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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2011 07:01:59 -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/16/t1324037053q0eugfd11g2eiyk.htm/, Retrieved Sun, 05 May 2024 12:57:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=155838, Retrieved Sun, 05 May 2024 12:57:57 +0000

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User-defined keywords

Estimated Impact

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMPD    [(Partial) Autocorrelation Function] [(P)ACF volumes ta...] [2011-12-16 12:01:59] [3bdb54d050744f47368418ea7c7e8e96] [Current]
-   P       [(Partial) Autocorrelation Function] [(P)ACF volumes ta...] [2011-12-20 18:35:24] [30ad580cd6d52fd70fb475df3c05f95d] 
-    D        [(Partial) Autocorrelation Function] [(P)ACF volumes bier] [2011-12-20 18:40:31] [30ad580cd6d52fd70fb475df3c05f95d] 

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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=155838&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=155838&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155838&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	0.667179	7.8942	0
2	0.528808	6.2569	0
3	0.573984	6.7915	0
4	0.520501	6.1586	0
5	0.507158	6.0008	0
6	0.480604	5.6866	0
7	0.443298	5.2452	0
8	0.448209	5.3033	0
9	0.470841	5.5711	0
10	0.427213	5.0548	1e-06
11	0.405642	4.7996	2e-06
12	0.384085	4.5446	6e-06
13	0.410028	4.8515	2e-06
14	0.40988	4.8498	2e-06
15	0.384944	4.5547	6e-06
16	0.421271	4.9845	1e-06
17	0.372497	4.4074	1e-05
18	0.371705	4.3981	1.1e-05
19	0.321223	3.8008	0.000107
20	0.273361	3.2345	0.00076
21	0.21502	2.5441	0.00602

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.667179 & 7.8942 & 0 \tabularnewline
2 & 0.528808 & 6.2569 & 0 \tabularnewline
3 & 0.573984 & 6.7915 & 0 \tabularnewline
4 & 0.520501 & 6.1586 & 0 \tabularnewline
5 & 0.507158 & 6.0008 & 0 \tabularnewline
6 & 0.480604 & 5.6866 & 0 \tabularnewline
7 & 0.443298 & 5.2452 & 0 \tabularnewline
8 & 0.448209 & 5.3033 & 0 \tabularnewline
9 & 0.470841 & 5.5711 & 0 \tabularnewline
10 & 0.427213 & 5.0548 & 1e-06 \tabularnewline
11 & 0.405642 & 4.7996 & 2e-06 \tabularnewline
12 & 0.384085 & 4.5446 & 6e-06 \tabularnewline
13 & 0.410028 & 4.8515 & 2e-06 \tabularnewline
14 & 0.40988 & 4.8498 & 2e-06 \tabularnewline
15 & 0.384944 & 4.5547 & 6e-06 \tabularnewline
16 & 0.421271 & 4.9845 & 1e-06 \tabularnewline
17 & 0.372497 & 4.4074 & 1e-05 \tabularnewline
18 & 0.371705 & 4.3981 & 1.1e-05 \tabularnewline
19 & 0.321223 & 3.8008 & 0.000107 \tabularnewline
20 & 0.273361 & 3.2345 & 0.00076 \tabularnewline
21 & 0.21502 & 2.5441 & 0.00602 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155838&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]0.667179[/C][C]7.8942[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.528808[/C][C]6.2569[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.573984[/C][C]6.7915[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.520501[/C][C]6.1586[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.507158[/C][C]6.0008[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.480604[/C][C]5.6866[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.443298[/C][C]5.2452[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.448209[/C][C]5.3033[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.470841[/C][C]5.5711[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.427213[/C][C]5.0548[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.405642[/C][C]4.7996[/C][C]2e-06[/C][/ROW]
[ROW][C]12[/C][C]0.384085[/C][C]4.5446[/C][C]6e-06[/C][/ROW]
[ROW][C]13[/C][C]0.410028[/C][C]4.8515[/C][C]2e-06[/C][/ROW]
[ROW][C]14[/C][C]0.40988[/C][C]4.8498[/C][C]2e-06[/C][/ROW]
[ROW][C]15[/C][C]0.384944[/C][C]4.5547[/C][C]6e-06[/C][/ROW]
[ROW][C]16[/C][C]0.421271[/C][C]4.9845[/C][C]1e-06[/C][/ROW]
[ROW][C]17[/C][C]0.372497[/C][C]4.4074[/C][C]1e-05[/C][/ROW]
[ROW][C]18[/C][C]0.371705[/C][C]4.3981[/C][C]1.1e-05[/C][/ROW]
[ROW][C]19[/C][C]0.321223[/C][C]3.8008[/C][C]0.000107[/C][/ROW]
[ROW][C]20[/C][C]0.273361[/C][C]3.2345[/C][C]0.00076[/C][/ROW]
[ROW][C]21[/C][C]0.21502[/C][C]2.5441[/C][C]0.00602[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155838&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155838&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	0.667179	7.8942	0
2	0.528808	6.2569	0
3	0.573984	6.7915	0
4	0.520501	6.1586	0
5	0.507158	6.0008	0
6	0.480604	5.6866	0
7	0.443298	5.2452	0
8	0.448209	5.3033	0
9	0.470841	5.5711	0
10	0.427213	5.0548	1e-06
11	0.405642	4.7996	2e-06
12	0.384085	4.5446	6e-06
13	0.410028	4.8515	2e-06
14	0.40988	4.8498	2e-06
15	0.384944	4.5547	6e-06
16	0.421271	4.9845	1e-06
17	0.372497	4.4074	1e-05
18	0.371705	4.3981	1.1e-05
19	0.321223	3.8008	0.000107
20	0.273361	3.2345	0.00076
21	0.21502	2.5441	0.00602

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.667179	7.8942	0
2	0.15081	1.7844	0.038261
3	0.320448	3.7916	0.000111
4	0.052415	0.6202	0.268074
5	0.150069	1.7756	0.038982
6	0.019945	0.236	0.406893
7	0.036614	0.4332	0.332758
8	0.061908	0.7325	0.232541
9	0.110886	1.312	0.09583
10	-0.015085	-0.1785	0.429298
11	0.028724	0.3399	0.367233
12	-0.035417	-0.4191	0.337907
13	0.107477	1.2717	0.102796
14	0.014009	0.1658	0.434295
15	0.034685	0.4104	0.341068
16	0.099145	1.1731	0.121374
17	-0.071277	-0.8434	0.200233
18	0.053611	0.6343	0.26345
19	-0.141262	-1.6714	0.048435
20	-0.034439	-0.4075	0.342134
21	-0.177386	-2.0989	0.018812

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.667179 & 7.8942 & 0 \tabularnewline
2 & 0.15081 & 1.7844 & 0.038261 \tabularnewline
3 & 0.320448 & 3.7916 & 0.000111 \tabularnewline
4 & 0.052415 & 0.6202 & 0.268074 \tabularnewline
5 & 0.150069 & 1.7756 & 0.038982 \tabularnewline
6 & 0.019945 & 0.236 & 0.406893 \tabularnewline
7 & 0.036614 & 0.4332 & 0.332758 \tabularnewline
8 & 0.061908 & 0.7325 & 0.232541 \tabularnewline
9 & 0.110886 & 1.312 & 0.09583 \tabularnewline
10 & -0.015085 & -0.1785 & 0.429298 \tabularnewline
11 & 0.028724 & 0.3399 & 0.367233 \tabularnewline
12 & -0.035417 & -0.4191 & 0.337907 \tabularnewline
13 & 0.107477 & 1.2717 & 0.102796 \tabularnewline
14 & 0.014009 & 0.1658 & 0.434295 \tabularnewline
15 & 0.034685 & 0.4104 & 0.341068 \tabularnewline
16 & 0.099145 & 1.1731 & 0.121374 \tabularnewline
17 & -0.071277 & -0.8434 & 0.200233 \tabularnewline
18 & 0.053611 & 0.6343 & 0.26345 \tabularnewline
19 & -0.141262 & -1.6714 & 0.048435 \tabularnewline
20 & -0.034439 & -0.4075 & 0.342134 \tabularnewline
21 & -0.177386 & -2.0989 & 0.018812 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155838&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]0.667179[/C][C]7.8942[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.15081[/C][C]1.7844[/C][C]0.038261[/C][/ROW]
[ROW][C]3[/C][C]0.320448[/C][C]3.7916[/C][C]0.000111[/C][/ROW]
[ROW][C]4[/C][C]0.052415[/C][C]0.6202[/C][C]0.268074[/C][/ROW]
[ROW][C]5[/C][C]0.150069[/C][C]1.7756[/C][C]0.038982[/C][/ROW]
[ROW][C]6[/C][C]0.019945[/C][C]0.236[/C][C]0.406893[/C][/ROW]
[ROW][C]7[/C][C]0.036614[/C][C]0.4332[/C][C]0.332758[/C][/ROW]
[ROW][C]8[/C][C]0.061908[/C][C]0.7325[/C][C]0.232541[/C][/ROW]
[ROW][C]9[/C][C]0.110886[/C][C]1.312[/C][C]0.09583[/C][/ROW]
[ROW][C]10[/C][C]-0.015085[/C][C]-0.1785[/C][C]0.429298[/C][/ROW]
[ROW][C]11[/C][C]0.028724[/C][C]0.3399[/C][C]0.367233[/C][/ROW]
[ROW][C]12[/C][C]-0.035417[/C][C]-0.4191[/C][C]0.337907[/C][/ROW]
[ROW][C]13[/C][C]0.107477[/C][C]1.2717[/C][C]0.102796[/C][/ROW]
[ROW][C]14[/C][C]0.014009[/C][C]0.1658[/C][C]0.434295[/C][/ROW]
[ROW][C]15[/C][C]0.034685[/C][C]0.4104[/C][C]0.341068[/C][/ROW]
[ROW][C]16[/C][C]0.099145[/C][C]1.1731[/C][C]0.121374[/C][/ROW]
[ROW][C]17[/C][C]-0.071277[/C][C]-0.8434[/C][C]0.200233[/C][/ROW]
[ROW][C]18[/C][C]0.053611[/C][C]0.6343[/C][C]0.26345[/C][/ROW]
[ROW][C]19[/C][C]-0.141262[/C][C]-1.6714[/C][C]0.048435[/C][/ROW]
[ROW][C]20[/C][C]-0.034439[/C][C]-0.4075[/C][C]0.342134[/C][/ROW]
[ROW][C]21[/C][C]-0.177386[/C][C]-2.0989[/C][C]0.018812[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155838&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155838&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	0.667179	7.8942	0
2	0.15081	1.7844	0.038261
3	0.320448	3.7916	0.000111
4	0.052415	0.6202	0.268074
5	0.150069	1.7756	0.038982
6	0.019945	0.236	0.406893
7	0.036614	0.4332	0.332758
8	0.061908	0.7325	0.232541
9	0.110886	1.312	0.09583
10	-0.015085	-0.1785	0.429298
11	0.028724	0.3399	0.367233
12	-0.035417	-0.4191	0.337907
13	0.107477	1.2717	0.102796
14	0.014009	0.1658	0.434295
15	0.034685	0.4104	0.341068
16	0.099145	1.1731	0.121374
17	-0.071277	-0.8434	0.200233
18	0.053611	0.6343	0.26345
19	-0.141262	-1.6714	0.048435
20	-0.034439	-0.4075	0.342134
21	-0.177386	-2.0989	0.018812

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code