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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2011 13:57:39 -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/2011/Dec/23/t13246666724u179alku3k94ln.htm/, Retrieved Mon, 29 Apr 2024 19:34:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160650, Retrieved Mon, 29 Apr 2024 19:34:55 +0000

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

-     [Spectral Analysis] [] [2011-12-23 18:50:40] [2ba7ee2cbaa966a49160c7cfb7436069]
- RMP     [(Partial) Autocorrelation Function] [] [2011-12-23 18:57:39] [393d554610c677f923bed472882d0fdb] [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=160650&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=160650&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160650&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	0.648176	6.6418	0
2	0.242032	2.4801	0.007362
3	-0.130821	-1.3405	0.091485
4	-0.400746	-4.1064	4e-05
5	-0.489154	-5.0123	1e-06
6	-0.516494	-5.2925	0
7	-0.499305	-5.1164	1e-06
8	-0.376324	-3.8562	9.9e-05
9	-0.141676	-1.4517	0.074777
10	0.203526	2.0855	0.019723
11	0.56527	5.7923	0
12	0.757449	7.7615	0
13	0.614727	6.2991	0
14	0.213188	2.1845	0.015574
15	-0.105016	-1.0761	0.142176
16	-0.335808	-3.441	0.000416
17	-0.431448	-4.421	1.2e-05
18	-0.440915	-4.518	8e-06
19	-0.416758	-4.2705	2.1e-05
20	-0.328084	-3.3619	0.00054

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.648176 & 6.6418 & 0 \tabularnewline
2 & 0.242032 & 2.4801 & 0.007362 \tabularnewline
3 & -0.130821 & -1.3405 & 0.091485 \tabularnewline
4 & -0.400746 & -4.1064 & 4e-05 \tabularnewline
5 & -0.489154 & -5.0123 & 1e-06 \tabularnewline
6 & -0.516494 & -5.2925 & 0 \tabularnewline
7 & -0.499305 & -5.1164 & 1e-06 \tabularnewline
8 & -0.376324 & -3.8562 & 9.9e-05 \tabularnewline
9 & -0.141676 & -1.4517 & 0.074777 \tabularnewline
10 & 0.203526 & 2.0855 & 0.019723 \tabularnewline
11 & 0.56527 & 5.7923 & 0 \tabularnewline
12 & 0.757449 & 7.7615 & 0 \tabularnewline
13 & 0.614727 & 6.2991 & 0 \tabularnewline
14 & 0.213188 & 2.1845 & 0.015574 \tabularnewline
15 & -0.105016 & -1.0761 & 0.142176 \tabularnewline
16 & -0.335808 & -3.441 & 0.000416 \tabularnewline
17 & -0.431448 & -4.421 & 1.2e-05 \tabularnewline
18 & -0.440915 & -4.518 & 8e-06 \tabularnewline
19 & -0.416758 & -4.2705 & 2.1e-05 \tabularnewline
20 & -0.328084 & -3.3619 & 0.00054 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160650&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]0.648176[/C][C]6.6418[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.242032[/C][C]2.4801[/C][C]0.007362[/C][/ROW]
[ROW][C]3[/C][C]-0.130821[/C][C]-1.3405[/C][C]0.091485[/C][/ROW]
[ROW][C]4[/C][C]-0.400746[/C][C]-4.1064[/C][C]4e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.489154[/C][C]-5.0123[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]-0.516494[/C][C]-5.2925[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.499305[/C][C]-5.1164[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]-0.376324[/C][C]-3.8562[/C][C]9.9e-05[/C][/ROW]
[ROW][C]9[/C][C]-0.141676[/C][C]-1.4517[/C][C]0.074777[/C][/ROW]
[ROW][C]10[/C][C]0.203526[/C][C]2.0855[/C][C]0.019723[/C][/ROW]
[ROW][C]11[/C][C]0.56527[/C][C]5.7923[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.757449[/C][C]7.7615[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.614727[/C][C]6.2991[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.213188[/C][C]2.1845[/C][C]0.015574[/C][/ROW]
[ROW][C]15[/C][C]-0.105016[/C][C]-1.0761[/C][C]0.142176[/C][/ROW]
[ROW][C]16[/C][C]-0.335808[/C][C]-3.441[/C][C]0.000416[/C][/ROW]
[ROW][C]17[/C][C]-0.431448[/C][C]-4.421[/C][C]1.2e-05[/C][/ROW]
[ROW][C]18[/C][C]-0.440915[/C][C]-4.518[/C][C]8e-06[/C][/ROW]
[ROW][C]19[/C][C]-0.416758[/C][C]-4.2705[/C][C]2.1e-05[/C][/ROW]
[ROW][C]20[/C][C]-0.328084[/C][C]-3.3619[/C][C]0.00054[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160650&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160650&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	0.648176	6.6418	0
2	0.242032	2.4801	0.007362
3	-0.130821	-1.3405	0.091485
4	-0.400746	-4.1064	4e-05
5	-0.489154	-5.0123	1e-06
6	-0.516494	-5.2925	0
7	-0.499305	-5.1164	1e-06
8	-0.376324	-3.8562	9.9e-05
9	-0.141676	-1.4517	0.074777
10	0.203526	2.0855	0.019723
11	0.56527	5.7923	0
12	0.757449	7.7615	0
13	0.614727	6.2991	0
14	0.213188	2.1845	0.015574
15	-0.105016	-1.0761	0.142176
16	-0.335808	-3.441	0.000416
17	-0.431448	-4.421	1.2e-05
18	-0.440915	-4.518	8e-06
19	-0.416758	-4.2705	2.1e-05
20	-0.328084	-3.3619	0.00054

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.648176	6.6418	0
2	-0.307138	-3.1472	0.001073
3	-0.260498	-2.6693	0.004404
4	-0.225946	-2.3153	0.011272
5	-0.111052	-1.1379	0.128867
6	-0.291862	-2.9907	0.001734
7	-0.352175	-3.6087	0.000237
8	-0.285823	-2.9288	0.002087
9	-0.211664	-2.1689	0.016173
10	-0.025506	-0.2614	0.397162
11	0.199241	2.0416	0.021849
12	0.271618	2.7833	0.003192
13	0.005657	0.058	0.476943
14	-0.272154	-2.7887	0.003142
15	0.040258	0.4125	0.340399
16	-0.003711	-0.038	0.484868
17	0.010591	0.1085	0.456893
18	0.001311	0.0134	0.494653
19	0.041411	0.4243	0.336094
20	-0.040445	-0.4144	0.339699

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.648176 & 6.6418 & 0 \tabularnewline
2 & -0.307138 & -3.1472 & 0.001073 \tabularnewline
3 & -0.260498 & -2.6693 & 0.004404 \tabularnewline
4 & -0.225946 & -2.3153 & 0.011272 \tabularnewline
5 & -0.111052 & -1.1379 & 0.128867 \tabularnewline
6 & -0.291862 & -2.9907 & 0.001734 \tabularnewline
7 & -0.352175 & -3.6087 & 0.000237 \tabularnewline
8 & -0.285823 & -2.9288 & 0.002087 \tabularnewline
9 & -0.211664 & -2.1689 & 0.016173 \tabularnewline
10 & -0.025506 & -0.2614 & 0.397162 \tabularnewline
11 & 0.199241 & 2.0416 & 0.021849 \tabularnewline
12 & 0.271618 & 2.7833 & 0.003192 \tabularnewline
13 & 0.005657 & 0.058 & 0.476943 \tabularnewline
14 & -0.272154 & -2.7887 & 0.003142 \tabularnewline
15 & 0.040258 & 0.4125 & 0.340399 \tabularnewline
16 & -0.003711 & -0.038 & 0.484868 \tabularnewline
17 & 0.010591 & 0.1085 & 0.456893 \tabularnewline
18 & 0.001311 & 0.0134 & 0.494653 \tabularnewline
19 & 0.041411 & 0.4243 & 0.336094 \tabularnewline
20 & -0.040445 & -0.4144 & 0.339699 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160650&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]0.648176[/C][C]6.6418[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.307138[/C][C]-3.1472[/C][C]0.001073[/C][/ROW]
[ROW][C]3[/C][C]-0.260498[/C][C]-2.6693[/C][C]0.004404[/C][/ROW]
[ROW][C]4[/C][C]-0.225946[/C][C]-2.3153[/C][C]0.011272[/C][/ROW]
[ROW][C]5[/C][C]-0.111052[/C][C]-1.1379[/C][C]0.128867[/C][/ROW]
[ROW][C]6[/C][C]-0.291862[/C][C]-2.9907[/C][C]0.001734[/C][/ROW]
[ROW][C]7[/C][C]-0.352175[/C][C]-3.6087[/C][C]0.000237[/C][/ROW]
[ROW][C]8[/C][C]-0.285823[/C][C]-2.9288[/C][C]0.002087[/C][/ROW]
[ROW][C]9[/C][C]-0.211664[/C][C]-2.1689[/C][C]0.016173[/C][/ROW]
[ROW][C]10[/C][C]-0.025506[/C][C]-0.2614[/C][C]0.397162[/C][/ROW]
[ROW][C]11[/C][C]0.199241[/C][C]2.0416[/C][C]0.021849[/C][/ROW]
[ROW][C]12[/C][C]0.271618[/C][C]2.7833[/C][C]0.003192[/C][/ROW]
[ROW][C]13[/C][C]0.005657[/C][C]0.058[/C][C]0.476943[/C][/ROW]
[ROW][C]14[/C][C]-0.272154[/C][C]-2.7887[/C][C]0.003142[/C][/ROW]
[ROW][C]15[/C][C]0.040258[/C][C]0.4125[/C][C]0.340399[/C][/ROW]
[ROW][C]16[/C][C]-0.003711[/C][C]-0.038[/C][C]0.484868[/C][/ROW]
[ROW][C]17[/C][C]0.010591[/C][C]0.1085[/C][C]0.456893[/C][/ROW]
[ROW][C]18[/C][C]0.001311[/C][C]0.0134[/C][C]0.494653[/C][/ROW]
[ROW][C]19[/C][C]0.041411[/C][C]0.4243[/C][C]0.336094[/C][/ROW]
[ROW][C]20[/C][C]-0.040445[/C][C]-0.4144[/C][C]0.339699[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160650&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160650&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	0.648176	6.6418	0
2	-0.307138	-3.1472	0.001073
3	-0.260498	-2.6693	0.004404
4	-0.225946	-2.3153	0.011272
5	-0.111052	-1.1379	0.128867
6	-0.291862	-2.9907	0.001734
7	-0.352175	-3.6087	0.000237
8	-0.285823	-2.9288	0.002087
9	-0.211664	-2.1689	0.016173
10	-0.025506	-0.2614	0.397162
11	0.199241	2.0416	0.021849
12	0.271618	2.7833	0.003192
13	0.005657	0.058	0.476943
14	-0.272154	-2.7887	0.003142
15	0.040258	0.4125	0.340399
16	-0.003711	-0.038	0.484868
17	0.010591	0.1085	0.456893
18	0.001311	0.0134	0.494653
19	0.041411	0.4243	0.336094
20	-0.040445	-0.4144	0.339699

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)
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