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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 01 Dec 2012 09:22:50 -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/2012/Dec/01/t1354371901cw8ud39hxbdo6lc.htm/, Retrieved Mon, 29 Apr 2024 04:12:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=195319, Retrieved Mon, 29 Apr 2024 04:12:59 +0000

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User-defined keywords

Estimated Impact

164

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

-     [Univariate Explorative Data Analysis] [Monthly US soldie...] [2010-11-02 12:07:39] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Soldiers] [2010-11-29 09:48:36] [b98453cac15ba1066b407e146608df68]
- R P     [(Partial) Autocorrelation Function] [Soldiers autocorr...] [2012-12-01 14:17:53] [22a7ed72f77de7f3efc5689ed05063a7]
- R P         [(Partial) Autocorrelation Function] [Soldiers] [2012-12-01 14:22:50] [8a8ce1ece063ce616102c2c7ff02990f] [Current]
-   P           [(Partial) Autocorrelation Function] [Soldiers] [2012-12-01 14:26:54] [22a7ed72f77de7f3efc5689ed05063a7] 
- RMP           [Spectral Analysis] [Soldiers] [2012-12-01 14:31:07] [22a7ed72f77de7f3efc5689ed05063a7] 
- RMP           [Variance Reduction Matrix] [Soldiers VRM] [2012-12-01 14:39:07] [22a7ed72f77de7f3efc5689ed05063a7] 

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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 Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195319&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195319&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195319&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 Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.499656	-3.7055	0.000246
2	0.295678	2.1928	0.016285
3	-0.264763	-1.9635	0.027324
4	0.082638	0.6129	0.271249
5	-0.021712	-0.161	0.436335
6	0.074972	0.556	0.29023
7	-0.147892	-1.0968	0.138754
8	0.075459	0.5596	0.289006
9	0.11329	0.8402	0.202222
10	-0.132761	-0.9846	0.164571
11	0.179671	1.3325	0.094099
12	-0.425017	-3.152	0.001312
13	0.151682	1.1249	0.132758
14	-0.064027	-0.4748	0.318392
15	0.067801	0.5028	0.308548
16	-0.001858	-0.0138	0.494528
17	-0.028948	-0.2147	0.415404
18	-0.09464	-0.7019	0.24286
19	0.184718	1.3699	0.088142

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.499656 & -3.7055 & 0.000246 \tabularnewline
2 & 0.295678 & 2.1928 & 0.016285 \tabularnewline
3 & -0.264763 & -1.9635 & 0.027324 \tabularnewline
4 & 0.082638 & 0.6129 & 0.271249 \tabularnewline
5 & -0.021712 & -0.161 & 0.436335 \tabularnewline
6 & 0.074972 & 0.556 & 0.29023 \tabularnewline
7 & -0.147892 & -1.0968 & 0.138754 \tabularnewline
8 & 0.075459 & 0.5596 & 0.289006 \tabularnewline
9 & 0.11329 & 0.8402 & 0.202222 \tabularnewline
10 & -0.132761 & -0.9846 & 0.164571 \tabularnewline
11 & 0.179671 & 1.3325 & 0.094099 \tabularnewline
12 & -0.425017 & -3.152 & 0.001312 \tabularnewline
13 & 0.151682 & 1.1249 & 0.132758 \tabularnewline
14 & -0.064027 & -0.4748 & 0.318392 \tabularnewline
15 & 0.067801 & 0.5028 & 0.308548 \tabularnewline
16 & -0.001858 & -0.0138 & 0.494528 \tabularnewline
17 & -0.028948 & -0.2147 & 0.415404 \tabularnewline
18 & -0.09464 & -0.7019 & 0.24286 \tabularnewline
19 & 0.184718 & 1.3699 & 0.088142 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195319&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]-0.499656[/C][C]-3.7055[/C][C]0.000246[/C][/ROW]
[ROW][C]2[/C][C]0.295678[/C][C]2.1928[/C][C]0.016285[/C][/ROW]
[ROW][C]3[/C][C]-0.264763[/C][C]-1.9635[/C][C]0.027324[/C][/ROW]
[ROW][C]4[/C][C]0.082638[/C][C]0.6129[/C][C]0.271249[/C][/ROW]
[ROW][C]5[/C][C]-0.021712[/C][C]-0.161[/C][C]0.436335[/C][/ROW]
[ROW][C]6[/C][C]0.074972[/C][C]0.556[/C][C]0.29023[/C][/ROW]
[ROW][C]7[/C][C]-0.147892[/C][C]-1.0968[/C][C]0.138754[/C][/ROW]
[ROW][C]8[/C][C]0.075459[/C][C]0.5596[/C][C]0.289006[/C][/ROW]
[ROW][C]9[/C][C]0.11329[/C][C]0.8402[/C][C]0.202222[/C][/ROW]
[ROW][C]10[/C][C]-0.132761[/C][C]-0.9846[/C][C]0.164571[/C][/ROW]
[ROW][C]11[/C][C]0.179671[/C][C]1.3325[/C][C]0.094099[/C][/ROW]
[ROW][C]12[/C][C]-0.425017[/C][C]-3.152[/C][C]0.001312[/C][/ROW]
[ROW][C]13[/C][C]0.151682[/C][C]1.1249[/C][C]0.132758[/C][/ROW]
[ROW][C]14[/C][C]-0.064027[/C][C]-0.4748[/C][C]0.318392[/C][/ROW]
[ROW][C]15[/C][C]0.067801[/C][C]0.5028[/C][C]0.308548[/C][/ROW]
[ROW][C]16[/C][C]-0.001858[/C][C]-0.0138[/C][C]0.494528[/C][/ROW]
[ROW][C]17[/C][C]-0.028948[/C][C]-0.2147[/C][C]0.415404[/C][/ROW]
[ROW][C]18[/C][C]-0.09464[/C][C]-0.7019[/C][C]0.24286[/C][/ROW]
[ROW][C]19[/C][C]0.184718[/C][C]1.3699[/C][C]0.088142[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195319&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195319&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	-0.499656	-3.7055	0.000246
2	0.295678	2.1928	0.016285
3	-0.264763	-1.9635	0.027324
4	0.082638	0.6129	0.271249
5	-0.021712	-0.161	0.436335
6	0.074972	0.556	0.29023
7	-0.147892	-1.0968	0.138754
8	0.075459	0.5596	0.289006
9	0.11329	0.8402	0.202222
10	-0.132761	-0.9846	0.164571
11	0.179671	1.3325	0.094099
12	-0.425017	-3.152	0.001312
13	0.151682	1.1249	0.132758
14	-0.064027	-0.4748	0.318392
15	0.067801	0.5028	0.308548
16	-0.001858	-0.0138	0.494528
17	-0.028948	-0.2147	0.415404
18	-0.09464	-0.7019	0.24286
19	0.184718	1.3699	0.088142

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.499656	-3.7055	0.000246
2	0.061334	0.4549	0.325498
3	-0.127678	-0.9469	0.17392
4	-0.141011	-1.0458	0.150123
5	0.006727	0.0499	0.480195
6	0.079677	0.5909	0.278504
7	-0.149456	-1.1084	0.136257
8	-0.072121	-0.5349	0.29745
9	0.260154	1.9294	0.029426
10	-0.061461	-0.4558	0.325162
11	0.044363	0.329	0.371702
12	-0.320161	-2.3744	0.010548
13	-0.292914	-2.1723	0.01708
14	-0.037925	-0.2813	0.389784
15	-0.077412	-0.5741	0.284118
16	-0.022414	-0.1662	0.434295
17	-0.072285	-0.5361	0.297033
18	-0.187774	-1.3926	0.084677
19	0.031346	0.2325	0.408518

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.499656 & -3.7055 & 0.000246 \tabularnewline
2 & 0.061334 & 0.4549 & 0.325498 \tabularnewline
3 & -0.127678 & -0.9469 & 0.17392 \tabularnewline
4 & -0.141011 & -1.0458 & 0.150123 \tabularnewline
5 & 0.006727 & 0.0499 & 0.480195 \tabularnewline
6 & 0.079677 & 0.5909 & 0.278504 \tabularnewline
7 & -0.149456 & -1.1084 & 0.136257 \tabularnewline
8 & -0.072121 & -0.5349 & 0.29745 \tabularnewline
9 & 0.260154 & 1.9294 & 0.029426 \tabularnewline
10 & -0.061461 & -0.4558 & 0.325162 \tabularnewline
11 & 0.044363 & 0.329 & 0.371702 \tabularnewline
12 & -0.320161 & -2.3744 & 0.010548 \tabularnewline
13 & -0.292914 & -2.1723 & 0.01708 \tabularnewline
14 & -0.037925 & -0.2813 & 0.389784 \tabularnewline
15 & -0.077412 & -0.5741 & 0.284118 \tabularnewline
16 & -0.022414 & -0.1662 & 0.434295 \tabularnewline
17 & -0.072285 & -0.5361 & 0.297033 \tabularnewline
18 & -0.187774 & -1.3926 & 0.084677 \tabularnewline
19 & 0.031346 & 0.2325 & 0.408518 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195319&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]-0.499656[/C][C]-3.7055[/C][C]0.000246[/C][/ROW]
[ROW][C]2[/C][C]0.061334[/C][C]0.4549[/C][C]0.325498[/C][/ROW]
[ROW][C]3[/C][C]-0.127678[/C][C]-0.9469[/C][C]0.17392[/C][/ROW]
[ROW][C]4[/C][C]-0.141011[/C][C]-1.0458[/C][C]0.150123[/C][/ROW]
[ROW][C]5[/C][C]0.006727[/C][C]0.0499[/C][C]0.480195[/C][/ROW]
[ROW][C]6[/C][C]0.079677[/C][C]0.5909[/C][C]0.278504[/C][/ROW]
[ROW][C]7[/C][C]-0.149456[/C][C]-1.1084[/C][C]0.136257[/C][/ROW]
[ROW][C]8[/C][C]-0.072121[/C][C]-0.5349[/C][C]0.29745[/C][/ROW]
[ROW][C]9[/C][C]0.260154[/C][C]1.9294[/C][C]0.029426[/C][/ROW]
[ROW][C]10[/C][C]-0.061461[/C][C]-0.4558[/C][C]0.325162[/C][/ROW]
[ROW][C]11[/C][C]0.044363[/C][C]0.329[/C][C]0.371702[/C][/ROW]
[ROW][C]12[/C][C]-0.320161[/C][C]-2.3744[/C][C]0.010548[/C][/ROW]
[ROW][C]13[/C][C]-0.292914[/C][C]-2.1723[/C][C]0.01708[/C][/ROW]
[ROW][C]14[/C][C]-0.037925[/C][C]-0.2813[/C][C]0.389784[/C][/ROW]
[ROW][C]15[/C][C]-0.077412[/C][C]-0.5741[/C][C]0.284118[/C][/ROW]
[ROW][C]16[/C][C]-0.022414[/C][C]-0.1662[/C][C]0.434295[/C][/ROW]
[ROW][C]17[/C][C]-0.072285[/C][C]-0.5361[/C][C]0.297033[/C][/ROW]
[ROW][C]18[/C][C]-0.187774[/C][C]-1.3926[/C][C]0.084677[/C][/ROW]
[ROW][C]19[/C][C]0.031346[/C][C]0.2325[/C][C]0.408518[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195319&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195319&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	-0.499656	-3.7055	0.000246
2	0.061334	0.4549	0.325498
3	-0.127678	-0.9469	0.17392
4	-0.141011	-1.0458	0.150123
5	0.006727	0.0499	0.480195
6	0.079677	0.5909	0.278504
7	-0.149456	-1.1084	0.136257
8	-0.072121	-0.5349	0.29745
9	0.260154	1.9294	0.029426
10	-0.061461	-0.4558	0.325162
11	0.044363	0.329	0.371702
12	-0.320161	-2.3744	0.010548
13	-0.292914	-2.1723	0.01708
14	-0.037925	-0.2813	0.389784
15	-0.077412	-0.5741	0.284118
16	-0.022414	-0.1662	0.434295
17	-0.072285	-0.5361	0.297033
18	-0.187774	-1.3926	0.084677
19	0.031346	0.2325	0.408518

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 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 2 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code