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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 03 Dec 2007 13:38:33 -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/03/t11967135896byrcp2cc1s6khg.htm/, Retrieved Sat, 04 May 2024 03:58:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2357, Retrieved Sat, 04 May 2024 03:58:51 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

207

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

-       [(Partial) Autocorrelation Function] [ARMA 2] [2007-12-03 20:38:33] [640491d00f3c9cca22cbf779aa38ac16] [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=2357&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=2357&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2357&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	8.0623	0
1	0.970988	7.8284	0
2	0.935722	7.544	0
3	0.896829	7.2305	0
4	0.853462	6.8808	0
5	0.808917	6.5217	0
6	0.763227	6.1533	0
7	0.714627	5.7615	0
8	0.665086	5.3621	1e-06
9	0.616487	4.9703	3e-06
10	0.562048	4.5314	1.3e-05
11	0.50126	4.0413	7.2e-05
12	0.446256	3.5978	0.00031
13	0.390257	3.1464	0.001247
14	0.329887	2.6596	0.00492
15	0.270856	2.1837	0.016299
16	0.207966	1.6767	0.049205
17	0.148979	1.2011	0.117034

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.0623 & 0 \tabularnewline
1 & 0.970988 & 7.8284 & 0 \tabularnewline
2 & 0.935722 & 7.544 & 0 \tabularnewline
3 & 0.896829 & 7.2305 & 0 \tabularnewline
4 & 0.853462 & 6.8808 & 0 \tabularnewline
5 & 0.808917 & 6.5217 & 0 \tabularnewline
6 & 0.763227 & 6.1533 & 0 \tabularnewline
7 & 0.714627 & 5.7615 & 0 \tabularnewline
8 & 0.665086 & 5.3621 & 1e-06 \tabularnewline
9 & 0.616487 & 4.9703 & 3e-06 \tabularnewline
10 & 0.562048 & 4.5314 & 1.3e-05 \tabularnewline
11 & 0.50126 & 4.0413 & 7.2e-05 \tabularnewline
12 & 0.446256 & 3.5978 & 0.00031 \tabularnewline
13 & 0.390257 & 3.1464 & 0.001247 \tabularnewline
14 & 0.329887 & 2.6596 & 0.00492 \tabularnewline
15 & 0.270856 & 2.1837 & 0.016299 \tabularnewline
16 & 0.207966 & 1.6767 & 0.049205 \tabularnewline
17 & 0.148979 & 1.2011 & 0.117034 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2357&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]8.0623[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.970988[/C][C]7.8284[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.935722[/C][C]7.544[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.896829[/C][C]7.2305[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.853462[/C][C]6.8808[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.808917[/C][C]6.5217[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.763227[/C][C]6.1533[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.714627[/C][C]5.7615[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.665086[/C][C]5.3621[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]0.616487[/C][C]4.9703[/C][C]3e-06[/C][/ROW]
[ROW][C]10[/C][C]0.562048[/C][C]4.5314[/C][C]1.3e-05[/C][/ROW]
[ROW][C]11[/C][C]0.50126[/C][C]4.0413[/C][C]7.2e-05[/C][/ROW]
[ROW][C]12[/C][C]0.446256[/C][C]3.5978[/C][C]0.00031[/C][/ROW]
[ROW][C]13[/C][C]0.390257[/C][C]3.1464[/C][C]0.001247[/C][/ROW]
[ROW][C]14[/C][C]0.329887[/C][C]2.6596[/C][C]0.00492[/C][/ROW]
[ROW][C]15[/C][C]0.270856[/C][C]2.1837[/C][C]0.016299[/C][/ROW]
[ROW][C]16[/C][C]0.207966[/C][C]1.6767[/C][C]0.049205[/C][/ROW]
[ROW][C]17[/C][C]0.148979[/C][C]1.2011[/C][C]0.117034[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2357&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2357&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	8.0623	0
1	0.970988	7.8284	0
2	0.935722	7.544	0
3	0.896829	7.2305	0
4	0.853462	6.8808	0
5	0.808917	6.5217	0
6	0.763227	6.1533	0
7	0.714627	5.7615	0
8	0.665086	5.3621	1e-06
9	0.616487	4.9703	3e-06
10	0.562048	4.5314	1.3e-05
11	0.50126	4.0413	7.2e-05
12	0.446256	3.5978	0.00031
13	0.390257	3.1464	0.001247
14	0.329887	2.6596	0.00492
15	0.270856	2.1837	0.016299
16	0.207966	1.6767	0.049205
17	0.148979	1.2011	0.117034

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.970988	7.8284	0
1	-0.124087	-1.0004	0.839591
2	-0.071049	-0.5728	0.715628
3	-0.088585	-0.7142	0.761169
4	-0.02753	-0.222	0.587478
5	-0.035739	-0.2881	0.612921
6	-0.069578	-0.561	0.711621
7	-0.034322	-0.2767	0.608561
8	-0.004942	-0.0398	0.515831
9	-0.132731	-1.0701	0.855737
10	-0.134401	-1.0836	0.858722
11	0.089979	0.7254	0.235396
12	-0.054634	-0.4405	0.669472
13	-0.120147	-0.9687	0.831847
14	-0.020083	-0.1619	0.564062
15	-0.107173	-0.8641	0.804633
16	0.044283	0.357	0.361115
17	0.144692	1.1665	0.123828

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.970988 & 7.8284 & 0 \tabularnewline
1 & -0.124087 & -1.0004 & 0.839591 \tabularnewline
2 & -0.071049 & -0.5728 & 0.715628 \tabularnewline
3 & -0.088585 & -0.7142 & 0.761169 \tabularnewline
4 & -0.02753 & -0.222 & 0.587478 \tabularnewline
5 & -0.035739 & -0.2881 & 0.612921 \tabularnewline
6 & -0.069578 & -0.561 & 0.711621 \tabularnewline
7 & -0.034322 & -0.2767 & 0.608561 \tabularnewline
8 & -0.004942 & -0.0398 & 0.515831 \tabularnewline
9 & -0.132731 & -1.0701 & 0.855737 \tabularnewline
10 & -0.134401 & -1.0836 & 0.858722 \tabularnewline
11 & 0.089979 & 0.7254 & 0.235396 \tabularnewline
12 & -0.054634 & -0.4405 & 0.669472 \tabularnewline
13 & -0.120147 & -0.9687 & 0.831847 \tabularnewline
14 & -0.020083 & -0.1619 & 0.564062 \tabularnewline
15 & -0.107173 & -0.8641 & 0.804633 \tabularnewline
16 & 0.044283 & 0.357 & 0.361115 \tabularnewline
17 & 0.144692 & 1.1665 & 0.123828 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2357&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]0.970988[/C][C]7.8284[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.124087[/C][C]-1.0004[/C][C]0.839591[/C][/ROW]
[ROW][C]2[/C][C]-0.071049[/C][C]-0.5728[/C][C]0.715628[/C][/ROW]
[ROW][C]3[/C][C]-0.088585[/C][C]-0.7142[/C][C]0.761169[/C][/ROW]
[ROW][C]4[/C][C]-0.02753[/C][C]-0.222[/C][C]0.587478[/C][/ROW]
[ROW][C]5[/C][C]-0.035739[/C][C]-0.2881[/C][C]0.612921[/C][/ROW]
[ROW][C]6[/C][C]-0.069578[/C][C]-0.561[/C][C]0.711621[/C][/ROW]
[ROW][C]7[/C][C]-0.034322[/C][C]-0.2767[/C][C]0.608561[/C][/ROW]
[ROW][C]8[/C][C]-0.004942[/C][C]-0.0398[/C][C]0.515831[/C][/ROW]
[ROW][C]9[/C][C]-0.132731[/C][C]-1.0701[/C][C]0.855737[/C][/ROW]
[ROW][C]10[/C][C]-0.134401[/C][C]-1.0836[/C][C]0.858722[/C][/ROW]
[ROW][C]11[/C][C]0.089979[/C][C]0.7254[/C][C]0.235396[/C][/ROW]
[ROW][C]12[/C][C]-0.054634[/C][C]-0.4405[/C][C]0.669472[/C][/ROW]
[ROW][C]13[/C][C]-0.120147[/C][C]-0.9687[/C][C]0.831847[/C][/ROW]
[ROW][C]14[/C][C]-0.020083[/C][C]-0.1619[/C][C]0.564062[/C][/ROW]
[ROW][C]15[/C][C]-0.107173[/C][C]-0.8641[/C][C]0.804633[/C][/ROW]
[ROW][C]16[/C][C]0.044283[/C][C]0.357[/C][C]0.361115[/C][/ROW]
[ROW][C]17[/C][C]0.144692[/C][C]1.1665[/C][C]0.123828[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2357&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2357&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	0.970988	7.8284	0
1	-0.124087	-1.0004	0.839591
2	-0.071049	-0.5728	0.715628
3	-0.088585	-0.7142	0.761169
4	-0.02753	-0.222	0.587478
5	-0.035739	-0.2881	0.612921
6	-0.069578	-0.561	0.711621
7	-0.034322	-0.2767	0.608561
8	-0.004942	-0.0398	0.515831
9	-0.132731	-1.0701	0.855737
10	-0.134401	-1.0836	0.858722
11	0.089979	0.7254	0.235396
12	-0.054634	-0.4405	0.669472
13	-0.120147	-0.9687	0.831847
14	-0.020083	-0.1619	0.564062
15	-0.107173	-0.8641	0.804633
16	0.044283	0.357	0.361115
17	0.144692	1.1665	0.123828

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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