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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 16 Dec 2007 03:52:58 -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/16/t1197801509nhdv5vch5ej30zj.htm/, Retrieved Thu, 02 May 2024 12:04:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4128, Retrieved Thu, 02 May 2024 12:04:00 +0000

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No (this computation is public)

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Estimated Impact

239

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

-       [(Partial) Autocorrelation Function] [autocorrelatiefun...] [2007-12-16 10:52:58] [bd02e85be52eb1cb060a2c60779eb820] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4128&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]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=4128&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4128&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.6811	0
1	0.014962	0.1149	0.454448
2	-0.135055	-1.0374	0.848104
3	-0.212342	-1.631	0.945895
4	0.020169	0.1549	0.438705
5	0.107245	0.8238	0.206697
6	0.092621	0.7114	0.239808
7	0.190307	1.4618	0.074555
8	-0.057085	-0.4385	0.668679
9	-0.048947	-0.376	0.645857
10	-0.173621	-1.3336	0.906271
11	0.045201	0.3472	0.36484
12	-0.014881	-0.1143	0.545306
13	0.061584	0.473	0.318968
14	0.09378	0.7203	0.237082
15	0.029558	0.227	0.41059
16	-0.226977	-1.7434	0.956768
17	-0.064836	-0.498	0.689838

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & 0.014962 & 0.1149 & 0.454448 \tabularnewline
2 & -0.135055 & -1.0374 & 0.848104 \tabularnewline
3 & -0.212342 & -1.631 & 0.945895 \tabularnewline
4 & 0.020169 & 0.1549 & 0.438705 \tabularnewline
5 & 0.107245 & 0.8238 & 0.206697 \tabularnewline
6 & 0.092621 & 0.7114 & 0.239808 \tabularnewline
7 & 0.190307 & 1.4618 & 0.074555 \tabularnewline
8 & -0.057085 & -0.4385 & 0.668679 \tabularnewline
9 & -0.048947 & -0.376 & 0.645857 \tabularnewline
10 & -0.173621 & -1.3336 & 0.906271 \tabularnewline
11 & 0.045201 & 0.3472 & 0.36484 \tabularnewline
12 & -0.014881 & -0.1143 & 0.545306 \tabularnewline
13 & 0.061584 & 0.473 & 0.318968 \tabularnewline
14 & 0.09378 & 0.7203 & 0.237082 \tabularnewline
15 & 0.029558 & 0.227 & 0.41059 \tabularnewline
16 & -0.226977 & -1.7434 & 0.956768 \tabularnewline
17 & -0.064836 & -0.498 & 0.689838 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4128&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]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.014962[/C][C]0.1149[/C][C]0.454448[/C][/ROW]
[ROW][C]2[/C][C]-0.135055[/C][C]-1.0374[/C][C]0.848104[/C][/ROW]
[ROW][C]3[/C][C]-0.212342[/C][C]-1.631[/C][C]0.945895[/C][/ROW]
[ROW][C]4[/C][C]0.020169[/C][C]0.1549[/C][C]0.438705[/C][/ROW]
[ROW][C]5[/C][C]0.107245[/C][C]0.8238[/C][C]0.206697[/C][/ROW]
[ROW][C]6[/C][C]0.092621[/C][C]0.7114[/C][C]0.239808[/C][/ROW]
[ROW][C]7[/C][C]0.190307[/C][C]1.4618[/C][C]0.074555[/C][/ROW]
[ROW][C]8[/C][C]-0.057085[/C][C]-0.4385[/C][C]0.668679[/C][/ROW]
[ROW][C]9[/C][C]-0.048947[/C][C]-0.376[/C][C]0.645857[/C][/ROW]
[ROW][C]10[/C][C]-0.173621[/C][C]-1.3336[/C][C]0.906271[/C][/ROW]
[ROW][C]11[/C][C]0.045201[/C][C]0.3472[/C][C]0.36484[/C][/ROW]
[ROW][C]12[/C][C]-0.014881[/C][C]-0.1143[/C][C]0.545306[/C][/ROW]
[ROW][C]13[/C][C]0.061584[/C][C]0.473[/C][C]0.318968[/C][/ROW]
[ROW][C]14[/C][C]0.09378[/C][C]0.7203[/C][C]0.237082[/C][/ROW]
[ROW][C]15[/C][C]0.029558[/C][C]0.227[/C][C]0.41059[/C][/ROW]
[ROW][C]16[/C][C]-0.226977[/C][C]-1.7434[/C][C]0.956768[/C][/ROW]
[ROW][C]17[/C][C]-0.064836[/C][C]-0.498[/C][C]0.689838[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4128&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4128&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	7.6811	0
1	0.014962	0.1149	0.454448
2	-0.135055	-1.0374	0.848104
3	-0.212342	-1.631	0.945895
4	0.020169	0.1549	0.438705
5	0.107245	0.8238	0.206697
6	0.092621	0.7114	0.239808
7	0.190307	1.4618	0.074555
8	-0.057085	-0.4385	0.668679
9	-0.048947	-0.376	0.645857
10	-0.173621	-1.3336	0.906271
11	0.045201	0.3472	0.36484
12	-0.014881	-0.1143	0.545306
13	0.061584	0.473	0.318968
14	0.09378	0.7203	0.237082
15	0.029558	0.227	0.41059
16	-0.226977	-1.7434	0.956768
17	-0.064836	-0.498	0.689838

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.014962	0.1149	0.454448
1	-0.13531	-1.0393	0.848555
2	-0.211951	-1.628	0.945576
3	0.003274	0.0252	0.49001
4	0.054324	0.4173	0.338998
5	0.056133	0.4312	0.33396
6	0.233156	1.7909	0.039219
7	0.002762	0.0212	0.491573
8	0.033411	0.2566	0.399177
9	-0.124835	-0.9589	0.829233
10	-0.005413	-0.0416	0.516512
11	-0.11581	-0.8896	0.81134
12	-0.01861	-0.1429	0.556589
13	0.074262	0.5704	0.28528
14	0.075261	0.5781	0.282702
15	-0.186984	-1.4362	0.921893
16	0.048484	0.3724	0.35546
17	-0.092053	-0.7071	0.758848

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.014962 & 0.1149 & 0.454448 \tabularnewline
1 & -0.13531 & -1.0393 & 0.848555 \tabularnewline
2 & -0.211951 & -1.628 & 0.945576 \tabularnewline
3 & 0.003274 & 0.0252 & 0.49001 \tabularnewline
4 & 0.054324 & 0.4173 & 0.338998 \tabularnewline
5 & 0.056133 & 0.4312 & 0.33396 \tabularnewline
6 & 0.233156 & 1.7909 & 0.039219 \tabularnewline
7 & 0.002762 & 0.0212 & 0.491573 \tabularnewline
8 & 0.033411 & 0.2566 & 0.399177 \tabularnewline
9 & -0.124835 & -0.9589 & 0.829233 \tabularnewline
10 & -0.005413 & -0.0416 & 0.516512 \tabularnewline
11 & -0.11581 & -0.8896 & 0.81134 \tabularnewline
12 & -0.01861 & -0.1429 & 0.556589 \tabularnewline
13 & 0.074262 & 0.5704 & 0.28528 \tabularnewline
14 & 0.075261 & 0.5781 & 0.282702 \tabularnewline
15 & -0.186984 & -1.4362 & 0.921893 \tabularnewline
16 & 0.048484 & 0.3724 & 0.35546 \tabularnewline
17 & -0.092053 & -0.7071 & 0.758848 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4128&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]0.014962[/C][C]0.1149[/C][C]0.454448[/C][/ROW]
[ROW][C]1[/C][C]-0.13531[/C][C]-1.0393[/C][C]0.848555[/C][/ROW]
[ROW][C]2[/C][C]-0.211951[/C][C]-1.628[/C][C]0.945576[/C][/ROW]
[ROW][C]3[/C][C]0.003274[/C][C]0.0252[/C][C]0.49001[/C][/ROW]
[ROW][C]4[/C][C]0.054324[/C][C]0.4173[/C][C]0.338998[/C][/ROW]
[ROW][C]5[/C][C]0.056133[/C][C]0.4312[/C][C]0.33396[/C][/ROW]
[ROW][C]6[/C][C]0.233156[/C][C]1.7909[/C][C]0.039219[/C][/ROW]
[ROW][C]7[/C][C]0.002762[/C][C]0.0212[/C][C]0.491573[/C][/ROW]
[ROW][C]8[/C][C]0.033411[/C][C]0.2566[/C][C]0.399177[/C][/ROW]
[ROW][C]9[/C][C]-0.124835[/C][C]-0.9589[/C][C]0.829233[/C][/ROW]
[ROW][C]10[/C][C]-0.005413[/C][C]-0.0416[/C][C]0.516512[/C][/ROW]
[ROW][C]11[/C][C]-0.11581[/C][C]-0.8896[/C][C]0.81134[/C][/ROW]
[ROW][C]12[/C][C]-0.01861[/C][C]-0.1429[/C][C]0.556589[/C][/ROW]
[ROW][C]13[/C][C]0.074262[/C][C]0.5704[/C][C]0.28528[/C][/ROW]
[ROW][C]14[/C][C]0.075261[/C][C]0.5781[/C][C]0.282702[/C][/ROW]
[ROW][C]15[/C][C]-0.186984[/C][C]-1.4362[/C][C]0.921893[/C][/ROW]
[ROW][C]16[/C][C]0.048484[/C][C]0.3724[/C][C]0.35546[/C][/ROW]
[ROW][C]17[/C][C]-0.092053[/C][C]-0.7071[/C][C]0.758848[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4128&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4128&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	0.014962	0.1149	0.454448
1	-0.13531	-1.0393	0.848555
2	-0.211951	-1.628	0.945576
3	0.003274	0.0252	0.49001
4	0.054324	0.4173	0.338998
5	0.056133	0.4312	0.33396
6	0.233156	1.7909	0.039219
7	0.002762	0.0212	0.491573
8	0.033411	0.2566	0.399177
9	-0.124835	-0.9589	0.829233
10	-0.005413	-0.0416	0.516512
11	-0.11581	-0.8896	0.81134
12	-0.01861	-0.1429	0.556589
13	0.074262	0.5704	0.28528
14	0.075261	0.5781	0.282702
15	-0.186984	-1.4362	0.921893
16	0.048484	0.3724	0.35546
17	-0.092053	-0.7071	0.758848

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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