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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 05 Dec 2007 07:04:46 -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/Dec/05/t11968630082v4xwxie1h7dlf3.htm/, Retrieved Thu, 02 May 2024 21:40:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2472, Retrieved Thu, 02 May 2024 21:40:33 +0000

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No (this computation is public)

User-defined keywords

bridome

Estimated Impact

271

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

-       [(Partial) Autocorrelation Function] [autocorrelation, ...] [2007-12-05 14:04:46] [ff60737d3854dcb913eacf6907ce202b] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2472&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]2 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=2472&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2472&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	9.6437	0
1	0.051343	0.4951	0.310838
2	-0.029015	-0.2798	0.60988
3	-0.052013	-0.5016	0.69143
4	0.061564	0.5937	0.277075
5	0.158814	1.5316	0.064514
6	0.09071	0.8748	0.191974
7	0.063414	0.6115	0.271167
8	0.132082	1.2738	0.102962
9	0.235898	2.2749	0.012604
10	-0.062273	-0.6005	0.725196
11	-0.095916	-0.925	0.821316
12	-0.152198	-1.4677	0.927227
13	0.147657	1.424	0.078904
14	0.313261	3.021	0.001627
15	0.022442	0.2164	0.414565
16	0.039126	0.3773	0.353398
17	-0.058133	-0.5606	0.711795
18	0.103753	1.0006	0.159819
19	0.027722	0.2673	0.394898

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 9.6437 & 0 \tabularnewline
1 & 0.051343 & 0.4951 & 0.310838 \tabularnewline
2 & -0.029015 & -0.2798 & 0.60988 \tabularnewline
3 & -0.052013 & -0.5016 & 0.69143 \tabularnewline
4 & 0.061564 & 0.5937 & 0.277075 \tabularnewline
5 & 0.158814 & 1.5316 & 0.064514 \tabularnewline
6 & 0.09071 & 0.8748 & 0.191974 \tabularnewline
7 & 0.063414 & 0.6115 & 0.271167 \tabularnewline
8 & 0.132082 & 1.2738 & 0.102962 \tabularnewline
9 & 0.235898 & 2.2749 & 0.012604 \tabularnewline
10 & -0.062273 & -0.6005 & 0.725196 \tabularnewline
11 & -0.095916 & -0.925 & 0.821316 \tabularnewline
12 & -0.152198 & -1.4677 & 0.927227 \tabularnewline
13 & 0.147657 & 1.424 & 0.078904 \tabularnewline
14 & 0.313261 & 3.021 & 0.001627 \tabularnewline
15 & 0.022442 & 0.2164 & 0.414565 \tabularnewline
16 & 0.039126 & 0.3773 & 0.353398 \tabularnewline
17 & -0.058133 & -0.5606 & 0.711795 \tabularnewline
18 & 0.103753 & 1.0006 & 0.159819 \tabularnewline
19 & 0.027722 & 0.2673 & 0.394898 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2472&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]9.6437[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.051343[/C][C]0.4951[/C][C]0.310838[/C][/ROW]
[ROW][C]2[/C][C]-0.029015[/C][C]-0.2798[/C][C]0.60988[/C][/ROW]
[ROW][C]3[/C][C]-0.052013[/C][C]-0.5016[/C][C]0.69143[/C][/ROW]
[ROW][C]4[/C][C]0.061564[/C][C]0.5937[/C][C]0.277075[/C][/ROW]
[ROW][C]5[/C][C]0.158814[/C][C]1.5316[/C][C]0.064514[/C][/ROW]
[ROW][C]6[/C][C]0.09071[/C][C]0.8748[/C][C]0.191974[/C][/ROW]
[ROW][C]7[/C][C]0.063414[/C][C]0.6115[/C][C]0.271167[/C][/ROW]
[ROW][C]8[/C][C]0.132082[/C][C]1.2738[/C][C]0.102962[/C][/ROW]
[ROW][C]9[/C][C]0.235898[/C][C]2.2749[/C][C]0.012604[/C][/ROW]
[ROW][C]10[/C][C]-0.062273[/C][C]-0.6005[/C][C]0.725196[/C][/ROW]
[ROW][C]11[/C][C]-0.095916[/C][C]-0.925[/C][C]0.821316[/C][/ROW]
[ROW][C]12[/C][C]-0.152198[/C][C]-1.4677[/C][C]0.927227[/C][/ROW]
[ROW][C]13[/C][C]0.147657[/C][C]1.424[/C][C]0.078904[/C][/ROW]
[ROW][C]14[/C][C]0.313261[/C][C]3.021[/C][C]0.001627[/C][/ROW]
[ROW][C]15[/C][C]0.022442[/C][C]0.2164[/C][C]0.414565[/C][/ROW]
[ROW][C]16[/C][C]0.039126[/C][C]0.3773[/C][C]0.353398[/C][/ROW]
[ROW][C]17[/C][C]-0.058133[/C][C]-0.5606[/C][C]0.711795[/C][/ROW]
[ROW][C]18[/C][C]0.103753[/C][C]1.0006[/C][C]0.159819[/C][/ROW]
[ROW][C]19[/C][C]0.027722[/C][C]0.2673[/C][C]0.394898[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2472&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2472&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	9.6437	0
1	0.051343	0.4951	0.310838
2	-0.029015	-0.2798	0.60988
3	-0.052013	-0.5016	0.69143
4	0.061564	0.5937	0.277075
5	0.158814	1.5316	0.064514
6	0.09071	0.8748	0.191974
7	0.063414	0.6115	0.271167
8	0.132082	1.2738	0.102962
9	0.235898	2.2749	0.012604
10	-0.062273	-0.6005	0.725196
11	-0.095916	-0.925	0.821316
12	-0.152198	-1.4677	0.927227
13	0.147657	1.424	0.078904
14	0.313261	3.021	0.001627
15	0.022442	0.2164	0.414565
16	0.039126	0.3773	0.353398
17	-0.058133	-0.5606	0.711795
18	0.103753	1.0006	0.159819
19	0.027722	0.2673	0.394898

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.051343	0.4951	0.310838
1	-0.031735	-0.306	0.619872
2	-0.049025	-0.4728	0.68126
3	0.066311	0.6395	0.262043
4	0.150676	1.4531	0.074786
5	0.07883	0.7602	0.224526
6	0.073139	0.7053	0.241186
7	0.150225	1.4487	0.075389
8	0.239301	2.3077	0.011616
9	-0.088239	-0.8509	0.801507
10	-0.10339	-0.9971	0.839338
11	-0.195122	-1.8817	0.968497
12	0.058168	0.561	0.288089
13	0.23225	2.2397	0.013745
14	-0.010697	-0.1032	0.540972
15	0.087634	0.8451	0.20011
16	-0.03421	-0.3299	0.628895
17	0.080666	0.7779	0.219298
18	0.019349	0.1866	0.426192
19	0.124896	1.2045	0.115736

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.051343 & 0.4951 & 0.310838 \tabularnewline
1 & -0.031735 & -0.306 & 0.619872 \tabularnewline
2 & -0.049025 & -0.4728 & 0.68126 \tabularnewline
3 & 0.066311 & 0.6395 & 0.262043 \tabularnewline
4 & 0.150676 & 1.4531 & 0.074786 \tabularnewline
5 & 0.07883 & 0.7602 & 0.224526 \tabularnewline
6 & 0.073139 & 0.7053 & 0.241186 \tabularnewline
7 & 0.150225 & 1.4487 & 0.075389 \tabularnewline
8 & 0.239301 & 2.3077 & 0.011616 \tabularnewline
9 & -0.088239 & -0.8509 & 0.801507 \tabularnewline
10 & -0.10339 & -0.9971 & 0.839338 \tabularnewline
11 & -0.195122 & -1.8817 & 0.968497 \tabularnewline
12 & 0.058168 & 0.561 & 0.288089 \tabularnewline
13 & 0.23225 & 2.2397 & 0.013745 \tabularnewline
14 & -0.010697 & -0.1032 & 0.540972 \tabularnewline
15 & 0.087634 & 0.8451 & 0.20011 \tabularnewline
16 & -0.03421 & -0.3299 & 0.628895 \tabularnewline
17 & 0.080666 & 0.7779 & 0.219298 \tabularnewline
18 & 0.019349 & 0.1866 & 0.426192 \tabularnewline
19 & 0.124896 & 1.2045 & 0.115736 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2472&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]0.051343[/C][C]0.4951[/C][C]0.310838[/C][/ROW]
[ROW][C]1[/C][C]-0.031735[/C][C]-0.306[/C][C]0.619872[/C][/ROW]
[ROW][C]2[/C][C]-0.049025[/C][C]-0.4728[/C][C]0.68126[/C][/ROW]
[ROW][C]3[/C][C]0.066311[/C][C]0.6395[/C][C]0.262043[/C][/ROW]
[ROW][C]4[/C][C]0.150676[/C][C]1.4531[/C][C]0.074786[/C][/ROW]
[ROW][C]5[/C][C]0.07883[/C][C]0.7602[/C][C]0.224526[/C][/ROW]
[ROW][C]6[/C][C]0.073139[/C][C]0.7053[/C][C]0.241186[/C][/ROW]
[ROW][C]7[/C][C]0.150225[/C][C]1.4487[/C][C]0.075389[/C][/ROW]
[ROW][C]8[/C][C]0.239301[/C][C]2.3077[/C][C]0.011616[/C][/ROW]
[ROW][C]9[/C][C]-0.088239[/C][C]-0.8509[/C][C]0.801507[/C][/ROW]
[ROW][C]10[/C][C]-0.10339[/C][C]-0.9971[/C][C]0.839338[/C][/ROW]
[ROW][C]11[/C][C]-0.195122[/C][C]-1.8817[/C][C]0.968497[/C][/ROW]
[ROW][C]12[/C][C]0.058168[/C][C]0.561[/C][C]0.288089[/C][/ROW]
[ROW][C]13[/C][C]0.23225[/C][C]2.2397[/C][C]0.013745[/C][/ROW]
[ROW][C]14[/C][C]-0.010697[/C][C]-0.1032[/C][C]0.540972[/C][/ROW]
[ROW][C]15[/C][C]0.087634[/C][C]0.8451[/C][C]0.20011[/C][/ROW]
[ROW][C]16[/C][C]-0.03421[/C][C]-0.3299[/C][C]0.628895[/C][/ROW]
[ROW][C]17[/C][C]0.080666[/C][C]0.7779[/C][C]0.219298[/C][/ROW]
[ROW][C]18[/C][C]0.019349[/C][C]0.1866[/C][C]0.426192[/C][/ROW]
[ROW][C]19[/C][C]0.124896[/C][C]1.2045[/C][C]0.115736[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2472&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2472&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	0.051343	0.4951	0.310838
1	-0.031735	-0.306	0.619872
2	-0.049025	-0.4728	0.68126
3	0.066311	0.6395	0.262043
4	0.150676	1.4531	0.074786
5	0.07883	0.7602	0.224526
6	0.073139	0.7053	0.241186
7	0.150225	1.4487	0.075389
8	0.239301	2.3077	0.011616
9	-0.088239	-0.8509	0.801507
10	-0.10339	-0.9971	0.839338
11	-0.195122	-1.8817	0.968497
12	0.058168	0.561	0.288089
13	0.23225	2.2397	0.013745
14	-0.010697	-0.1032	0.540972
15	0.087634	0.8451	0.20011
16	-0.03421	-0.3299	0.628895
17	0.080666	0.7779	0.219298
18	0.019349	0.1866	0.426192
19	0.124896	1.2045	0.115736

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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Tables (Output of Computation)

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Input Parameters & R Code