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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 10 Dec 2008 10:22:24 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/10/t1228929809h4vdvzb4gbyodum.htm/, Retrieved Fri, 17 May 2024 02:02:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32040, Retrieved Fri, 17 May 2024 02:02:39 +0000

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165

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-       [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2008-12-10 17:22:24] [c341394676dfca3684255efe82d168bf] [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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32040&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32040&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32040&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.939596	9.1097	0
2	0.872543	8.4596	0
3	0.809444	7.8479	0
4	0.743094	7.2046	0
5	0.679644	6.5894	0
6	0.620185	6.0129	0
7	0.557755	5.4076	0
8	0.495132	4.8005	3e-06
9	0.435204	4.2195	2.8e-05
10	0.389179	3.7732	0.000141
11	0.360941	3.4995	0.000357
12	0.344664	3.3416	0.000598
13	0.337755	3.2747	0.000741
14	0.333219	3.2307	0.000851
15	0.334381	3.2419	0.000822
16	0.340353	3.2998	0.000684
17	0.344737	3.3424	0.000597
18	0.345522	3.35	0.000582
19	0.347876	3.3728	0.000541

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.939596 & 9.1097 & 0 \tabularnewline
2 & 0.872543 & 8.4596 & 0 \tabularnewline
3 & 0.809444 & 7.8479 & 0 \tabularnewline
4 & 0.743094 & 7.2046 & 0 \tabularnewline
5 & 0.679644 & 6.5894 & 0 \tabularnewline
6 & 0.620185 & 6.0129 & 0 \tabularnewline
7 & 0.557755 & 5.4076 & 0 \tabularnewline
8 & 0.495132 & 4.8005 & 3e-06 \tabularnewline
9 & 0.435204 & 4.2195 & 2.8e-05 \tabularnewline
10 & 0.389179 & 3.7732 & 0.000141 \tabularnewline
11 & 0.360941 & 3.4995 & 0.000357 \tabularnewline
12 & 0.344664 & 3.3416 & 0.000598 \tabularnewline
13 & 0.337755 & 3.2747 & 0.000741 \tabularnewline
14 & 0.333219 & 3.2307 & 0.000851 \tabularnewline
15 & 0.334381 & 3.2419 & 0.000822 \tabularnewline
16 & 0.340353 & 3.2998 & 0.000684 \tabularnewline
17 & 0.344737 & 3.3424 & 0.000597 \tabularnewline
18 & 0.345522 & 3.35 & 0.000582 \tabularnewline
19 & 0.347876 & 3.3728 & 0.000541 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32040&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]0.939596[/C][C]9.1097[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.872543[/C][C]8.4596[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.809444[/C][C]7.8479[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.743094[/C][C]7.2046[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.679644[/C][C]6.5894[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.620185[/C][C]6.0129[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.557755[/C][C]5.4076[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.495132[/C][C]4.8005[/C][C]3e-06[/C][/ROW]
[ROW][C]9[/C][C]0.435204[/C][C]4.2195[/C][C]2.8e-05[/C][/ROW]
[ROW][C]10[/C][C]0.389179[/C][C]3.7732[/C][C]0.000141[/C][/ROW]
[ROW][C]11[/C][C]0.360941[/C][C]3.4995[/C][C]0.000357[/C][/ROW]
[ROW][C]12[/C][C]0.344664[/C][C]3.3416[/C][C]0.000598[/C][/ROW]
[ROW][C]13[/C][C]0.337755[/C][C]3.2747[/C][C]0.000741[/C][/ROW]
[ROW][C]14[/C][C]0.333219[/C][C]3.2307[/C][C]0.000851[/C][/ROW]
[ROW][C]15[/C][C]0.334381[/C][C]3.2419[/C][C]0.000822[/C][/ROW]
[ROW][C]16[/C][C]0.340353[/C][C]3.2998[/C][C]0.000684[/C][/ROW]
[ROW][C]17[/C][C]0.344737[/C][C]3.3424[/C][C]0.000597[/C][/ROW]
[ROW][C]18[/C][C]0.345522[/C][C]3.35[/C][C]0.000582[/C][/ROW]
[ROW][C]19[/C][C]0.347876[/C][C]3.3728[/C][C]0.000541[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32040&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32040&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	0.939596	9.1097	0
2	0.872543	8.4596	0
3	0.809444	7.8479	0
4	0.743094	7.2046	0
5	0.679644	6.5894	0
6	0.620185	6.0129	0
7	0.557755	5.4076	0
8	0.495132	4.8005	3e-06
9	0.435204	4.2195	2.8e-05
10	0.389179	3.7732	0.000141
11	0.360941	3.4995	0.000357
12	0.344664	3.3416	0.000598
13	0.337755	3.2747	0.000741
14	0.333219	3.2307	0.000851
15	0.334381	3.2419	0.000822
16	0.340353	3.2998	0.000684
17	0.344737	3.3424	0.000597
18	0.345522	3.35	0.000582
19	0.347876	3.3728	0.000541

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.939596	9.1097	0
2	-0.087896	-0.8522	0.19814
3	0.001141	0.0111	0.495599
4	-0.066652	-0.6462	0.259858
5	-0.008563	-0.083	0.467005
6	-0.008386	-0.0813	0.467685
7	-0.063329	-0.614	0.270349
8	-0.038168	-0.37	0.356089
9	-0.021497	-0.2084	0.417677
10	0.079569	0.7714	0.221188
11	0.108492	1.0519	0.147778
12	0.070136	0.68	0.249089
13	0.059291	0.5748	0.283385
14	0.004869	0.0472	0.481226
15	0.048895	0.4741	0.31828
16	0.032838	0.3184	0.375455
17	-0.019259	-0.1867	0.426138
18	-0.035607	-0.3452	0.365351
19	0.017804	0.1726	0.431661

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.939596 & 9.1097 & 0 \tabularnewline
2 & -0.087896 & -0.8522 & 0.19814 \tabularnewline
3 & 0.001141 & 0.0111 & 0.495599 \tabularnewline
4 & -0.066652 & -0.6462 & 0.259858 \tabularnewline
5 & -0.008563 & -0.083 & 0.467005 \tabularnewline
6 & -0.008386 & -0.0813 & 0.467685 \tabularnewline
7 & -0.063329 & -0.614 & 0.270349 \tabularnewline
8 & -0.038168 & -0.37 & 0.356089 \tabularnewline
9 & -0.021497 & -0.2084 & 0.417677 \tabularnewline
10 & 0.079569 & 0.7714 & 0.221188 \tabularnewline
11 & 0.108492 & 1.0519 & 0.147778 \tabularnewline
12 & 0.070136 & 0.68 & 0.249089 \tabularnewline
13 & 0.059291 & 0.5748 & 0.283385 \tabularnewline
14 & 0.004869 & 0.0472 & 0.481226 \tabularnewline
15 & 0.048895 & 0.4741 & 0.31828 \tabularnewline
16 & 0.032838 & 0.3184 & 0.375455 \tabularnewline
17 & -0.019259 & -0.1867 & 0.426138 \tabularnewline
18 & -0.035607 & -0.3452 & 0.365351 \tabularnewline
19 & 0.017804 & 0.1726 & 0.431661 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32040&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]0.939596[/C][C]9.1097[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.087896[/C][C]-0.8522[/C][C]0.19814[/C][/ROW]
[ROW][C]3[/C][C]0.001141[/C][C]0.0111[/C][C]0.495599[/C][/ROW]
[ROW][C]4[/C][C]-0.066652[/C][C]-0.6462[/C][C]0.259858[/C][/ROW]
[ROW][C]5[/C][C]-0.008563[/C][C]-0.083[/C][C]0.467005[/C][/ROW]
[ROW][C]6[/C][C]-0.008386[/C][C]-0.0813[/C][C]0.467685[/C][/ROW]
[ROW][C]7[/C][C]-0.063329[/C][C]-0.614[/C][C]0.270349[/C][/ROW]
[ROW][C]8[/C][C]-0.038168[/C][C]-0.37[/C][C]0.356089[/C][/ROW]
[ROW][C]9[/C][C]-0.021497[/C][C]-0.2084[/C][C]0.417677[/C][/ROW]
[ROW][C]10[/C][C]0.079569[/C][C]0.7714[/C][C]0.221188[/C][/ROW]
[ROW][C]11[/C][C]0.108492[/C][C]1.0519[/C][C]0.147778[/C][/ROW]
[ROW][C]12[/C][C]0.070136[/C][C]0.68[/C][C]0.249089[/C][/ROW]
[ROW][C]13[/C][C]0.059291[/C][C]0.5748[/C][C]0.283385[/C][/ROW]
[ROW][C]14[/C][C]0.004869[/C][C]0.0472[/C][C]0.481226[/C][/ROW]
[ROW][C]15[/C][C]0.048895[/C][C]0.4741[/C][C]0.31828[/C][/ROW]
[ROW][C]16[/C][C]0.032838[/C][C]0.3184[/C][C]0.375455[/C][/ROW]
[ROW][C]17[/C][C]-0.019259[/C][C]-0.1867[/C][C]0.426138[/C][/ROW]
[ROW][C]18[/C][C]-0.035607[/C][C]-0.3452[/C][C]0.365351[/C][/ROW]
[ROW][C]19[/C][C]0.017804[/C][C]0.1726[/C][C]0.431661[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32040&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32040&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	0.939596	9.1097	0
2	-0.087896	-0.8522	0.19814
3	0.001141	0.0111	0.495599
4	-0.066652	-0.6462	0.259858
5	-0.008563	-0.083	0.467005
6	-0.008386	-0.0813	0.467685
7	-0.063329	-0.614	0.270349
8	-0.038168	-0.37	0.356089
9	-0.021497	-0.2084	0.417677
10	0.079569	0.7714	0.221188
11	0.108492	1.0519	0.147778
12	0.070136	0.68	0.249089
13	0.059291	0.5748	0.283385
14	0.004869	0.0472	0.481226
15	0.048895	0.4741	0.31828
16	0.032838	0.3184	0.375455
17	-0.019259	-0.1867	0.426138
18	-0.035607	-0.3452	0.365351
19	0.017804	0.1726	0.431661

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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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