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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 20 Dec 2007 06:46:01 -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/Dec/20/t11981572873ybw3wiwg2ypy9b.htm/, Retrieved Mon, 29 Apr 2024 13:02:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4716, Retrieved Mon, 29 Apr 2024 13:02:34 +0000

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No (this computation is public)

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Estimated Impact

206

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-       [(Partial) Autocorrelation Function] [Q1] [2007-12-20 13:46:01] [157a0cf3c12a7482b4e6935b4c49d48f] [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	'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 & 2 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=4716&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4716&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4716&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.4261	0
1	0.237331	1.9998	0.024675
2	-0.067933	-0.5724	0.715574
3	-0.010448	-0.088	0.534953
4	-0.072056	-0.6072	0.727159
5	0.019748	0.1664	0.434158
6	-0.059576	-0.502	0.691388
7	-0.014698	-0.1238	0.549106
8	0.047451	0.3998	0.34524
9	-0.188034	-1.5844	0.941226
10	-0.129744	-1.0932	0.861009
11	0.0894	0.7533	0.226882
12	0.173707	1.4637	0.073848
13	0.036017	0.3035	0.381204
14	-0.27791	-2.3417	0.988997
15	-0.043356	-0.3653	0.642021
16	0.074439	0.6272	0.26626
17	0.01719	0.1448	0.442623

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4261 & 0 \tabularnewline
1 & 0.237331 & 1.9998 & 0.024675 \tabularnewline
2 & -0.067933 & -0.5724 & 0.715574 \tabularnewline
3 & -0.010448 & -0.088 & 0.534953 \tabularnewline
4 & -0.072056 & -0.6072 & 0.727159 \tabularnewline
5 & 0.019748 & 0.1664 & 0.434158 \tabularnewline
6 & -0.059576 & -0.502 & 0.691388 \tabularnewline
7 & -0.014698 & -0.1238 & 0.549106 \tabularnewline
8 & 0.047451 & 0.3998 & 0.34524 \tabularnewline
9 & -0.188034 & -1.5844 & 0.941226 \tabularnewline
10 & -0.129744 & -1.0932 & 0.861009 \tabularnewline
11 & 0.0894 & 0.7533 & 0.226882 \tabularnewline
12 & 0.173707 & 1.4637 & 0.073848 \tabularnewline
13 & 0.036017 & 0.3035 & 0.381204 \tabularnewline
14 & -0.27791 & -2.3417 & 0.988997 \tabularnewline
15 & -0.043356 & -0.3653 & 0.642021 \tabularnewline
16 & 0.074439 & 0.6272 & 0.26626 \tabularnewline
17 & 0.01719 & 0.1448 & 0.442623 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4716&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]8.4261[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.237331[/C][C]1.9998[/C][C]0.024675[/C][/ROW]
[ROW][C]2[/C][C]-0.067933[/C][C]-0.5724[/C][C]0.715574[/C][/ROW]
[ROW][C]3[/C][C]-0.010448[/C][C]-0.088[/C][C]0.534953[/C][/ROW]
[ROW][C]4[/C][C]-0.072056[/C][C]-0.6072[/C][C]0.727159[/C][/ROW]
[ROW][C]5[/C][C]0.019748[/C][C]0.1664[/C][C]0.434158[/C][/ROW]
[ROW][C]6[/C][C]-0.059576[/C][C]-0.502[/C][C]0.691388[/C][/ROW]
[ROW][C]7[/C][C]-0.014698[/C][C]-0.1238[/C][C]0.549106[/C][/ROW]
[ROW][C]8[/C][C]0.047451[/C][C]0.3998[/C][C]0.34524[/C][/ROW]
[ROW][C]9[/C][C]-0.188034[/C][C]-1.5844[/C][C]0.941226[/C][/ROW]
[ROW][C]10[/C][C]-0.129744[/C][C]-1.0932[/C][C]0.861009[/C][/ROW]
[ROW][C]11[/C][C]0.0894[/C][C]0.7533[/C][C]0.226882[/C][/ROW]
[ROW][C]12[/C][C]0.173707[/C][C]1.4637[/C][C]0.073848[/C][/ROW]
[ROW][C]13[/C][C]0.036017[/C][C]0.3035[/C][C]0.381204[/C][/ROW]
[ROW][C]14[/C][C]-0.27791[/C][C]-2.3417[/C][C]0.988997[/C][/ROW]
[ROW][C]15[/C][C]-0.043356[/C][C]-0.3653[/C][C]0.642021[/C][/ROW]
[ROW][C]16[/C][C]0.074439[/C][C]0.6272[/C][C]0.26626[/C][/ROW]
[ROW][C]17[/C][C]0.01719[/C][C]0.1448[/C][C]0.442623[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4716&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4716&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	8.4261	0
1	0.237331	1.9998	0.024675
2	-0.067933	-0.5724	0.715574
3	-0.010448	-0.088	0.534953
4	-0.072056	-0.6072	0.727159
5	0.019748	0.1664	0.434158
6	-0.059576	-0.502	0.691388
7	-0.014698	-0.1238	0.549106
8	0.047451	0.3998	0.34524
9	-0.188034	-1.5844	0.941226
10	-0.129744	-1.0932	0.861009
11	0.0894	0.7533	0.226882
12	0.173707	1.4637	0.073848
13	0.036017	0.3035	0.381204
14	-0.27791	-2.3417	0.988997
15	-0.043356	-0.3653	0.642021
16	0.074439	0.6272	0.26626
17	0.01719	0.1448	0.442623

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.237331	1.9998	0.024675
1	-0.131675	-1.1095	0.864524
2	0.042109	0.3548	0.361891
3	-0.096038	-0.8092	0.789457
4	0.071523	0.6027	0.274326
5	-0.110548	-0.9315	0.822622
6	0.049274	0.4152	0.339626
7	0.011448	0.0965	0.461714
8	-0.210706	-1.7754	0.959945
9	-0.029058	-0.2448	0.596359
10	0.108482	0.9141	0.181884
11	0.132139	1.1134	0.134642
12	-0.073507	-0.6194	0.731176
13	-0.281039	-2.3681	0.989696
14	0.116664	0.983	0.164466
15	0.029481	0.2484	0.402267
16	0.048033	0.4047	0.343444
17	0.045571	0.384	0.351068

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.237331 & 1.9998 & 0.024675 \tabularnewline
1 & -0.131675 & -1.1095 & 0.864524 \tabularnewline
2 & 0.042109 & 0.3548 & 0.361891 \tabularnewline
3 & -0.096038 & -0.8092 & 0.789457 \tabularnewline
4 & 0.071523 & 0.6027 & 0.274326 \tabularnewline
5 & -0.110548 & -0.9315 & 0.822622 \tabularnewline
6 & 0.049274 & 0.4152 & 0.339626 \tabularnewline
7 & 0.011448 & 0.0965 & 0.461714 \tabularnewline
8 & -0.210706 & -1.7754 & 0.959945 \tabularnewline
9 & -0.029058 & -0.2448 & 0.596359 \tabularnewline
10 & 0.108482 & 0.9141 & 0.181884 \tabularnewline
11 & 0.132139 & 1.1134 & 0.134642 \tabularnewline
12 & -0.073507 & -0.6194 & 0.731176 \tabularnewline
13 & -0.281039 & -2.3681 & 0.989696 \tabularnewline
14 & 0.116664 & 0.983 & 0.164466 \tabularnewline
15 & 0.029481 & 0.2484 & 0.402267 \tabularnewline
16 & 0.048033 & 0.4047 & 0.343444 \tabularnewline
17 & 0.045571 & 0.384 & 0.351068 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4716&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]0.237331[/C][C]1.9998[/C][C]0.024675[/C][/ROW]
[ROW][C]1[/C][C]-0.131675[/C][C]-1.1095[/C][C]0.864524[/C][/ROW]
[ROW][C]2[/C][C]0.042109[/C][C]0.3548[/C][C]0.361891[/C][/ROW]
[ROW][C]3[/C][C]-0.096038[/C][C]-0.8092[/C][C]0.789457[/C][/ROW]
[ROW][C]4[/C][C]0.071523[/C][C]0.6027[/C][C]0.274326[/C][/ROW]
[ROW][C]5[/C][C]-0.110548[/C][C]-0.9315[/C][C]0.822622[/C][/ROW]
[ROW][C]6[/C][C]0.049274[/C][C]0.4152[/C][C]0.339626[/C][/ROW]
[ROW][C]7[/C][C]0.011448[/C][C]0.0965[/C][C]0.461714[/C][/ROW]
[ROW][C]8[/C][C]-0.210706[/C][C]-1.7754[/C][C]0.959945[/C][/ROW]
[ROW][C]9[/C][C]-0.029058[/C][C]-0.2448[/C][C]0.596359[/C][/ROW]
[ROW][C]10[/C][C]0.108482[/C][C]0.9141[/C][C]0.181884[/C][/ROW]
[ROW][C]11[/C][C]0.132139[/C][C]1.1134[/C][C]0.134642[/C][/ROW]
[ROW][C]12[/C][C]-0.073507[/C][C]-0.6194[/C][C]0.731176[/C][/ROW]
[ROW][C]13[/C][C]-0.281039[/C][C]-2.3681[/C][C]0.989696[/C][/ROW]
[ROW][C]14[/C][C]0.116664[/C][C]0.983[/C][C]0.164466[/C][/ROW]
[ROW][C]15[/C][C]0.029481[/C][C]0.2484[/C][C]0.402267[/C][/ROW]
[ROW][C]16[/C][C]0.048033[/C][C]0.4047[/C][C]0.343444[/C][/ROW]
[ROW][C]17[/C][C]0.045571[/C][C]0.384[/C][C]0.351068[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4716&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4716&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	0.237331	1.9998	0.024675
1	-0.131675	-1.1095	0.864524
2	0.042109	0.3548	0.361891
3	-0.096038	-0.8092	0.789457
4	0.071523	0.6027	0.274326
5	-0.110548	-0.9315	0.822622
6	0.049274	0.4152	0.339626
7	0.011448	0.0965	0.461714
8	-0.210706	-1.7754	0.959945
9	-0.029058	-0.2448	0.596359
10	0.108482	0.9141	0.181884
11	0.132139	1.1134	0.134642
12	-0.073507	-0.6194	0.731176
13	-0.281039	-2.3681	0.989696
14	0.116664	0.983	0.164466
15	0.029481	0.2484	0.402267
16	0.048033	0.4047	0.343444
17	0.045571	0.384	0.351068

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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