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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 26 Nov 2007 05:54:35 -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/Nov/26/t1196081180xl53khh19elbn1u.htm/, Retrieved Thu, 02 May 2024 21:27:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6582, Retrieved Thu, 02 May 2024 21:27:41 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

191

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

-       [(Partial) Autocorrelation Function] [Q2 Autocorrelatio...] [2007-11-26 12:54:35] [6d644d07a16de69cd360f404f1ea3fa3] [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=6582&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=6582&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6582&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	8.3666	0
1	0.931432	7.7929	0
2	0.872195	7.2973	0
3	0.828253	6.9297	0
4	0.777002	6.5009	0
5	0.731296	6.1185	0
6	0.686885	5.7469	0
7	0.651536	5.4511	0
8	0.622844	5.2111	1e-06
9	0.608963	5.095	1e-06
10	0.603435	5.0487	2e-06
11	0.582994	4.8777	3e-06
12	0.549291	4.5957	9e-06
13	0.522712	4.3733	2.1e-05
14	0.494683	4.1388	4.8e-05
15	0.445277	3.7255	0.000196
16	0.382761	3.2024	0.001026
17	0.328303	2.7468	0.003823

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.3666 & 0 \tabularnewline
1 & 0.931432 & 7.7929 & 0 \tabularnewline
2 & 0.872195 & 7.2973 & 0 \tabularnewline
3 & 0.828253 & 6.9297 & 0 \tabularnewline
4 & 0.777002 & 6.5009 & 0 \tabularnewline
5 & 0.731296 & 6.1185 & 0 \tabularnewline
6 & 0.686885 & 5.7469 & 0 \tabularnewline
7 & 0.651536 & 5.4511 & 0 \tabularnewline
8 & 0.622844 & 5.2111 & 1e-06 \tabularnewline
9 & 0.608963 & 5.095 & 1e-06 \tabularnewline
10 & 0.603435 & 5.0487 & 2e-06 \tabularnewline
11 & 0.582994 & 4.8777 & 3e-06 \tabularnewline
12 & 0.549291 & 4.5957 & 9e-06 \tabularnewline
13 & 0.522712 & 4.3733 & 2.1e-05 \tabularnewline
14 & 0.494683 & 4.1388 & 4.8e-05 \tabularnewline
15 & 0.445277 & 3.7255 & 0.000196 \tabularnewline
16 & 0.382761 & 3.2024 & 0.001026 \tabularnewline
17 & 0.328303 & 2.7468 & 0.003823 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6582&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]8.3666[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.931432[/C][C]7.7929[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.872195[/C][C]7.2973[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.828253[/C][C]6.9297[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.777002[/C][C]6.5009[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.731296[/C][C]6.1185[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.686885[/C][C]5.7469[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.651536[/C][C]5.4511[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.622844[/C][C]5.2111[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]0.608963[/C][C]5.095[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.603435[/C][C]5.0487[/C][C]2e-06[/C][/ROW]
[ROW][C]11[/C][C]0.582994[/C][C]4.8777[/C][C]3e-06[/C][/ROW]
[ROW][C]12[/C][C]0.549291[/C][C]4.5957[/C][C]9e-06[/C][/ROW]
[ROW][C]13[/C][C]0.522712[/C][C]4.3733[/C][C]2.1e-05[/C][/ROW]
[ROW][C]14[/C][C]0.494683[/C][C]4.1388[/C][C]4.8e-05[/C][/ROW]
[ROW][C]15[/C][C]0.445277[/C][C]3.7255[/C][C]0.000196[/C][/ROW]
[ROW][C]16[/C][C]0.382761[/C][C]3.2024[/C][C]0.001026[/C][/ROW]
[ROW][C]17[/C][C]0.328303[/C][C]2.7468[/C][C]0.003823[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6582&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6582&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	8.3666	0
1	0.931432	7.7929	0
2	0.872195	7.2973	0
3	0.828253	6.9297	0
4	0.777002	6.5009	0
5	0.731296	6.1185	0
6	0.686885	5.7469	0
7	0.651536	5.4511	0
8	0.622844	5.2111	1e-06
9	0.608963	5.095	1e-06
10	0.603435	5.0487	2e-06
11	0.582994	4.8777	3e-06
12	0.549291	4.5957	9e-06
13	0.522712	4.3733	2.1e-05
14	0.494683	4.1388	4.8e-05
15	0.445277	3.7255	0.000196
16	0.382761	3.2024	0.001026
17	0.328303	2.7468	0.003823

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.931432	7.7929	0
1	0.034957	0.2925	0.385395
2	0.08846	0.7401	0.230855
3	-0.064479	-0.5395	0.704364
4	0.020294	0.1698	0.432832
5	-0.021245	-0.1777	0.570282
6	0.05576	0.4665	0.321146
7	0.035834	0.2998	0.382607
8	0.119985	1.0039	0.15945
9	0.076785	0.6424	0.261346
10	-0.080659	-0.6748	0.749002
11	-0.119456	-0.9994	0.839488
12	0.008191	0.0685	0.472778
13	-0.01987	-0.1662	0.565778
14	-0.154737	-1.2946	0.900148
15	-0.15282	-1.2786	0.897366
16	-0.017263	-0.1444	0.557214
17	-0.030292	-0.2534	0.599664

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.931432 & 7.7929 & 0 \tabularnewline
1 & 0.034957 & 0.2925 & 0.385395 \tabularnewline
2 & 0.08846 & 0.7401 & 0.230855 \tabularnewline
3 & -0.064479 & -0.5395 & 0.704364 \tabularnewline
4 & 0.020294 & 0.1698 & 0.432832 \tabularnewline
5 & -0.021245 & -0.1777 & 0.570282 \tabularnewline
6 & 0.05576 & 0.4665 & 0.321146 \tabularnewline
7 & 0.035834 & 0.2998 & 0.382607 \tabularnewline
8 & 0.119985 & 1.0039 & 0.15945 \tabularnewline
9 & 0.076785 & 0.6424 & 0.261346 \tabularnewline
10 & -0.080659 & -0.6748 & 0.749002 \tabularnewline
11 & -0.119456 & -0.9994 & 0.839488 \tabularnewline
12 & 0.008191 & 0.0685 & 0.472778 \tabularnewline
13 & -0.01987 & -0.1662 & 0.565778 \tabularnewline
14 & -0.154737 & -1.2946 & 0.900148 \tabularnewline
15 & -0.15282 & -1.2786 & 0.897366 \tabularnewline
16 & -0.017263 & -0.1444 & 0.557214 \tabularnewline
17 & -0.030292 & -0.2534 & 0.599664 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6582&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]0.931432[/C][C]7.7929[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.034957[/C][C]0.2925[/C][C]0.385395[/C][/ROW]
[ROW][C]2[/C][C]0.08846[/C][C]0.7401[/C][C]0.230855[/C][/ROW]
[ROW][C]3[/C][C]-0.064479[/C][C]-0.5395[/C][C]0.704364[/C][/ROW]
[ROW][C]4[/C][C]0.020294[/C][C]0.1698[/C][C]0.432832[/C][/ROW]
[ROW][C]5[/C][C]-0.021245[/C][C]-0.1777[/C][C]0.570282[/C][/ROW]
[ROW][C]6[/C][C]0.05576[/C][C]0.4665[/C][C]0.321146[/C][/ROW]
[ROW][C]7[/C][C]0.035834[/C][C]0.2998[/C][C]0.382607[/C][/ROW]
[ROW][C]8[/C][C]0.119985[/C][C]1.0039[/C][C]0.15945[/C][/ROW]
[ROW][C]9[/C][C]0.076785[/C][C]0.6424[/C][C]0.261346[/C][/ROW]
[ROW][C]10[/C][C]-0.080659[/C][C]-0.6748[/C][C]0.749002[/C][/ROW]
[ROW][C]11[/C][C]-0.119456[/C][C]-0.9994[/C][C]0.839488[/C][/ROW]
[ROW][C]12[/C][C]0.008191[/C][C]0.0685[/C][C]0.472778[/C][/ROW]
[ROW][C]13[/C][C]-0.01987[/C][C]-0.1662[/C][C]0.565778[/C][/ROW]
[ROW][C]14[/C][C]-0.154737[/C][C]-1.2946[/C][C]0.900148[/C][/ROW]
[ROW][C]15[/C][C]-0.15282[/C][C]-1.2786[/C][C]0.897366[/C][/ROW]
[ROW][C]16[/C][C]-0.017263[/C][C]-0.1444[/C][C]0.557214[/C][/ROW]
[ROW][C]17[/C][C]-0.030292[/C][C]-0.2534[/C][C]0.599664[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6582&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6582&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	0.931432	7.7929	0
1	0.034957	0.2925	0.385395
2	0.08846	0.7401	0.230855
3	-0.064479	-0.5395	0.704364
4	0.020294	0.1698	0.432832
5	-0.021245	-0.1777	0.570282
6	0.05576	0.4665	0.321146
7	0.035834	0.2998	0.382607
8	0.119985	1.0039	0.15945
9	0.076785	0.6424	0.261346
10	-0.080659	-0.6748	0.749002
11	-0.119456	-0.9994	0.839488
12	0.008191	0.0685	0.472778
13	-0.01987	-0.1662	0.565778
14	-0.154737	-1.2946	0.900148
15	-0.15282	-1.2786	0.897366
16	-0.017263	-0.1444	0.557214
17	-0.030292	-0.2534	0.599664

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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Dataset

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Figures (Output of Computation)

Input Parameters & R Code