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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 10 Dec 2008 06:57:47 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/10/t12289175190pbvxwkbh41fge2.htm/, Retrieved Fri, 01 Nov 2024 00:03:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31960, Retrieved Fri, 01 Nov 2024 00:03:23 +0000

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192

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-       [(Partial) Autocorrelation Function] [ACF] [2008-12-10 13:57:47] [5f3e73ccf1ddc75508eed47fa51813d3] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational 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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31960&T=0

[TABLE]
[ROW][C]Summary of computational 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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31960&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31960&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 computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.701568	5.6996	0
2	0.355873	2.8911	0.002596
3	0.004116	0.0334	0.486713
4	-0.429855	-3.4922	0.00043
5	-0.714959	-5.8084	0
6	-0.768645	-6.2445	0
7	-0.684701	-5.5625	0
8	-0.349138	-2.8364	0.003026
9	0.074546	0.6056	0.273423
10	0.364639	2.9623	0.002121
11	0.610181	4.9571	3e-06
12	0.779699	6.3343	0
13	0.572594	4.6518	8e-06
14	0.29033	2.3587	0.010656
15	-0.016233	-0.1319	0.447742
16	-0.334727	-2.7193	0.004175
17	-0.562763	-4.5719	1.1e-05
18	-0.623911	-5.0687	2e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.701568 & 5.6996 & 0 \tabularnewline
2 & 0.355873 & 2.8911 & 0.002596 \tabularnewline
3 & 0.004116 & 0.0334 & 0.486713 \tabularnewline
4 & -0.429855 & -3.4922 & 0.00043 \tabularnewline
5 & -0.714959 & -5.8084 & 0 \tabularnewline
6 & -0.768645 & -6.2445 & 0 \tabularnewline
7 & -0.684701 & -5.5625 & 0 \tabularnewline
8 & -0.349138 & -2.8364 & 0.003026 \tabularnewline
9 & 0.074546 & 0.6056 & 0.273423 \tabularnewline
10 & 0.364639 & 2.9623 & 0.002121 \tabularnewline
11 & 0.610181 & 4.9571 & 3e-06 \tabularnewline
12 & 0.779699 & 6.3343 & 0 \tabularnewline
13 & 0.572594 & 4.6518 & 8e-06 \tabularnewline
14 & 0.29033 & 2.3587 & 0.010656 \tabularnewline
15 & -0.016233 & -0.1319 & 0.447742 \tabularnewline
16 & -0.334727 & -2.7193 & 0.004175 \tabularnewline
17 & -0.562763 & -4.5719 & 1.1e-05 \tabularnewline
18 & -0.623911 & -5.0687 & 2e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31960&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]1[/C][C]0.701568[/C][C]5.6996[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.355873[/C][C]2.8911[/C][C]0.002596[/C][/ROW]
[ROW][C]3[/C][C]0.004116[/C][C]0.0334[/C][C]0.486713[/C][/ROW]
[ROW][C]4[/C][C]-0.429855[/C][C]-3.4922[/C][C]0.00043[/C][/ROW]
[ROW][C]5[/C][C]-0.714959[/C][C]-5.8084[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.768645[/C][C]-6.2445[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.684701[/C][C]-5.5625[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]-0.349138[/C][C]-2.8364[/C][C]0.003026[/C][/ROW]
[ROW][C]9[/C][C]0.074546[/C][C]0.6056[/C][C]0.273423[/C][/ROW]
[ROW][C]10[/C][C]0.364639[/C][C]2.9623[/C][C]0.002121[/C][/ROW]
[ROW][C]11[/C][C]0.610181[/C][C]4.9571[/C][C]3e-06[/C][/ROW]
[ROW][C]12[/C][C]0.779699[/C][C]6.3343[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.572594[/C][C]4.6518[/C][C]8e-06[/C][/ROW]
[ROW][C]14[/C][C]0.29033[/C][C]2.3587[/C][C]0.010656[/C][/ROW]
[ROW][C]15[/C][C]-0.016233[/C][C]-0.1319[/C][C]0.447742[/C][/ROW]
[ROW][C]16[/C][C]-0.334727[/C][C]-2.7193[/C][C]0.004175[/C][/ROW]
[ROW][C]17[/C][C]-0.562763[/C][C]-4.5719[/C][C]1.1e-05[/C][/ROW]
[ROW][C]18[/C][C]-0.623911[/C][C]-5.0687[/C][C]2e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31960&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31960&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
1	0.701568	5.6996	0
2	0.355873	2.8911	0.002596
3	0.004116	0.0334	0.486713
4	-0.429855	-3.4922	0.00043
5	-0.714959	-5.8084	0
6	-0.768645	-6.2445	0
7	-0.684701	-5.5625	0
8	-0.349138	-2.8364	0.003026
9	0.074546	0.6056	0.273423
10	0.364639	2.9623	0.002121
11	0.610181	4.9571	3e-06
12	0.779699	6.3343	0
13	0.572594	4.6518	8e-06
14	0.29033	2.3587	0.010656
15	-0.016233	-0.1319	0.447742
16	-0.334727	-2.7193	0.004175
17	-0.562763	-4.5719	1.1e-05
18	-0.623911	-5.0687	2e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.701568	5.6996	0
2	-0.268459	-2.181	0.016377
3	-0.263658	-2.142	0.017945
4	-0.538749	-4.3768	2.2e-05
5	-0.350103	-2.8442	0.002961
6	-0.229705	-1.8661	0.033234
7	-0.317188	-2.5769	0.006107
8	0.027852	0.2263	0.410845
9	0.035511	0.2885	0.386935
10	-0.209216	-1.6997	0.04695
11	-0.078678	-0.6392	0.262457
12	0.28161	2.2878	0.01268
13	-0.217727	-1.7688	0.040772
14	0.01769	0.1437	0.443081
15	0.026568	0.2158	0.414889
16	0.230331	1.8712	0.032874
17	-0.038547	-0.3132	0.377576
18	-0.029434	-0.2391	0.405875

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.701568 & 5.6996 & 0 \tabularnewline
2 & -0.268459 & -2.181 & 0.016377 \tabularnewline
3 & -0.263658 & -2.142 & 0.017945 \tabularnewline
4 & -0.538749 & -4.3768 & 2.2e-05 \tabularnewline
5 & -0.350103 & -2.8442 & 0.002961 \tabularnewline
6 & -0.229705 & -1.8661 & 0.033234 \tabularnewline
7 & -0.317188 & -2.5769 & 0.006107 \tabularnewline
8 & 0.027852 & 0.2263 & 0.410845 \tabularnewline
9 & 0.035511 & 0.2885 & 0.386935 \tabularnewline
10 & -0.209216 & -1.6997 & 0.04695 \tabularnewline
11 & -0.078678 & -0.6392 & 0.262457 \tabularnewline
12 & 0.28161 & 2.2878 & 0.01268 \tabularnewline
13 & -0.217727 & -1.7688 & 0.040772 \tabularnewline
14 & 0.01769 & 0.1437 & 0.443081 \tabularnewline
15 & 0.026568 & 0.2158 & 0.414889 \tabularnewline
16 & 0.230331 & 1.8712 & 0.032874 \tabularnewline
17 & -0.038547 & -0.3132 & 0.377576 \tabularnewline
18 & -0.029434 & -0.2391 & 0.405875 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31960&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]1[/C][C]0.701568[/C][C]5.6996[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.268459[/C][C]-2.181[/C][C]0.016377[/C][/ROW]
[ROW][C]3[/C][C]-0.263658[/C][C]-2.142[/C][C]0.017945[/C][/ROW]
[ROW][C]4[/C][C]-0.538749[/C][C]-4.3768[/C][C]2.2e-05[/C][/ROW]
[ROW][C]5[/C][C]-0.350103[/C][C]-2.8442[/C][C]0.002961[/C][/ROW]
[ROW][C]6[/C][C]-0.229705[/C][C]-1.8661[/C][C]0.033234[/C][/ROW]
[ROW][C]7[/C][C]-0.317188[/C][C]-2.5769[/C][C]0.006107[/C][/ROW]
[ROW][C]8[/C][C]0.027852[/C][C]0.2263[/C][C]0.410845[/C][/ROW]
[ROW][C]9[/C][C]0.035511[/C][C]0.2885[/C][C]0.386935[/C][/ROW]
[ROW][C]10[/C][C]-0.209216[/C][C]-1.6997[/C][C]0.04695[/C][/ROW]
[ROW][C]11[/C][C]-0.078678[/C][C]-0.6392[/C][C]0.262457[/C][/ROW]
[ROW][C]12[/C][C]0.28161[/C][C]2.2878[/C][C]0.01268[/C][/ROW]
[ROW][C]13[/C][C]-0.217727[/C][C]-1.7688[/C][C]0.040772[/C][/ROW]
[ROW][C]14[/C][C]0.01769[/C][C]0.1437[/C][C]0.443081[/C][/ROW]
[ROW][C]15[/C][C]0.026568[/C][C]0.2158[/C][C]0.414889[/C][/ROW]
[ROW][C]16[/C][C]0.230331[/C][C]1.8712[/C][C]0.032874[/C][/ROW]
[ROW][C]17[/C][C]-0.038547[/C][C]-0.3132[/C][C]0.377576[/C][/ROW]
[ROW][C]18[/C][C]-0.029434[/C][C]-0.2391[/C][C]0.405875[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31960&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31960&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
1	0.701568	5.6996	0
2	-0.268459	-2.181	0.016377
3	-0.263658	-2.142	0.017945
4	-0.538749	-4.3768	2.2e-05
5	-0.350103	-2.8442	0.002961
6	-0.229705	-1.8661	0.033234
7	-0.317188	-2.5769	0.006107
8	0.027852	0.2263	0.410845
9	0.035511	0.2885	0.386935
10	-0.209216	-1.6997	0.04695
11	-0.078678	-0.6392	0.262457
12	0.28161	2.2878	0.01268
13	-0.217727	-1.7688	0.040772
14	0.01769	0.1437	0.443081
15	0.026568	0.2158	0.414889
16	0.230331	1.8712	0.032874
17	-0.038547	-0.3132	0.377576
18	-0.029434	-0.2391	0.405875

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 2:(par1+1)) {
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(abs(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,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(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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