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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 21 May 2009 05:49:44 -0600

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/2009/May/21/t1242906627o4igo45ujy3cc3m.htm/, Retrieved Mon, 06 May 2024 23:56:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40238, Retrieved Mon, 06 May 2024 23:56:45 +0000

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Estimated Impact

155

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-       [(Partial) Autocorrelation Function] [opgave 6b - oef 2...] [2009-05-21 11:49:44] [822aa141fddc67f18188afbe1dd38d3f] [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	'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40238&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40238&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40238&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.848027	7.2455	0
2	0.759002	6.4849	0
3	0.659751	5.6369	0
4	0.572154	4.8885	3e-06
5	0.529723	4.526	1.1e-05
6	0.513947	4.3912	1.9e-05
7	0.491801	4.202	3.7e-05
8	0.466063	3.982	8e-05
9	0.423067	3.6147	0.000275
10	0.403452	3.4471	0.000472
11	0.373239	3.189	0.001052
12	0.344044	2.9395	0.0022
13	0.309928	2.648	0.004958
14	0.283712	2.424	0.008913
15	0.233986	1.9992	0.024656
16	0.217013	1.8542	0.033878
17	0.169132	1.4451	0.07636
18	0.150543	1.2862	0.101212

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.848027 & 7.2455 & 0 \tabularnewline
2 & 0.759002 & 6.4849 & 0 \tabularnewline
3 & 0.659751 & 5.6369 & 0 \tabularnewline
4 & 0.572154 & 4.8885 & 3e-06 \tabularnewline
5 & 0.529723 & 4.526 & 1.1e-05 \tabularnewline
6 & 0.513947 & 4.3912 & 1.9e-05 \tabularnewline
7 & 0.491801 & 4.202 & 3.7e-05 \tabularnewline
8 & 0.466063 & 3.982 & 8e-05 \tabularnewline
9 & 0.423067 & 3.6147 & 0.000275 \tabularnewline
10 & 0.403452 & 3.4471 & 0.000472 \tabularnewline
11 & 0.373239 & 3.189 & 0.001052 \tabularnewline
12 & 0.344044 & 2.9395 & 0.0022 \tabularnewline
13 & 0.309928 & 2.648 & 0.004958 \tabularnewline
14 & 0.283712 & 2.424 & 0.008913 \tabularnewline
15 & 0.233986 & 1.9992 & 0.024656 \tabularnewline
16 & 0.217013 & 1.8542 & 0.033878 \tabularnewline
17 & 0.169132 & 1.4451 & 0.07636 \tabularnewline
18 & 0.150543 & 1.2862 & 0.101212 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40238&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]0.848027[/C][C]7.2455[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.759002[/C][C]6.4849[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.659751[/C][C]5.6369[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.572154[/C][C]4.8885[/C][C]3e-06[/C][/ROW]
[ROW][C]5[/C][C]0.529723[/C][C]4.526[/C][C]1.1e-05[/C][/ROW]
[ROW][C]6[/C][C]0.513947[/C][C]4.3912[/C][C]1.9e-05[/C][/ROW]
[ROW][C]7[/C][C]0.491801[/C][C]4.202[/C][C]3.7e-05[/C][/ROW]
[ROW][C]8[/C][C]0.466063[/C][C]3.982[/C][C]8e-05[/C][/ROW]
[ROW][C]9[/C][C]0.423067[/C][C]3.6147[/C][C]0.000275[/C][/ROW]
[ROW][C]10[/C][C]0.403452[/C][C]3.4471[/C][C]0.000472[/C][/ROW]
[ROW][C]11[/C][C]0.373239[/C][C]3.189[/C][C]0.001052[/C][/ROW]
[ROW][C]12[/C][C]0.344044[/C][C]2.9395[/C][C]0.0022[/C][/ROW]
[ROW][C]13[/C][C]0.309928[/C][C]2.648[/C][C]0.004958[/C][/ROW]
[ROW][C]14[/C][C]0.283712[/C][C]2.424[/C][C]0.008913[/C][/ROW]
[ROW][C]15[/C][C]0.233986[/C][C]1.9992[/C][C]0.024656[/C][/ROW]
[ROW][C]16[/C][C]0.217013[/C][C]1.8542[/C][C]0.033878[/C][/ROW]
[ROW][C]17[/C][C]0.169132[/C][C]1.4451[/C][C]0.07636[/C][/ROW]
[ROW][C]18[/C][C]0.150543[/C][C]1.2862[/C][C]0.101212[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40238&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40238&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	0.848027	7.2455	0
2	0.759002	6.4849	0
3	0.659751	5.6369	0
4	0.572154	4.8885	3e-06
5	0.529723	4.526	1.1e-05
6	0.513947	4.3912	1.9e-05
7	0.491801	4.202	3.7e-05
8	0.466063	3.982	8e-05
9	0.423067	3.6147	0.000275
10	0.403452	3.4471	0.000472
11	0.373239	3.189	0.001052
12	0.344044	2.9395	0.0022
13	0.309928	2.648	0.004958
14	0.283712	2.424	0.008913
15	0.233986	1.9992	0.024656
16	0.217013	1.8542	0.033878
17	0.169132	1.4451	0.07636
18	0.150543	1.2862	0.101212

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.848027	7.2455	0
2	0.141901	1.2124	0.114634
3	-0.046891	-0.4006	0.344928
4	-0.02246	-0.1919	0.424179
5	0.122229	1.0443	0.14989
6	0.129245	1.1043	0.136552
7	0.008286	0.0708	0.471877
8	-0.021374	-0.1826	0.427802
9	-0.048712	-0.4162	0.339245
10	0.084238	0.7197	0.236994
11	0.001096	0.0094	0.496276
12	-0.032139	-0.2746	0.3922
13	-0.052417	-0.4478	0.327794
14	0.015606	0.1333	0.447146
15	-0.077089	-0.6586	0.256098
16	0.051411	0.4393	0.330886
17	-0.10486	-0.8959	0.186618
18	0.027447	0.2345	0.407625

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.848027 & 7.2455 & 0 \tabularnewline
2 & 0.141901 & 1.2124 & 0.114634 \tabularnewline
3 & -0.046891 & -0.4006 & 0.344928 \tabularnewline
4 & -0.02246 & -0.1919 & 0.424179 \tabularnewline
5 & 0.122229 & 1.0443 & 0.14989 \tabularnewline
6 & 0.129245 & 1.1043 & 0.136552 \tabularnewline
7 & 0.008286 & 0.0708 & 0.471877 \tabularnewline
8 & -0.021374 & -0.1826 & 0.427802 \tabularnewline
9 & -0.048712 & -0.4162 & 0.339245 \tabularnewline
10 & 0.084238 & 0.7197 & 0.236994 \tabularnewline
11 & 0.001096 & 0.0094 & 0.496276 \tabularnewline
12 & -0.032139 & -0.2746 & 0.3922 \tabularnewline
13 & -0.052417 & -0.4478 & 0.327794 \tabularnewline
14 & 0.015606 & 0.1333 & 0.447146 \tabularnewline
15 & -0.077089 & -0.6586 & 0.256098 \tabularnewline
16 & 0.051411 & 0.4393 & 0.330886 \tabularnewline
17 & -0.10486 & -0.8959 & 0.186618 \tabularnewline
18 & 0.027447 & 0.2345 & 0.407625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40238&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]0.848027[/C][C]7.2455[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.141901[/C][C]1.2124[/C][C]0.114634[/C][/ROW]
[ROW][C]3[/C][C]-0.046891[/C][C]-0.4006[/C][C]0.344928[/C][/ROW]
[ROW][C]4[/C][C]-0.02246[/C][C]-0.1919[/C][C]0.424179[/C][/ROW]
[ROW][C]5[/C][C]0.122229[/C][C]1.0443[/C][C]0.14989[/C][/ROW]
[ROW][C]6[/C][C]0.129245[/C][C]1.1043[/C][C]0.136552[/C][/ROW]
[ROW][C]7[/C][C]0.008286[/C][C]0.0708[/C][C]0.471877[/C][/ROW]
[ROW][C]8[/C][C]-0.021374[/C][C]-0.1826[/C][C]0.427802[/C][/ROW]
[ROW][C]9[/C][C]-0.048712[/C][C]-0.4162[/C][C]0.339245[/C][/ROW]
[ROW][C]10[/C][C]0.084238[/C][C]0.7197[/C][C]0.236994[/C][/ROW]
[ROW][C]11[/C][C]0.001096[/C][C]0.0094[/C][C]0.496276[/C][/ROW]
[ROW][C]12[/C][C]-0.032139[/C][C]-0.2746[/C][C]0.3922[/C][/ROW]
[ROW][C]13[/C][C]-0.052417[/C][C]-0.4478[/C][C]0.327794[/C][/ROW]
[ROW][C]14[/C][C]0.015606[/C][C]0.1333[/C][C]0.447146[/C][/ROW]
[ROW][C]15[/C][C]-0.077089[/C][C]-0.6586[/C][C]0.256098[/C][/ROW]
[ROW][C]16[/C][C]0.051411[/C][C]0.4393[/C][C]0.330886[/C][/ROW]
[ROW][C]17[/C][C]-0.10486[/C][C]-0.8959[/C][C]0.186618[/C][/ROW]
[ROW][C]18[/C][C]0.027447[/C][C]0.2345[/C][C]0.407625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40238&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40238&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	0.848027	7.2455	0
2	0.141901	1.2124	0.114634
3	-0.046891	-0.4006	0.344928
4	-0.02246	-0.1919	0.424179
5	0.122229	1.0443	0.14989
6	0.129245	1.1043	0.136552
7	0.008286	0.0708	0.471877
8	-0.021374	-0.1826	0.427802
9	-0.048712	-0.4162	0.339245
10	0.084238	0.7197	0.236994
11	0.001096	0.0094	0.496276
12	-0.032139	-0.2746	0.3922
13	-0.052417	-0.4478	0.327794
14	0.015606	0.1333	0.447146
15	-0.077089	-0.6586	0.256098
16	0.051411	0.4393	0.330886
17	-0.10486	-0.8959	0.186618
18	0.027447	0.2345	0.407625

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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Input Parameters & R Code