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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 27 Nov 2007 12:30:46 -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/27/t1196191282e53sz3b8gqsegua.htm/, Retrieved Sun, 05 May 2024 18:15:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6925, Retrieved Sun, 05 May 2024 18:15:43 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

184

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2007-11-27 19:30:46] [bebbf4ab6ac77d61a56e6916ab0650f9] [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=6925&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=6925&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6925&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	8.1854	0
1	0.941593	7.7073	0
2	0.888364	7.2716	0
3	0.846644	6.9301	0
4	0.805104	6.5901	0
5	0.767613	6.2832	0
6	0.731486	5.9875	0
7	0.706919	5.7864	0
8	0.672033	5.5008	0
9	0.646872	5.2949	1e-06
10	0.625722	5.1218	1e-06
11	0.590729	4.8353	4e-06
12	0.537833	4.4024	2e-05
13	0.484294	3.9641	9.1e-05
14	0.440444	3.6052	0.000297
15	0.389351	3.187	0.001092
16	0.329789	2.6994	0.004392
17	0.2812	2.3017	0.012233

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.1854 & 0 \tabularnewline
1 & 0.941593 & 7.7073 & 0 \tabularnewline
2 & 0.888364 & 7.2716 & 0 \tabularnewline
3 & 0.846644 & 6.9301 & 0 \tabularnewline
4 & 0.805104 & 6.5901 & 0 \tabularnewline
5 & 0.767613 & 6.2832 & 0 \tabularnewline
6 & 0.731486 & 5.9875 & 0 \tabularnewline
7 & 0.706919 & 5.7864 & 0 \tabularnewline
8 & 0.672033 & 5.5008 & 0 \tabularnewline
9 & 0.646872 & 5.2949 & 1e-06 \tabularnewline
10 & 0.625722 & 5.1218 & 1e-06 \tabularnewline
11 & 0.590729 & 4.8353 & 4e-06 \tabularnewline
12 & 0.537833 & 4.4024 & 2e-05 \tabularnewline
13 & 0.484294 & 3.9641 & 9.1e-05 \tabularnewline
14 & 0.440444 & 3.6052 & 0.000297 \tabularnewline
15 & 0.389351 & 3.187 & 0.001092 \tabularnewline
16 & 0.329789 & 2.6994 & 0.004392 \tabularnewline
17 & 0.2812 & 2.3017 & 0.012233 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6925&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]8.1854[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.941593[/C][C]7.7073[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.888364[/C][C]7.2716[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.846644[/C][C]6.9301[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.805104[/C][C]6.5901[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.767613[/C][C]6.2832[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.731486[/C][C]5.9875[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.706919[/C][C]5.7864[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.672033[/C][C]5.5008[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.646872[/C][C]5.2949[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.625722[/C][C]5.1218[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.590729[/C][C]4.8353[/C][C]4e-06[/C][/ROW]
[ROW][C]12[/C][C]0.537833[/C][C]4.4024[/C][C]2e-05[/C][/ROW]
[ROW][C]13[/C][C]0.484294[/C][C]3.9641[/C][C]9.1e-05[/C][/ROW]
[ROW][C]14[/C][C]0.440444[/C][C]3.6052[/C][C]0.000297[/C][/ROW]
[ROW][C]15[/C][C]0.389351[/C][C]3.187[/C][C]0.001092[/C][/ROW]
[ROW][C]16[/C][C]0.329789[/C][C]2.6994[/C][C]0.004392[/C][/ROW]
[ROW][C]17[/C][C]0.2812[/C][C]2.3017[/C][C]0.012233[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6925&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6925&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	8.1854	0
1	0.941593	7.7073	0
2	0.888364	7.2716	0
3	0.846644	6.9301	0
4	0.805104	6.5901	0
5	0.767613	6.2832	0
6	0.731486	5.9875	0
7	0.706919	5.7864	0
8	0.672033	5.5008	0
9	0.646872	5.2949	1e-06
10	0.625722	5.1218	1e-06
11	0.590729	4.8353	4e-06
12	0.537833	4.4024	2e-05
13	0.484294	3.9641	9.1e-05
14	0.440444	3.6052	0.000297
15	0.389351	3.187	0.001092
16	0.329789	2.6994	0.004392
17	0.2812	2.3017	0.012233

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.941593	7.7073	0
1	0.015577	0.1275	0.449463
2	0.075229	0.6158	0.270065
3	-0.012476	-0.1021	0.540517
4	0.023131	0.1893	0.425201
5	-0.004579	-0.0375	0.514893
6	0.090791	0.7432	0.229992
7	-0.095176	-0.779	0.780652
8	0.083679	0.6849	0.247871
9	0.011246	0.0921	0.463466
10	-0.109156	-0.8935	0.8126
11	-0.190174	-1.5566	0.937867
12	-0.056482	-0.4623	0.677328
13	0.005316	0.0435	0.482712
14	-0.082819	-0.6779	0.749916
15	-0.139901	-1.1451	0.871887
16	0.014962	0.1225	0.451448
17	-0.026187	-0.2144	0.584537

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.941593 & 7.7073 & 0 \tabularnewline
1 & 0.015577 & 0.1275 & 0.449463 \tabularnewline
2 & 0.075229 & 0.6158 & 0.270065 \tabularnewline
3 & -0.012476 & -0.1021 & 0.540517 \tabularnewline
4 & 0.023131 & 0.1893 & 0.425201 \tabularnewline
5 & -0.004579 & -0.0375 & 0.514893 \tabularnewline
6 & 0.090791 & 0.7432 & 0.229992 \tabularnewline
7 & -0.095176 & -0.779 & 0.780652 \tabularnewline
8 & 0.083679 & 0.6849 & 0.247871 \tabularnewline
9 & 0.011246 & 0.0921 & 0.463466 \tabularnewline
10 & -0.109156 & -0.8935 & 0.8126 \tabularnewline
11 & -0.190174 & -1.5566 & 0.937867 \tabularnewline
12 & -0.056482 & -0.4623 & 0.677328 \tabularnewline
13 & 0.005316 & 0.0435 & 0.482712 \tabularnewline
14 & -0.082819 & -0.6779 & 0.749916 \tabularnewline
15 & -0.139901 & -1.1451 & 0.871887 \tabularnewline
16 & 0.014962 & 0.1225 & 0.451448 \tabularnewline
17 & -0.026187 & -0.2144 & 0.584537 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6925&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]0.941593[/C][C]7.7073[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.015577[/C][C]0.1275[/C][C]0.449463[/C][/ROW]
[ROW][C]2[/C][C]0.075229[/C][C]0.6158[/C][C]0.270065[/C][/ROW]
[ROW][C]3[/C][C]-0.012476[/C][C]-0.1021[/C][C]0.540517[/C][/ROW]
[ROW][C]4[/C][C]0.023131[/C][C]0.1893[/C][C]0.425201[/C][/ROW]
[ROW][C]5[/C][C]-0.004579[/C][C]-0.0375[/C][C]0.514893[/C][/ROW]
[ROW][C]6[/C][C]0.090791[/C][C]0.7432[/C][C]0.229992[/C][/ROW]
[ROW][C]7[/C][C]-0.095176[/C][C]-0.779[/C][C]0.780652[/C][/ROW]
[ROW][C]8[/C][C]0.083679[/C][C]0.6849[/C][C]0.247871[/C][/ROW]
[ROW][C]9[/C][C]0.011246[/C][C]0.0921[/C][C]0.463466[/C][/ROW]
[ROW][C]10[/C][C]-0.109156[/C][C]-0.8935[/C][C]0.8126[/C][/ROW]
[ROW][C]11[/C][C]-0.190174[/C][C]-1.5566[/C][C]0.937867[/C][/ROW]
[ROW][C]12[/C][C]-0.056482[/C][C]-0.4623[/C][C]0.677328[/C][/ROW]
[ROW][C]13[/C][C]0.005316[/C][C]0.0435[/C][C]0.482712[/C][/ROW]
[ROW][C]14[/C][C]-0.082819[/C][C]-0.6779[/C][C]0.749916[/C][/ROW]
[ROW][C]15[/C][C]-0.139901[/C][C]-1.1451[/C][C]0.871887[/C][/ROW]
[ROW][C]16[/C][C]0.014962[/C][C]0.1225[/C][C]0.451448[/C][/ROW]
[ROW][C]17[/C][C]-0.026187[/C][C]-0.2144[/C][C]0.584537[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6925&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6925&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	0.941593	7.7073	0
1	0.015577	0.1275	0.449463
2	0.075229	0.6158	0.270065
3	-0.012476	-0.1021	0.540517
4	0.023131	0.1893	0.425201
5	-0.004579	-0.0375	0.514893
6	0.090791	0.7432	0.229992
7	-0.095176	-0.779	0.780652
8	0.083679	0.6849	0.247871
9	0.011246	0.0921	0.463466
10	-0.109156	-0.8935	0.8126
11	-0.190174	-1.5566	0.937867
12	-0.056482	-0.4623	0.677328
13	0.005316	0.0435	0.482712
14	-0.082819	-0.6779	0.749916
15	-0.139901	-1.1451	0.871887
16	0.014962	0.1225	0.451448
17	-0.026187	-0.2144	0.584537

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

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code