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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 05 Mar 2015 22:47:25 +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/2015/Mar/05/t14255957031m0bflh9nhfgczv.htm/, Retrieved Fri, 17 May 2024 00:41:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278042, Retrieved Fri, 17 May 2024 00:41:22 +0000

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-       [(Partial) Autocorrelation Function] [Autocorrelatie - ...] [2015-03-05 22:47:25] [780a12e068e7a755e562c551b60f6f33] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278042&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]1 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=278042&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278042&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	1 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.982321	10.7608	0
2	0.96292	10.5483	0
3	0.943021	10.3303	0
4	0.921644	10.0961	0
5	0.899406	9.8525	0
6	0.876448	9.601	0
7	0.851622	9.329	0
8	0.826678	9.0558	0
9	0.802854	8.7948	0
10	0.778751	8.5308	0
11	0.755704	8.2783	0
12	0.732753	8.0269	0
13	0.709399	7.7711	0
14	0.685587	7.5102	0
15	0.660137	7.2314	0
16	0.633462	6.9392	0
17	0.607436	6.6541	0
18	0.580963	6.3641	0
19	0.55506	6.0804	0
20	0.528086	5.7849	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.982321 & 10.7608 & 0 \tabularnewline
2 & 0.96292 & 10.5483 & 0 \tabularnewline
3 & 0.943021 & 10.3303 & 0 \tabularnewline
4 & 0.921644 & 10.0961 & 0 \tabularnewline
5 & 0.899406 & 9.8525 & 0 \tabularnewline
6 & 0.876448 & 9.601 & 0 \tabularnewline
7 & 0.851622 & 9.329 & 0 \tabularnewline
8 & 0.826678 & 9.0558 & 0 \tabularnewline
9 & 0.802854 & 8.7948 & 0 \tabularnewline
10 & 0.778751 & 8.5308 & 0 \tabularnewline
11 & 0.755704 & 8.2783 & 0 \tabularnewline
12 & 0.732753 & 8.0269 & 0 \tabularnewline
13 & 0.709399 & 7.7711 & 0 \tabularnewline
14 & 0.685587 & 7.5102 & 0 \tabularnewline
15 & 0.660137 & 7.2314 & 0 \tabularnewline
16 & 0.633462 & 6.9392 & 0 \tabularnewline
17 & 0.607436 & 6.6541 & 0 \tabularnewline
18 & 0.580963 & 6.3641 & 0 \tabularnewline
19 & 0.55506 & 6.0804 & 0 \tabularnewline
20 & 0.528086 & 5.7849 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278042&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]0.982321[/C][C]10.7608[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.96292[/C][C]10.5483[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.943021[/C][C]10.3303[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.921644[/C][C]10.0961[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.899406[/C][C]9.8525[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.876448[/C][C]9.601[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.851622[/C][C]9.329[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.826678[/C][C]9.0558[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.802854[/C][C]8.7948[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.778751[/C][C]8.5308[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.755704[/C][C]8.2783[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.732753[/C][C]8.0269[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.709399[/C][C]7.7711[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.685587[/C][C]7.5102[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.660137[/C][C]7.2314[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.633462[/C][C]6.9392[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.607436[/C][C]6.6541[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.580963[/C][C]6.3641[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.55506[/C][C]6.0804[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.528086[/C][C]5.7849[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278042&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278042&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	0.982321	10.7608	0
2	0.96292	10.5483	0
3	0.943021	10.3303	0
4	0.921644	10.0961	0
5	0.899406	9.8525	0
6	0.876448	9.601	0
7	0.851622	9.329	0
8	0.826678	9.0558	0
9	0.802854	8.7948	0
10	0.778751	8.5308	0
11	0.755704	8.2783	0
12	0.732753	8.0269	0
13	0.709399	7.7711	0
14	0.685587	7.5102	0
15	0.660137	7.2314	0
16	0.633462	6.9392	0
17	0.607436	6.6541	0
18	0.580963	6.3641	0
19	0.55506	6.0804	0
20	0.528086	5.7849	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.982321	10.7608	0
2	-0.058061	-0.636	0.262986
3	-0.021796	-0.2388	0.405849
4	-0.051327	-0.5623	0.287495
5	-0.031838	-0.3488	0.363939
6	-0.029426	-0.3223	0.373878
7	-0.062193	-0.6813	0.248499
8	-0.010267	-0.1125	0.455322
9	0.021337	0.2337	0.407794
10	-0.019513	-0.2138	0.415552
11	0.019473	0.2133	0.415723
12	-0.013649	-0.1495	0.440698
13	-0.023789	-0.2606	0.397427
14	-0.029111	-0.3189	0.37518
15	-0.064862	-0.7105	0.239379
16	-0.046373	-0.508	0.306196
17	0.005099	0.0559	0.477774
18	-0.026747	-0.293	0.385013
19	0.008778	0.0962	0.461776
20	-0.046659	-0.5111	0.305101

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.982321 & 10.7608 & 0 \tabularnewline
2 & -0.058061 & -0.636 & 0.262986 \tabularnewline
3 & -0.021796 & -0.2388 & 0.405849 \tabularnewline
4 & -0.051327 & -0.5623 & 0.287495 \tabularnewline
5 & -0.031838 & -0.3488 & 0.363939 \tabularnewline
6 & -0.029426 & -0.3223 & 0.373878 \tabularnewline
7 & -0.062193 & -0.6813 & 0.248499 \tabularnewline
8 & -0.010267 & -0.1125 & 0.455322 \tabularnewline
9 & 0.021337 & 0.2337 & 0.407794 \tabularnewline
10 & -0.019513 & -0.2138 & 0.415552 \tabularnewline
11 & 0.019473 & 0.2133 & 0.415723 \tabularnewline
12 & -0.013649 & -0.1495 & 0.440698 \tabularnewline
13 & -0.023789 & -0.2606 & 0.397427 \tabularnewline
14 & -0.029111 & -0.3189 & 0.37518 \tabularnewline
15 & -0.064862 & -0.7105 & 0.239379 \tabularnewline
16 & -0.046373 & -0.508 & 0.306196 \tabularnewline
17 & 0.005099 & 0.0559 & 0.477774 \tabularnewline
18 & -0.026747 & -0.293 & 0.385013 \tabularnewline
19 & 0.008778 & 0.0962 & 0.461776 \tabularnewline
20 & -0.046659 & -0.5111 & 0.305101 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278042&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]0.982321[/C][C]10.7608[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.058061[/C][C]-0.636[/C][C]0.262986[/C][/ROW]
[ROW][C]3[/C][C]-0.021796[/C][C]-0.2388[/C][C]0.405849[/C][/ROW]
[ROW][C]4[/C][C]-0.051327[/C][C]-0.5623[/C][C]0.287495[/C][/ROW]
[ROW][C]5[/C][C]-0.031838[/C][C]-0.3488[/C][C]0.363939[/C][/ROW]
[ROW][C]6[/C][C]-0.029426[/C][C]-0.3223[/C][C]0.373878[/C][/ROW]
[ROW][C]7[/C][C]-0.062193[/C][C]-0.6813[/C][C]0.248499[/C][/ROW]
[ROW][C]8[/C][C]-0.010267[/C][C]-0.1125[/C][C]0.455322[/C][/ROW]
[ROW][C]9[/C][C]0.021337[/C][C]0.2337[/C][C]0.407794[/C][/ROW]
[ROW][C]10[/C][C]-0.019513[/C][C]-0.2138[/C][C]0.415552[/C][/ROW]
[ROW][C]11[/C][C]0.019473[/C][C]0.2133[/C][C]0.415723[/C][/ROW]
[ROW][C]12[/C][C]-0.013649[/C][C]-0.1495[/C][C]0.440698[/C][/ROW]
[ROW][C]13[/C][C]-0.023789[/C][C]-0.2606[/C][C]0.397427[/C][/ROW]
[ROW][C]14[/C][C]-0.029111[/C][C]-0.3189[/C][C]0.37518[/C][/ROW]
[ROW][C]15[/C][C]-0.064862[/C][C]-0.7105[/C][C]0.239379[/C][/ROW]
[ROW][C]16[/C][C]-0.046373[/C][C]-0.508[/C][C]0.306196[/C][/ROW]
[ROW][C]17[/C][C]0.005099[/C][C]0.0559[/C][C]0.477774[/C][/ROW]
[ROW][C]18[/C][C]-0.026747[/C][C]-0.293[/C][C]0.385013[/C][/ROW]
[ROW][C]19[/C][C]0.008778[/C][C]0.0962[/C][C]0.461776[/C][/ROW]
[ROW][C]20[/C][C]-0.046659[/C][C]-0.5111[/C][C]0.305101[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278042&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278042&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	0.982321	10.7608	0
2	-0.058061	-0.636	0.262986
3	-0.021796	-0.2388	0.405849
4	-0.051327	-0.5623	0.287495
5	-0.031838	-0.3488	0.363939
6	-0.029426	-0.3223	0.373878
7	-0.062193	-0.6813	0.248499
8	-0.010267	-0.1125	0.455322
9	0.021337	0.2337	0.407794
10	-0.019513	-0.2138	0.415552
11	0.019473	0.2133	0.415723
12	-0.013649	-0.1495	0.440698
13	-0.023789	-0.2606	0.397427
14	-0.029111	-0.3189	0.37518
15	-0.064862	-0.7105	0.239379
16	-0.046373	-0.508	0.306196
17	0.005099	0.0559	0.477774
18	-0.026747	-0.293	0.385013
19	0.008778	0.0962	0.461776
20	-0.046659	-0.5111	0.305101

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code