954[/C][C]0.384402[/C][/ROW]
[ROW][C]7[/C][C]-0.276751[/C][C]-2.0337[/C][C]0.023454[/C][/ROW]
[ROW][C]8[/C][C]-0.080467[/C][C]-0.5913[/C][C]0.278391[/C][/ROW]
[ROW][C]9[/C][C]-0.030562[/C][C]-0.2246[/C][C]0.411574[/C][/ROW]
[ROW][C]10[/C][C]-0.07395[/C][C]-0.5434[/C][C]0.294539[/C][/ROW]
[ROW][C]11[/C][C]0.124518[/C][C]0.915[/C][C]0.182126[/C][/ROW]
[ROW][C]12[/C][C]-0.396048[/C][C]-2.9103[/C][C]0.002618[/C][/ROW]
[ROW][C]13[/C][C]0.051474[/C][C]0.3783[/C][C]0.353362[/C][/ROW]
[ROW][C]14[/C][C]0.096162[/C][C]0.7066[/C][C]0.241414[/C][/ROW]
[ROW][C]15[/C][C]-0.097579[/C][C]-0.7171[/C][C]0.238216[/C][/ROW]
[ROW][C]16[/C][C]0.088568[/C][C]0.6508[/C][C]0.258954[/C][/ROW]
[ROW][C]17[/C][C]-0.09034[/C][C]-0.6639[/C][C]0.254803[/C][/ROW]
[ROW][C]18[/C][C]-0.052876[/C][C]-0.3886[/C][C]0.349566[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111727&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111727&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	0.279509	2.054	0.022417
2	-0.032815	-0.2411	0.405181
3	0.099836	0.7336	0.23317
4	0.290401	2.134	0.0187
5	0.173668	1.2762	0.103674
6	0.040202	0.2954	0.384402
7	-0.276751	-2.0337	0.023454
8	-0.080467	-0.5913	0.278391
9	-0.030562	-0.2246	0.411574
10	-0.07395	-0.5434	0.294539
11	0.124518	0.915	0.182126
12	-0.396048	-2.9103	0.002618
13	0.051474	0.3783	0.353362
14	0.096162	0.7066	0.241414
15	-0.097579	-0.7171	0.238216
16	0.088568	0.6508	0.258954
17	-0.09034	-0.6639	0.254803
18	-0.052876	-0.3886	0.349566

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 = 1 ; par4 = 1 ; 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