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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 27 Nov 2007 03:05:57 -0700

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/2007/Nov/27/t1196157391676ritc29bsb0v7.htm/, Retrieved Sun, 05 May 2024 18:25:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6791, Retrieved Sun, 05 May 2024 18:25:16 +0000

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Estimated Impact

182

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-       [(Partial) Autocorrelation Function] [Opdracht 3 Q2 Kolom3] [2007-11-27 10:05:57] [00ef4a509c2a49a63e98610ffa741e39] [Current]

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Summary of compuational 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 compuational 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=6791&T=0

[TABLE]
[ROW][C]Summary of compuational 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=6791&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6791&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 compuational 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
0	1	8.4853	0
1	0.563537	4.7818	4e-06
2	0.167163	1.4184	0.080191
3	-0.015364	-0.1304	0.551681
4	-0.117431	-0.9964	0.838811
5	-0.13353	-1.133	0.869522
6	-0.173906	-1.4756	0.9278
7	-0.195917	-1.6624	0.949611
8	-0.167537	-1.4216	0.92027
9	-0.081412	-0.6908	0.754046
10	0.087537	0.7428	0.230017
11	0.351329	2.9811	0.001958
12	0.537532	4.5611	1e-05
13	0.303936	2.579	0.005976
14	0.057493	0.4878	0.31357
15	-0.068198	-0.5787	0.717696
16	-0.183464	-1.5567	0.938042
17	-0.181456	-1.5397	0.935992

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.563537 & 4.7818 & 4e-06 \tabularnewline
2 & 0.167163 & 1.4184 & 0.080191 \tabularnewline
3 & -0.015364 & -0.1304 & 0.551681 \tabularnewline
4 & -0.117431 & -0.9964 & 0.838811 \tabularnewline
5 & -0.13353 & -1.133 & 0.869522 \tabularnewline
6 & -0.173906 & -1.4756 & 0.9278 \tabularnewline
7 & -0.195917 & -1.6624 & 0.949611 \tabularnewline
8 & -0.167537 & -1.4216 & 0.92027 \tabularnewline
9 & -0.081412 & -0.6908 & 0.754046 \tabularnewline
10 & 0.087537 & 0.7428 & 0.230017 \tabularnewline
11 & 0.351329 & 2.9811 & 0.001958 \tabularnewline
12 & 0.537532 & 4.5611 & 1e-05 \tabularnewline
13 & 0.303936 & 2.579 & 0.005976 \tabularnewline
14 & 0.057493 & 0.4878 & 0.31357 \tabularnewline
15 & -0.068198 & -0.5787 & 0.717696 \tabularnewline
16 & -0.183464 & -1.5567 & 0.938042 \tabularnewline
17 & -0.181456 & -1.5397 & 0.935992 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6791&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]0[/C][C]1[/C][C]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.563537[/C][C]4.7818[/C][C]4e-06[/C][/ROW]
[ROW][C]2[/C][C]0.167163[/C][C]1.4184[/C][C]0.080191[/C][/ROW]
[ROW][C]3[/C][C]-0.015364[/C][C]-0.1304[/C][C]0.551681[/C][/ROW]
[ROW][C]4[/C][C]-0.117431[/C][C]-0.9964[/C][C]0.838811[/C][/ROW]
[ROW][C]5[/C][C]-0.13353[/C][C]-1.133[/C][C]0.869522[/C][/ROW]
[ROW][C]6[/C][C]-0.173906[/C][C]-1.4756[/C][C]0.9278[/C][/ROW]
[ROW][C]7[/C][C]-0.195917[/C][C]-1.6624[/C][C]0.949611[/C][/ROW]
[ROW][C]8[/C][C]-0.167537[/C][C]-1.4216[/C][C]0.92027[/C][/ROW]
[ROW][C]9[/C][C]-0.081412[/C][C]-0.6908[/C][C]0.754046[/C][/ROW]
[ROW][C]10[/C][C]0.087537[/C][C]0.7428[/C][C]0.230017[/C][/ROW]
[ROW][C]11[/C][C]0.351329[/C][C]2.9811[/C][C]0.001958[/C][/ROW]
[ROW][C]12[/C][C]0.537532[/C][C]4.5611[/C][C]1e-05[/C][/ROW]
[ROW][C]13[/C][C]0.303936[/C][C]2.579[/C][C]0.005976[/C][/ROW]
[ROW][C]14[/C][C]0.057493[/C][C]0.4878[/C][C]0.31357[/C][/ROW]
[ROW][C]15[/C][C]-0.068198[/C][C]-0.5787[/C][C]0.717696[/C][/ROW]
[ROW][C]16[/C][C]-0.183464[/C][C]-1.5567[/C][C]0.938042[/C][/ROW]
[ROW][C]17[/C][C]-0.181456[/C][C]-1.5397[/C][C]0.935992[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6791&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6791&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
0	1	8.4853	0
1	0.563537	4.7818	4e-06
2	0.167163	1.4184	0.080191
3	-0.015364	-0.1304	0.551681
4	-0.117431	-0.9964	0.838811
5	-0.13353	-1.133	0.869522
6	-0.173906	-1.4756	0.9278
7	-0.195917	-1.6624	0.949611
8	-0.167537	-1.4216	0.92027
9	-0.081412	-0.6908	0.754046
10	0.087537	0.7428	0.230017
11	0.351329	2.9811	0.001958
12	0.537532	4.5611	1e-05
13	0.303936	2.579	0.005976
14	0.057493	0.4878	0.31357
15	-0.068198	-0.5787	0.717696
16	-0.183464	-1.5567	0.938042
17	-0.181456	-1.5397	0.935992

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.563537	4.7818	4e-06
1	-0.220406	-1.8702	0.96724
2	-0.009429	-0.08	0.531774
3	-0.101388	-0.8603	0.803762
4	-0.015023	-0.1275	0.55054
5	-0.133373	-1.1317	0.869245
6	-0.06709	-0.5693	0.714529
7	-0.049205	-0.4175	0.661229
8	0.024464	0.2076	0.418069
9	0.135407	1.149	0.127185
10	0.311229	2.6409	0.005067
11	0.279446	2.3712	0.010205
12	-0.234181	-1.9871	0.974641
13	-0.018806	-0.1596	0.563167
14	-0.050767	-0.4308	0.666039
15	-0.132911	-1.1278	0.868422
16	0.024196	0.2053	0.418955
17	-0.040014	-0.3395	0.632402

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.563537 & 4.7818 & 4e-06 \tabularnewline
1 & -0.220406 & -1.8702 & 0.96724 \tabularnewline
2 & -0.009429 & -0.08 & 0.531774 \tabularnewline
3 & -0.101388 & -0.8603 & 0.803762 \tabularnewline
4 & -0.015023 & -0.1275 & 0.55054 \tabularnewline
5 & -0.133373 & -1.1317 & 0.869245 \tabularnewline
6 & -0.06709 & -0.5693 & 0.714529 \tabularnewline
7 & -0.049205 & -0.4175 & 0.661229 \tabularnewline
8 & 0.024464 & 0.2076 & 0.418069 \tabularnewline
9 & 0.135407 & 1.149 & 0.127185 \tabularnewline
10 & 0.311229 & 2.6409 & 0.005067 \tabularnewline
11 & 0.279446 & 2.3712 & 0.010205 \tabularnewline
12 & -0.234181 & -1.9871 & 0.974641 \tabularnewline
13 & -0.018806 & -0.1596 & 0.563167 \tabularnewline
14 & -0.050767 & -0.4308 & 0.666039 \tabularnewline
15 & -0.132911 & -1.1278 & 0.868422 \tabularnewline
16 & 0.024196 & 0.2053 & 0.418955 \tabularnewline
17 & -0.040014 & -0.3395 & 0.632402 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6791&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]0[/C][C]0.563537[/C][C]4.7818[/C][C]4e-06[/C][/ROW]
[ROW][C]1[/C][C]-0.220406[/C][C]-1.8702[/C][C]0.96724[/C][/ROW]
[ROW][C]2[/C][C]-0.009429[/C][C]-0.08[/C][C]0.531774[/C][/ROW]
[ROW][C]3[/C][C]-0.101388[/C][C]-0.8603[/C][C]0.803762[/C][/ROW]
[ROW][C]4[/C][C]-0.015023[/C][C]-0.1275[/C][C]0.55054[/C][/ROW]
[ROW][C]5[/C][C]-0.133373[/C][C]-1.1317[/C][C]0.869245[/C][/ROW]
[ROW][C]6[/C][C]-0.06709[/C][C]-0.5693[/C][C]0.714529[/C][/ROW]
[ROW][C]7[/C][C]-0.049205[/C][C]-0.4175[/C][C]0.661229[/C][/ROW]
[ROW][C]8[/C][C]0.024464[/C][C]0.2076[/C][C]0.418069[/C][/ROW]
[ROW][C]9[/C][C]0.135407[/C][C]1.149[/C][C]0.127185[/C][/ROW]
[ROW][C]10[/C][C]0.311229[/C][C]2.6409[/C][C]0.005067[/C][/ROW]
[ROW][C]11[/C][C]0.279446[/C][C]2.3712[/C][C]0.010205[/C][/ROW]
[ROW][C]12[/C][C]-0.234181[/C][C]-1.9871[/C][C]0.974641[/C][/ROW]
[ROW][C]13[/C][C]-0.018806[/C][C]-0.1596[/C][C]0.563167[/C][/ROW]
[ROW][C]14[/C][C]-0.050767[/C][C]-0.4308[/C][C]0.666039[/C][/ROW]
[ROW][C]15[/C][C]-0.132911[/C][C]-1.1278[/C][C]0.868422[/C][/ROW]
[ROW][C]16[/C][C]0.024196[/C][C]0.2053[/C][C]0.418955[/C][/ROW]
[ROW][C]17[/C][C]-0.040014[/C][C]-0.3395[/C][C]0.632402[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6791&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6791&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
0	0.563537	4.7818	4e-06
1	-0.220406	-1.8702	0.96724
2	-0.009429	-0.08	0.531774
3	-0.101388	-0.8603	0.803762
4	-0.015023	-0.1275	0.55054
5	-0.133373	-1.1317	0.869245
6	-0.06709	-0.5693	0.714529
7	-0.049205	-0.4175	0.661229
8	0.024464	0.2076	0.418069
9	0.135407	1.149	0.127185
10	0.311229	2.6409	0.005067
11	0.279446	2.3712	0.010205
12	-0.234181	-1.9871	0.974641
13	-0.018806	-0.1596	0.563167
14	-0.050767	-0.4308	0.666039
15	-0.132911	-1.1278	0.868422
16	0.024196	0.2053	0.418955
17	-0.040014	-0.3395	0.632402

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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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