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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 21 Dec 2007 04:13:01 -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/21/t1198234496l23rw2mnquil0aq.htm/, Retrieved Tue, 07 May 2024 05:04:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4796, Retrieved Tue, 07 May 2024 05:04:44 +0000

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Estimated Impact

235

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

-       [(Partial) Autocorrelation Function] [] [2007-12-21 11:13:01] [d41d8cd98f00b204e9800998ecf8427e] [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=4796&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=4796&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4796&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	8.4853	0
1	0.79963	6.7851	0
2	0.513833	4.36	2.1e-05
3	0.261503	2.2189	0.014822
4	0.100401	0.8519	0.198538
5	0.03718	0.3155	0.376653
6	0.000199	0.0017	0.499328
7	0.004282	0.0363	0.485558
8	0.039986	0.3393	0.367688
9	0.155265	1.3175	0.09593
10	0.326173	2.7677	0.003586
11	0.509282	4.3214	2.4e-05
12	0.612641	5.1984	1e-06
13	0.440121	3.7345	0.000187
14	0.220794	1.8735	0.032529
15	0.031464	0.267	0.395122
16	-0.088201	-0.7484	0.771674
17	-0.142218	-1.2068	0.884262

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.79963 & 6.7851 & 0 \tabularnewline
2 & 0.513833 & 4.36 & 2.1e-05 \tabularnewline
3 & 0.261503 & 2.2189 & 0.014822 \tabularnewline
4 & 0.100401 & 0.8519 & 0.198538 \tabularnewline
5 & 0.03718 & 0.3155 & 0.376653 \tabularnewline
6 & 0.000199 & 0.0017 & 0.499328 \tabularnewline
7 & 0.004282 & 0.0363 & 0.485558 \tabularnewline
8 & 0.039986 & 0.3393 & 0.367688 \tabularnewline
9 & 0.155265 & 1.3175 & 0.09593 \tabularnewline
10 & 0.326173 & 2.7677 & 0.003586 \tabularnewline
11 & 0.509282 & 4.3214 & 2.4e-05 \tabularnewline
12 & 0.612641 & 5.1984 & 1e-06 \tabularnewline
13 & 0.440121 & 3.7345 & 0.000187 \tabularnewline
14 & 0.220794 & 1.8735 & 0.032529 \tabularnewline
15 & 0.031464 & 0.267 & 0.395122 \tabularnewline
16 & -0.088201 & -0.7484 & 0.771674 \tabularnewline
17 & -0.142218 & -1.2068 & 0.884262 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4796&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]0.79963[/C][C]6.7851[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.513833[/C][C]4.36[/C][C]2.1e-05[/C][/ROW]
[ROW][C]3[/C][C]0.261503[/C][C]2.2189[/C][C]0.014822[/C][/ROW]
[ROW][C]4[/C][C]0.100401[/C][C]0.8519[/C][C]0.198538[/C][/ROW]
[ROW][C]5[/C][C]0.03718[/C][C]0.3155[/C][C]0.376653[/C][/ROW]
[ROW][C]6[/C][C]0.000199[/C][C]0.0017[/C][C]0.499328[/C][/ROW]
[ROW][C]7[/C][C]0.004282[/C][C]0.0363[/C][C]0.485558[/C][/ROW]
[ROW][C]8[/C][C]0.039986[/C][C]0.3393[/C][C]0.367688[/C][/ROW]
[ROW][C]9[/C][C]0.155265[/C][C]1.3175[/C][C]0.09593[/C][/ROW]
[ROW][C]10[/C][C]0.326173[/C][C]2.7677[/C][C]0.003586[/C][/ROW]
[ROW][C]11[/C][C]0.509282[/C][C]4.3214[/C][C]2.4e-05[/C][/ROW]
[ROW][C]12[/C][C]0.612641[/C][C]5.1984[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.440121[/C][C]3.7345[/C][C]0.000187[/C][/ROW]
[ROW][C]14[/C][C]0.220794[/C][C]1.8735[/C][C]0.032529[/C][/ROW]
[ROW][C]15[/C][C]0.031464[/C][C]0.267[/C][C]0.395122[/C][/ROW]
[ROW][C]16[/C][C]-0.088201[/C][C]-0.7484[/C][C]0.771674[/C][/ROW]
[ROW][C]17[/C][C]-0.142218[/C][C]-1.2068[/C][C]0.884262[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4796&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4796&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	0.79963	6.7851	0
2	0.513833	4.36	2.1e-05
3	0.261503	2.2189	0.014822
4	0.100401	0.8519	0.198538
5	0.03718	0.3155	0.376653
6	0.000199	0.0017	0.499328
7	0.004282	0.0363	0.485558
8	0.039986	0.3393	0.367688
9	0.155265	1.3175	0.09593
10	0.326173	2.7677	0.003586
11	0.509282	4.3214	2.4e-05
12	0.612641	5.1984	1e-06
13	0.440121	3.7345	0.000187
14	0.220794	1.8735	0.032529
15	0.031464	0.267	0.395122
16	-0.088201	-0.7484	0.771674
17	-0.142218	-1.2068	0.884262

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.79963	6.7851	0
1	-0.348249	-2.955	0.997888
2	-0.044152	-0.3746	0.645487
3	0.038846	0.3296	0.371324
4	0.05926	0.5028	0.308307
5	-0.088534	-0.7512	0.772521
6	0.086829	0.7368	0.231829
7	0.062796	0.5328	0.297891
8	0.256775	2.1788	0.01631
9	0.210526	1.7864	0.039124
10	0.260511	2.2105	0.015124
11	0.08445	0.7166	0.237975
12	-0.550817	-4.6738	0.999993
13	0.174299	1.479	0.071754
14	-0.040867	-0.3468	0.635111
15	-0.091243	-0.7742	0.779333
16	-0.088394	-0.75	0.772165
17	0.041631	0.3532	0.362467

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.79963 & 6.7851 & 0 \tabularnewline
1 & -0.348249 & -2.955 & 0.997888 \tabularnewline
2 & -0.044152 & -0.3746 & 0.645487 \tabularnewline
3 & 0.038846 & 0.3296 & 0.371324 \tabularnewline
4 & 0.05926 & 0.5028 & 0.308307 \tabularnewline
5 & -0.088534 & -0.7512 & 0.772521 \tabularnewline
6 & 0.086829 & 0.7368 & 0.231829 \tabularnewline
7 & 0.062796 & 0.5328 & 0.297891 \tabularnewline
8 & 0.256775 & 2.1788 & 0.01631 \tabularnewline
9 & 0.210526 & 1.7864 & 0.039124 \tabularnewline
10 & 0.260511 & 2.2105 & 0.015124 \tabularnewline
11 & 0.08445 & 0.7166 & 0.237975 \tabularnewline
12 & -0.550817 & -4.6738 & 0.999993 \tabularnewline
13 & 0.174299 & 1.479 & 0.071754 \tabularnewline
14 & -0.040867 & -0.3468 & 0.635111 \tabularnewline
15 & -0.091243 & -0.7742 & 0.779333 \tabularnewline
16 & -0.088394 & -0.75 & 0.772165 \tabularnewline
17 & 0.041631 & 0.3532 & 0.362467 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4796&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]0.79963[/C][C]6.7851[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.348249[/C][C]-2.955[/C][C]0.997888[/C][/ROW]
[ROW][C]2[/C][C]-0.044152[/C][C]-0.3746[/C][C]0.645487[/C][/ROW]
[ROW][C]3[/C][C]0.038846[/C][C]0.3296[/C][C]0.371324[/C][/ROW]
[ROW][C]4[/C][C]0.05926[/C][C]0.5028[/C][C]0.308307[/C][/ROW]
[ROW][C]5[/C][C]-0.088534[/C][C]-0.7512[/C][C]0.772521[/C][/ROW]
[ROW][C]6[/C][C]0.086829[/C][C]0.7368[/C][C]0.231829[/C][/ROW]
[ROW][C]7[/C][C]0.062796[/C][C]0.5328[/C][C]0.297891[/C][/ROW]
[ROW][C]8[/C][C]0.256775[/C][C]2.1788[/C][C]0.01631[/C][/ROW]
[ROW][C]9[/C][C]0.210526[/C][C]1.7864[/C][C]0.039124[/C][/ROW]
[ROW][C]10[/C][C]0.260511[/C][C]2.2105[/C][C]0.015124[/C][/ROW]
[ROW][C]11[/C][C]0.08445[/C][C]0.7166[/C][C]0.237975[/C][/ROW]
[ROW][C]12[/C][C]-0.550817[/C][C]-4.6738[/C][C]0.999993[/C][/ROW]
[ROW][C]13[/C][C]0.174299[/C][C]1.479[/C][C]0.071754[/C][/ROW]
[ROW][C]14[/C][C]-0.040867[/C][C]-0.3468[/C][C]0.635111[/C][/ROW]
[ROW][C]15[/C][C]-0.091243[/C][C]-0.7742[/C][C]0.779333[/C][/ROW]
[ROW][C]16[/C][C]-0.088394[/C][C]-0.75[/C][C]0.772165[/C][/ROW]
[ROW][C]17[/C][C]0.041631[/C][C]0.3532[/C][C]0.362467[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4796&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4796&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	0.79963	6.7851	0
1	-0.348249	-2.955	0.997888
2	-0.044152	-0.3746	0.645487
3	0.038846	0.3296	0.371324
4	0.05926	0.5028	0.308307
5	-0.088534	-0.7512	0.772521
6	0.086829	0.7368	0.231829
7	0.062796	0.5328	0.297891
8	0.256775	2.1788	0.01631
9	0.210526	1.7864	0.039124
10	0.260511	2.2105	0.015124
11	0.08445	0.7166	0.237975
12	-0.550817	-4.6738	0.999993
13	0.174299	1.479	0.071754
14	-0.040867	-0.3468	0.635111
15	-0.091243	-0.7742	0.779333
16	-0.088394	-0.75	0.772165
17	0.041631	0.3532	0.362467

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = Default ; par2 = -2.0 ; 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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