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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 14 Mar 2016 19:30:21 +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/2016/Mar/14/t1457983856raiefr5tafbq2sj.htm/, Retrieved Sun, 28 Apr 2024 22:48:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294043, Retrieved Sun, 28 Apr 2024 22:48:44 +0000

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User-defined keywords

Estimated Impact

106

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

-       [(Partial) Autocorrelation Function] [Moerman Nicola�] [2016-03-14 19:30:21] [ab100cc47aff291ae023e643a55282f8] [Current]
- R P     [(Partial) Autocorrelation Function] [Moerman Nicola�] [2016-05-20 11:11:23] [5928cb88c67ea2385eb5355d4562c8d3] 

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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' @ fisher.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 Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294043&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294043&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294043&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' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.53758	4.1292	5.8e-05
2	0.234412	1.8006	0.038443
3	0.115205	0.8849	0.189899
4	0.069899	0.5369	0.296676
5	0.107194	0.8234	0.206807
6	0.06298	0.4838	0.315174
7	0.090105	0.6921	0.245791
8	0.085129	0.6539	0.257861
9	0.164057	1.2601	0.10629
10	0.28343	2.1771	0.016744
11	0.359559	2.7618	0.003825
12	0.244251	1.8761	0.032794
13	0.167308	1.2851	0.101887
14	0.027179	0.2088	0.417676
15	-0.016166	-0.1242	0.4508
16	0.024158	0.1856	0.426713
17	-0.020622	-0.1584	0.437341

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.53758 & 4.1292 & 5.8e-05 \tabularnewline
2 & 0.234412 & 1.8006 & 0.038443 \tabularnewline
3 & 0.115205 & 0.8849 & 0.189899 \tabularnewline
4 & 0.069899 & 0.5369 & 0.296676 \tabularnewline
5 & 0.107194 & 0.8234 & 0.206807 \tabularnewline
6 & 0.06298 & 0.4838 & 0.315174 \tabularnewline
7 & 0.090105 & 0.6921 & 0.245791 \tabularnewline
8 & 0.085129 & 0.6539 & 0.257861 \tabularnewline
9 & 0.164057 & 1.2601 & 0.10629 \tabularnewline
10 & 0.28343 & 2.1771 & 0.016744 \tabularnewline
11 & 0.359559 & 2.7618 & 0.003825 \tabularnewline
12 & 0.244251 & 1.8761 & 0.032794 \tabularnewline
13 & 0.167308 & 1.2851 & 0.101887 \tabularnewline
14 & 0.027179 & 0.2088 & 0.417676 \tabularnewline
15 & -0.016166 & -0.1242 & 0.4508 \tabularnewline
16 & 0.024158 & 0.1856 & 0.426713 \tabularnewline
17 & -0.020622 & -0.1584 & 0.437341 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294043&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]0.53758[/C][C]4.1292[/C][C]5.8e-05[/C][/ROW]
[ROW][C]2[/C][C]0.234412[/C][C]1.8006[/C][C]0.038443[/C][/ROW]
[ROW][C]3[/C][C]0.115205[/C][C]0.8849[/C][C]0.189899[/C][/ROW]
[ROW][C]4[/C][C]0.069899[/C][C]0.5369[/C][C]0.296676[/C][/ROW]
[ROW][C]5[/C][C]0.107194[/C][C]0.8234[/C][C]0.206807[/C][/ROW]
[ROW][C]6[/C][C]0.06298[/C][C]0.4838[/C][C]0.315174[/C][/ROW]
[ROW][C]7[/C][C]0.090105[/C][C]0.6921[/C][C]0.245791[/C][/ROW]
[ROW][C]8[/C][C]0.085129[/C][C]0.6539[/C][C]0.257861[/C][/ROW]
[ROW][C]9[/C][C]0.164057[/C][C]1.2601[/C][C]0.10629[/C][/ROW]
[ROW][C]10[/C][C]0.28343[/C][C]2.1771[/C][C]0.016744[/C][/ROW]
[ROW][C]11[/C][C]0.359559[/C][C]2.7618[/C][C]0.003825[/C][/ROW]
[ROW][C]12[/C][C]0.244251[/C][C]1.8761[/C][C]0.032794[/C][/ROW]
[ROW][C]13[/C][C]0.167308[/C][C]1.2851[/C][C]0.101887[/C][/ROW]
[ROW][C]14[/C][C]0.027179[/C][C]0.2088[/C][C]0.417676[/C][/ROW]
[ROW][C]15[/C][C]-0.016166[/C][C]-0.1242[/C][C]0.4508[/C][/ROW]
[ROW][C]16[/C][C]0.024158[/C][C]0.1856[/C][C]0.426713[/C][/ROW]
[ROW][C]17[/C][C]-0.020622[/C][C]-0.1584[/C][C]0.437341[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294043&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294043&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	0.53758	4.1292	5.8e-05
2	0.234412	1.8006	0.038443
3	0.115205	0.8849	0.189899
4	0.069899	0.5369	0.296676
5	0.107194	0.8234	0.206807
6	0.06298	0.4838	0.315174
7	0.090105	0.6921	0.245791
8	0.085129	0.6539	0.257861
9	0.164057	1.2601	0.10629
10	0.28343	2.1771	0.016744
11	0.359559	2.7618	0.003825
12	0.244251	1.8761	0.032794
13	0.167308	1.2851	0.101887
14	0.027179	0.2088	0.417676
15	-0.016166	-0.1242	0.4508
16	0.024158	0.1856	0.426713
17	-0.020622	-0.1584	0.437341

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.53758	4.1292	5.8e-05
2	-0.076764	-0.5896	0.278842
3	0.029405	0.2259	0.411044
4	0.012927	0.0993	0.460619
5	0.092319	0.7091	0.240524
6	-0.051607	-0.3964	0.346619
7	0.094206	0.7236	0.236083
8	-0.003484	-0.0268	0.489371
9	0.15754	1.2101	0.115535
10	0.169694	1.3034	0.098743
11	0.182168	1.3993	0.083485
12	-0.077519	-0.5954	0.276915
13	0.078779	0.6051	0.273712
14	-0.160295	-1.2313	0.111557
15	0.017865	0.1372	0.445661
16	-0.008251	-0.0634	0.474841
17	-0.065261	-0.5013	0.309019

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.53758 & 4.1292 & 5.8e-05 \tabularnewline
2 & -0.076764 & -0.5896 & 0.278842 \tabularnewline
3 & 0.029405 & 0.2259 & 0.411044 \tabularnewline
4 & 0.012927 & 0.0993 & 0.460619 \tabularnewline
5 & 0.092319 & 0.7091 & 0.240524 \tabularnewline
6 & -0.051607 & -0.3964 & 0.346619 \tabularnewline
7 & 0.094206 & 0.7236 & 0.236083 \tabularnewline
8 & -0.003484 & -0.0268 & 0.489371 \tabularnewline
9 & 0.15754 & 1.2101 & 0.115535 \tabularnewline
10 & 0.169694 & 1.3034 & 0.098743 \tabularnewline
11 & 0.182168 & 1.3993 & 0.083485 \tabularnewline
12 & -0.077519 & -0.5954 & 0.276915 \tabularnewline
13 & 0.078779 & 0.6051 & 0.273712 \tabularnewline
14 & -0.160295 & -1.2313 & 0.111557 \tabularnewline
15 & 0.017865 & 0.1372 & 0.445661 \tabularnewline
16 & -0.008251 & -0.0634 & 0.474841 \tabularnewline
17 & -0.065261 & -0.5013 & 0.309019 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294043&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]0.53758[/C][C]4.1292[/C][C]5.8e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.076764[/C][C]-0.5896[/C][C]0.278842[/C][/ROW]
[ROW][C]3[/C][C]0.029405[/C][C]0.2259[/C][C]0.411044[/C][/ROW]
[ROW][C]4[/C][C]0.012927[/C][C]0.0993[/C][C]0.460619[/C][/ROW]
[ROW][C]5[/C][C]0.092319[/C][C]0.7091[/C][C]0.240524[/C][/ROW]
[ROW][C]6[/C][C]-0.051607[/C][C]-0.3964[/C][C]0.346619[/C][/ROW]
[ROW][C]7[/C][C]0.094206[/C][C]0.7236[/C][C]0.236083[/C][/ROW]
[ROW][C]8[/C][C]-0.003484[/C][C]-0.0268[/C][C]0.489371[/C][/ROW]
[ROW][C]9[/C][C]0.15754[/C][C]1.2101[/C][C]0.115535[/C][/ROW]
[ROW][C]10[/C][C]0.169694[/C][C]1.3034[/C][C]0.098743[/C][/ROW]
[ROW][C]11[/C][C]0.182168[/C][C]1.3993[/C][C]0.083485[/C][/ROW]
[ROW][C]12[/C][C]-0.077519[/C][C]-0.5954[/C][C]0.276915[/C][/ROW]
[ROW][C]13[/C][C]0.078779[/C][C]0.6051[/C][C]0.273712[/C][/ROW]
[ROW][C]14[/C][C]-0.160295[/C][C]-1.2313[/C][C]0.111557[/C][/ROW]
[ROW][C]15[/C][C]0.017865[/C][C]0.1372[/C][C]0.445661[/C][/ROW]
[ROW][C]16[/C][C]-0.008251[/C][C]-0.0634[/C][C]0.474841[/C][/ROW]
[ROW][C]17[/C][C]-0.065261[/C][C]-0.5013[/C][C]0.309019[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294043&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294043&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	0.53758	4.1292	5.8e-05
2	-0.076764	-0.5896	0.278842
3	0.029405	0.2259	0.411044
4	0.012927	0.0993	0.460619
5	0.092319	0.7091	0.240524
6	-0.051607	-0.3964	0.346619
7	0.094206	0.7236	0.236083
8	-0.003484	-0.0268	0.489371
9	0.15754	1.2101	0.115535
10	0.169694	1.3034	0.098743
11	0.182168	1.3993	0.083485
12	-0.077519	-0.5954	0.276915
13	0.078779	0.6051	0.273712
14	-0.160295	-1.2313	0.111557
15	0.017865	0.1372	0.445661
16	-0.008251	-0.0634	0.474841
17	-0.065261	-0.5013	0.309019

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)
x <- na.omit(x)
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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Input Parameters & R Code