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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Nov 2007 12:46:43 -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/22/t1195760418zfhbpagafmebbuq.htm/, Retrieved Fri, 03 May 2024 01:52:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6095, Retrieved Fri, 03 May 2024 01:52:06 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

194

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

-       [(Partial) Autocorrelation Function] [WS9Q2ACFEb] [2007-11-22 19:46:43] [142ab5472309a9ae9a3b52678758dc4a] [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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6095&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6095&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6095&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	6.9282	0
1	-0.295354	-2.0463	0.976886
2	-0.043196	-0.2993	0.616987
3	0.346586	2.4012	0.010131
4	-0.187861	-1.3015	0.900357
5	0.005158	0.0357	0.485821
6	0.190542	1.3201	0.096529
7	-0.179663	-1.2447	0.890365
8	-0.084844	-0.5878	0.720295
9	0.224965	1.5586	0.06283
10	-0.093371	-0.6469	0.739608
11	-0.020343	-0.1409	0.555746
12	0.109941	0.7617	0.224985
13	-0.207665	-1.4387	0.921644
14	0.144377	1.0003	0.161098
15	-0.029739	-0.206	0.581183
16	-0.116755	-0.8089	0.788719

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.9282 & 0 \tabularnewline
1 & -0.295354 & -2.0463 & 0.976886 \tabularnewline
2 & -0.043196 & -0.2993 & 0.616987 \tabularnewline
3 & 0.346586 & 2.4012 & 0.010131 \tabularnewline
4 & -0.187861 & -1.3015 & 0.900357 \tabularnewline
5 & 0.005158 & 0.0357 & 0.485821 \tabularnewline
6 & 0.190542 & 1.3201 & 0.096529 \tabularnewline
7 & -0.179663 & -1.2447 & 0.890365 \tabularnewline
8 & -0.084844 & -0.5878 & 0.720295 \tabularnewline
9 & 0.224965 & 1.5586 & 0.06283 \tabularnewline
10 & -0.093371 & -0.6469 & 0.739608 \tabularnewline
11 & -0.020343 & -0.1409 & 0.555746 \tabularnewline
12 & 0.109941 & 0.7617 & 0.224985 \tabularnewline
13 & -0.207665 & -1.4387 & 0.921644 \tabularnewline
14 & 0.144377 & 1.0003 & 0.161098 \tabularnewline
15 & -0.029739 & -0.206 & 0.581183 \tabularnewline
16 & -0.116755 & -0.8089 & 0.788719 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6095&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]6.9282[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.295354[/C][C]-2.0463[/C][C]0.976886[/C][/ROW]
[ROW][C]2[/C][C]-0.043196[/C][C]-0.2993[/C][C]0.616987[/C][/ROW]
[ROW][C]3[/C][C]0.346586[/C][C]2.4012[/C][C]0.010131[/C][/ROW]
[ROW][C]4[/C][C]-0.187861[/C][C]-1.3015[/C][C]0.900357[/C][/ROW]
[ROW][C]5[/C][C]0.005158[/C][C]0.0357[/C][C]0.485821[/C][/ROW]
[ROW][C]6[/C][C]0.190542[/C][C]1.3201[/C][C]0.096529[/C][/ROW]
[ROW][C]7[/C][C]-0.179663[/C][C]-1.2447[/C][C]0.890365[/C][/ROW]
[ROW][C]8[/C][C]-0.084844[/C][C]-0.5878[/C][C]0.720295[/C][/ROW]
[ROW][C]9[/C][C]0.224965[/C][C]1.5586[/C][C]0.06283[/C][/ROW]
[ROW][C]10[/C][C]-0.093371[/C][C]-0.6469[/C][C]0.739608[/C][/ROW]
[ROW][C]11[/C][C]-0.020343[/C][C]-0.1409[/C][C]0.555746[/C][/ROW]
[ROW][C]12[/C][C]0.109941[/C][C]0.7617[/C][C]0.224985[/C][/ROW]
[ROW][C]13[/C][C]-0.207665[/C][C]-1.4387[/C][C]0.921644[/C][/ROW]
[ROW][C]14[/C][C]0.144377[/C][C]1.0003[/C][C]0.161098[/C][/ROW]
[ROW][C]15[/C][C]-0.029739[/C][C]-0.206[/C][C]0.581183[/C][/ROW]
[ROW][C]16[/C][C]-0.116755[/C][C]-0.8089[/C][C]0.788719[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6095&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6095&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	6.9282	0
1	-0.295354	-2.0463	0.976886
2	-0.043196	-0.2993	0.616987
3	0.346586	2.4012	0.010131
4	-0.187861	-1.3015	0.900357
5	0.005158	0.0357	0.485821
6	0.190542	1.3201	0.096529
7	-0.179663	-1.2447	0.890365
8	-0.084844	-0.5878	0.720295
9	0.224965	1.5586	0.06283
10	-0.093371	-0.6469	0.739608
11	-0.020343	-0.1409	0.555746
12	0.109941	0.7617	0.224985
13	-0.207665	-1.4387	0.921644
14	0.144377	1.0003	0.161098
15	-0.029739	-0.206	0.581183
16	-0.116755	-0.8089	0.788719

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.295354	-2.0463	0.976886
1	-0.142895	-0.99	0.836433
2	0.324114	2.2455	0.014688
3	0.0092	0.0637	0.47472
4	-0.027224	-0.1886	0.574404
5	0.083246	0.5767	0.283403
6	-0.056013	-0.3881	0.650159
7	-0.179104	-1.2409	0.889658
8	0.092208	0.6388	0.262982
9	0.108339	0.7506	0.228279
10	0.044761	0.3101	0.378908
11	-0.021499	-0.1489	0.55889
12	-0.182226	-1.2625	0.893566
13	0.080258	0.556	0.290383
14	-0.05992	-0.4151	0.660054
15	-0.034822	-0.2413	0.594808
16	-0.092542	-0.6411	0.737762

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.295354 & -2.0463 & 0.976886 \tabularnewline
1 & -0.142895 & -0.99 & 0.836433 \tabularnewline
2 & 0.324114 & 2.2455 & 0.014688 \tabularnewline
3 & 0.0092 & 0.0637 & 0.47472 \tabularnewline
4 & -0.027224 & -0.1886 & 0.574404 \tabularnewline
5 & 0.083246 & 0.5767 & 0.283403 \tabularnewline
6 & -0.056013 & -0.3881 & 0.650159 \tabularnewline
7 & -0.179104 & -1.2409 & 0.889658 \tabularnewline
8 & 0.092208 & 0.6388 & 0.262982 \tabularnewline
9 & 0.108339 & 0.7506 & 0.228279 \tabularnewline
10 & 0.044761 & 0.3101 & 0.378908 \tabularnewline
11 & -0.021499 & -0.1489 & 0.55889 \tabularnewline
12 & -0.182226 & -1.2625 & 0.893566 \tabularnewline
13 & 0.080258 & 0.556 & 0.290383 \tabularnewline
14 & -0.05992 & -0.4151 & 0.660054 \tabularnewline
15 & -0.034822 & -0.2413 & 0.594808 \tabularnewline
16 & -0.092542 & -0.6411 & 0.737762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6095&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]-0.295354[/C][C]-2.0463[/C][C]0.976886[/C][/ROW]
[ROW][C]1[/C][C]-0.142895[/C][C]-0.99[/C][C]0.836433[/C][/ROW]
[ROW][C]2[/C][C]0.324114[/C][C]2.2455[/C][C]0.014688[/C][/ROW]
[ROW][C]3[/C][C]0.0092[/C][C]0.0637[/C][C]0.47472[/C][/ROW]
[ROW][C]4[/C][C]-0.027224[/C][C]-0.1886[/C][C]0.574404[/C][/ROW]
[ROW][C]5[/C][C]0.083246[/C][C]0.5767[/C][C]0.283403[/C][/ROW]
[ROW][C]6[/C][C]-0.056013[/C][C]-0.3881[/C][C]0.650159[/C][/ROW]
[ROW][C]7[/C][C]-0.179104[/C][C]-1.2409[/C][C]0.889658[/C][/ROW]
[ROW][C]8[/C][C]0.092208[/C][C]0.6388[/C][C]0.262982[/C][/ROW]
[ROW][C]9[/C][C]0.108339[/C][C]0.7506[/C][C]0.228279[/C][/ROW]
[ROW][C]10[/C][C]0.044761[/C][C]0.3101[/C][C]0.378908[/C][/ROW]
[ROW][C]11[/C][C]-0.021499[/C][C]-0.1489[/C][C]0.55889[/C][/ROW]
[ROW][C]12[/C][C]-0.182226[/C][C]-1.2625[/C][C]0.893566[/C][/ROW]
[ROW][C]13[/C][C]0.080258[/C][C]0.556[/C][C]0.290383[/C][/ROW]
[ROW][C]14[/C][C]-0.05992[/C][C]-0.4151[/C][C]0.660054[/C][/ROW]
[ROW][C]15[/C][C]-0.034822[/C][C]-0.2413[/C][C]0.594808[/C][/ROW]
[ROW][C]16[/C][C]-0.092542[/C][C]-0.6411[/C][C]0.737762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6095&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6095&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	-0.295354	-2.0463	0.976886
1	-0.142895	-0.99	0.836433
2	0.324114	2.2455	0.014688
3	0.0092	0.0637	0.47472
4	-0.027224	-0.1886	0.574404
5	0.083246	0.5767	0.283403
6	-0.056013	-0.3881	0.650159
7	-0.179104	-1.2409	0.889658
8	0.092208	0.6388	0.262982
9	0.108339	0.7506	0.228279
10	0.044761	0.3101	0.378908
11	-0.021499	-0.1489	0.55889
12	-0.182226	-1.2625	0.893566
13	0.080258	0.556	0.290383
14	-0.05992	-0.4151	0.660054
15	-0.034822	-0.2413	0.594808
16	-0.092542	-0.6411	0.737762

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.5 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.5 ; par3 = 0 ; par4 = 1 ; 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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Figures (Output of Computation)

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