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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 25 Nov 2007 05:03:04 -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/25/t11959916281ozf39n0pa5d7b8.htm/, Retrieved Sat, 04 May 2024 15:12:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6414, Retrieved Sat, 04 May 2024 15:12:06 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

209

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

-       [(Partial) Autocorrelation Function] [Autocorrelation f...] [2007-11-25 12:03:04] [9fe578921d87f9af8e79a90d6142ba02] [Current]

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Dataseries X:

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Boxplots

8.1
8.2
8
8.1
8.3
8.2
8.1
7.7
7.6
7.7
8.2
8.4
8.4
8.6
8.4
8.5
8.7
8.7
8.6
7.4
7.3
7.4
9
9.2
9.2
8.5
8.3
8.3
8.6
8.6
8.5
8.1
8.1
8
8.6
8.7
8.7
8.6
8.4
8.4
8.7
8.7
8.5
8.3
8.3
8.3
8.1
8.2
8.1
8.1
7.9
7.7
8.1
8
7.7
7.8
7.6
7.4
7.7
7.9
7.6

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=6414&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=6414&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6414&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	6.9282	0
1	0.01466	0.1016	0.459763
2	-0.083888	-0.5812	0.718086
3	-0.546476	-3.7861	0.999787
4	-0.041528	-0.2877	0.612598
5	-0.001341	-0.0093	0.503687
6	0.099334	0.6882	0.247318
7	-0.006428	-0.0445	0.517669
8	0.050407	0.3492	0.364222
9	0.183269	1.2697	0.105153
10	0.027562	0.191	0.424683
11	-0.045736	-0.3169	0.623642
12	-0.287458	-1.9916	0.973938
13	-0.020024	-0.1387	0.554878
14	0.054846	0.38	0.352815
15	0.158851	1.1006	0.13829
16	-0.009896	-0.0686	0.527189

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.9282 & 0 \tabularnewline
1 & 0.01466 & 0.1016 & 0.459763 \tabularnewline
2 & -0.083888 & -0.5812 & 0.718086 \tabularnewline
3 & -0.546476 & -3.7861 & 0.999787 \tabularnewline
4 & -0.041528 & -0.2877 & 0.612598 \tabularnewline
5 & -0.001341 & -0.0093 & 0.503687 \tabularnewline
6 & 0.099334 & 0.6882 & 0.247318 \tabularnewline
7 & -0.006428 & -0.0445 & 0.517669 \tabularnewline
8 & 0.050407 & 0.3492 & 0.364222 \tabularnewline
9 & 0.183269 & 1.2697 & 0.105153 \tabularnewline
10 & 0.027562 & 0.191 & 0.424683 \tabularnewline
11 & -0.045736 & -0.3169 & 0.623642 \tabularnewline
12 & -0.287458 & -1.9916 & 0.973938 \tabularnewline
13 & -0.020024 & -0.1387 & 0.554878 \tabularnewline
14 & 0.054846 & 0.38 & 0.352815 \tabularnewline
15 & 0.158851 & 1.1006 & 0.13829 \tabularnewline
16 & -0.009896 & -0.0686 & 0.527189 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6414&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]6.9282[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.01466[/C][C]0.1016[/C][C]0.459763[/C][/ROW]
[ROW][C]2[/C][C]-0.083888[/C][C]-0.5812[/C][C]0.718086[/C][/ROW]
[ROW][C]3[/C][C]-0.546476[/C][C]-3.7861[/C][C]0.999787[/C][/ROW]
[ROW][C]4[/C][C]-0.041528[/C][C]-0.2877[/C][C]0.612598[/C][/ROW]
[ROW][C]5[/C][C]-0.001341[/C][C]-0.0093[/C][C]0.503687[/C][/ROW]
[ROW][C]6[/C][C]0.099334[/C][C]0.6882[/C][C]0.247318[/C][/ROW]
[ROW][C]7[/C][C]-0.006428[/C][C]-0.0445[/C][C]0.517669[/C][/ROW]
[ROW][C]8[/C][C]0.050407[/C][C]0.3492[/C][C]0.364222[/C][/ROW]
[ROW][C]9[/C][C]0.183269[/C][C]1.2697[/C][C]0.105153[/C][/ROW]
[ROW][C]10[/C][C]0.027562[/C][C]0.191[/C][C]0.424683[/C][/ROW]
[ROW][C]11[/C][C]-0.045736[/C][C]-0.3169[/C][C]0.623642[/C][/ROW]
[ROW][C]12[/C][C]-0.287458[/C][C]-1.9916[/C][C]0.973938[/C][/ROW]
[ROW][C]13[/C][C]-0.020024[/C][C]-0.1387[/C][C]0.554878[/C][/ROW]
[ROW][C]14[/C][C]0.054846[/C][C]0.38[/C][C]0.352815[/C][/ROW]
[ROW][C]15[/C][C]0.158851[/C][C]1.1006[/C][C]0.13829[/C][/ROW]
[ROW][C]16[/C][C]-0.009896[/C][C]-0.0686[/C][C]0.527189[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6414&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6414&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	6.9282	0
1	0.01466	0.1016	0.459763
2	-0.083888	-0.5812	0.718086
3	-0.546476	-3.7861	0.999787
4	-0.041528	-0.2877	0.612598
5	-0.001341	-0.0093	0.503687
6	0.099334	0.6882	0.247318
7	-0.006428	-0.0445	0.517669
8	0.050407	0.3492	0.364222
9	0.183269	1.2697	0.105153
10	0.027562	0.191	0.424683
11	-0.045736	-0.3169	0.623642
12	-0.287458	-1.9916	0.973938
13	-0.020024	-0.1387	0.554878
14	0.054846	0.38	0.352815
15	0.158851	1.1006	0.13829
16	-0.009896	-0.0686	0.527189

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.01466	0.1016	0.459763
1	-0.084121	-0.5828	0.718625
2	-0.547904	-3.796	0.999794
3	-0.081077	-0.5617	0.71154
4	-0.136166	-0.9434	0.824895
5	-0.324443	-2.2478	0.98539
6	-0.183585	-1.2719	0.895235
7	-0.131021	-0.9077	0.815724
8	0.064592	0.4475	0.328262
9	-0.047529	-0.3293	0.628316
10	-0.004292	-0.0297	0.5118
11	-0.138733	-0.9612	0.829358
12	-0.029317	-0.2031	0.580047
13	0.014751	0.1022	0.459511
14	-0.096206	-0.6665	0.745869
15	-0.068742	-0.4763	0.681975
16	-0.005933	-0.0411	0.516309

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.01466 & 0.1016 & 0.459763 \tabularnewline
1 & -0.084121 & -0.5828 & 0.718625 \tabularnewline
2 & -0.547904 & -3.796 & 0.999794 \tabularnewline
3 & -0.081077 & -0.5617 & 0.71154 \tabularnewline
4 & -0.136166 & -0.9434 & 0.824895 \tabularnewline
5 & -0.324443 & -2.2478 & 0.98539 \tabularnewline
6 & -0.183585 & -1.2719 & 0.895235 \tabularnewline
7 & -0.131021 & -0.9077 & 0.815724 \tabularnewline
8 & 0.064592 & 0.4475 & 0.328262 \tabularnewline
9 & -0.047529 & -0.3293 & 0.628316 \tabularnewline
10 & -0.004292 & -0.0297 & 0.5118 \tabularnewline
11 & -0.138733 & -0.9612 & 0.829358 \tabularnewline
12 & -0.029317 & -0.2031 & 0.580047 \tabularnewline
13 & 0.014751 & 0.1022 & 0.459511 \tabularnewline
14 & -0.096206 & -0.6665 & 0.745869 \tabularnewline
15 & -0.068742 & -0.4763 & 0.681975 \tabularnewline
16 & -0.005933 & -0.0411 & 0.516309 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6414&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]0.01466[/C][C]0.1016[/C][C]0.459763[/C][/ROW]
[ROW][C]1[/C][C]-0.084121[/C][C]-0.5828[/C][C]0.718625[/C][/ROW]
[ROW][C]2[/C][C]-0.547904[/C][C]-3.796[/C][C]0.999794[/C][/ROW]
[ROW][C]3[/C][C]-0.081077[/C][C]-0.5617[/C][C]0.71154[/C][/ROW]
[ROW][C]4[/C][C]-0.136166[/C][C]-0.9434[/C][C]0.824895[/C][/ROW]
[ROW][C]5[/C][C]-0.324443[/C][C]-2.2478[/C][C]0.98539[/C][/ROW]
[ROW][C]6[/C][C]-0.183585[/C][C]-1.2719[/C][C]0.895235[/C][/ROW]
[ROW][C]7[/C][C]-0.131021[/C][C]-0.9077[/C][C]0.815724[/C][/ROW]
[ROW][C]8[/C][C]0.064592[/C][C]0.4475[/C][C]0.328262[/C][/ROW]
[ROW][C]9[/C][C]-0.047529[/C][C]-0.3293[/C][C]0.628316[/C][/ROW]
[ROW][C]10[/C][C]-0.004292[/C][C]-0.0297[/C][C]0.5118[/C][/ROW]
[ROW][C]11[/C][C]-0.138733[/C][C]-0.9612[/C][C]0.829358[/C][/ROW]
[ROW][C]12[/C][C]-0.029317[/C][C]-0.2031[/C][C]0.580047[/C][/ROW]
[ROW][C]13[/C][C]0.014751[/C][C]0.1022[/C][C]0.459511[/C][/ROW]
[ROW][C]14[/C][C]-0.096206[/C][C]-0.6665[/C][C]0.745869[/C][/ROW]
[ROW][C]15[/C][C]-0.068742[/C][C]-0.4763[/C][C]0.681975[/C][/ROW]
[ROW][C]16[/C][C]-0.005933[/C][C]-0.0411[/C][C]0.516309[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6414&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6414&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	0.01466	0.1016	0.459763
1	-0.084121	-0.5828	0.718625
2	-0.547904	-3.796	0.999794
3	-0.081077	-0.5617	0.71154
4	-0.136166	-0.9434	0.824895
5	-0.324443	-2.2478	0.98539
6	-0.183585	-1.2719	0.895235
7	-0.131021	-0.9077	0.815724
8	0.064592	0.4475	0.328262
9	-0.047529	-0.3293	0.628316
10	-0.004292	-0.0297	0.5118
11	-0.138733	-0.9612	0.829358
12	-0.029317	-0.2031	0.580047
13	0.014751	0.1022	0.459511
14	-0.096206	-0.6665	0.745869
15	-0.068742	-0.4763	0.681975
16	-0.005933	-0.0411	0.516309

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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code