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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 13 Dec 2007 02:19:40 -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/13/t1197536753wadovk05te8kc8r.htm/, Retrieved Sun, 05 May 2024 09:12:13 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3332, Retrieved Sun, 05 May 2024 09:12:13 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

218

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

-       [(Partial) Autocorrelation Function] [Paper (P)ACF tijd...] [2007-12-13 09:19:40] [cb172450b25aceeff04d58e88e905157] [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	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=3332&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=3332&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3332&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	7.6811	0
1	0.362524	2.7846	0.003596
2	0.404246	3.1051	0.001461
3	0.446263	3.4278	0.000558
4	0.289802	2.226	0.014923
5	0.332901	2.5571	0.006574
6	0.223329	1.7154	0.045758
7	0.236582	1.8172	0.037131
8	0.19819	1.5223	0.066634
9	0.083296	0.6398	0.262388
10	0.187992	1.444	0.077015
11	-0.007714	-0.0593	0.523524
12	0.027165	0.2087	0.417717
13	0.116396	0.8941	0.187462
14	-0.054821	-0.4211	0.662389
15	0.04235	0.3253	0.373054
16	-0.066315	-0.5094	0.693804

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.6811 & 0 \tabularnewline
1 & 0.362524 & 2.7846 & 0.003596 \tabularnewline
2 & 0.404246 & 3.1051 & 0.001461 \tabularnewline
3 & 0.446263 & 3.4278 & 0.000558 \tabularnewline
4 & 0.289802 & 2.226 & 0.014923 \tabularnewline
5 & 0.332901 & 2.5571 & 0.006574 \tabularnewline
6 & 0.223329 & 1.7154 & 0.045758 \tabularnewline
7 & 0.236582 & 1.8172 & 0.037131 \tabularnewline
8 & 0.19819 & 1.5223 & 0.066634 \tabularnewline
9 & 0.083296 & 0.6398 & 0.262388 \tabularnewline
10 & 0.187992 & 1.444 & 0.077015 \tabularnewline
11 & -0.007714 & -0.0593 & 0.523524 \tabularnewline
12 & 0.027165 & 0.2087 & 0.417717 \tabularnewline
13 & 0.116396 & 0.8941 & 0.187462 \tabularnewline
14 & -0.054821 & -0.4211 & 0.662389 \tabularnewline
15 & 0.04235 & 0.3253 & 0.373054 \tabularnewline
16 & -0.066315 & -0.5094 & 0.693804 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3332&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]7.6811[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.362524[/C][C]2.7846[/C][C]0.003596[/C][/ROW]
[ROW][C]2[/C][C]0.404246[/C][C]3.1051[/C][C]0.001461[/C][/ROW]
[ROW][C]3[/C][C]0.446263[/C][C]3.4278[/C][C]0.000558[/C][/ROW]
[ROW][C]4[/C][C]0.289802[/C][C]2.226[/C][C]0.014923[/C][/ROW]
[ROW][C]5[/C][C]0.332901[/C][C]2.5571[/C][C]0.006574[/C][/ROW]
[ROW][C]6[/C][C]0.223329[/C][C]1.7154[/C][C]0.045758[/C][/ROW]
[ROW][C]7[/C][C]0.236582[/C][C]1.8172[/C][C]0.037131[/C][/ROW]
[ROW][C]8[/C][C]0.19819[/C][C]1.5223[/C][C]0.066634[/C][/ROW]
[ROW][C]9[/C][C]0.083296[/C][C]0.6398[/C][C]0.262388[/C][/ROW]
[ROW][C]10[/C][C]0.187992[/C][C]1.444[/C][C]0.077015[/C][/ROW]
[ROW][C]11[/C][C]-0.007714[/C][C]-0.0593[/C][C]0.523524[/C][/ROW]
[ROW][C]12[/C][C]0.027165[/C][C]0.2087[/C][C]0.417717[/C][/ROW]
[ROW][C]13[/C][C]0.116396[/C][C]0.8941[/C][C]0.187462[/C][/ROW]
[ROW][C]14[/C][C]-0.054821[/C][C]-0.4211[/C][C]0.662389[/C][/ROW]
[ROW][C]15[/C][C]0.04235[/C][C]0.3253[/C][C]0.373054[/C][/ROW]
[ROW][C]16[/C][C]-0.066315[/C][C]-0.5094[/C][C]0.693804[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3332&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3332&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	7.6811	0
1	0.362524	2.7846	0.003596
2	0.404246	3.1051	0.001461
3	0.446263	3.4278	0.000558
4	0.289802	2.226	0.014923
5	0.332901	2.5571	0.006574
6	0.223329	1.7154	0.045758
7	0.236582	1.8172	0.037131
8	0.19819	1.5223	0.066634
9	0.083296	0.6398	0.262388
10	0.187992	1.444	0.077015
11	-0.007714	-0.0593	0.523524
12	0.027165	0.2087	0.417717
13	0.116396	0.8941	0.187462
14	-0.054821	-0.4211	0.662389
15	0.04235	0.3253	0.373054
16	-0.066315	-0.5094	0.693804

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.362524	2.7846	0.003596
1	0.314102	2.4127	0.009481
2	0.296182	2.275	0.013277
3	0.022091	0.1697	0.43292
4	0.081827	0.6285	0.266043
5	-0.060105	-0.4617	0.676994
6	0.032722	0.2513	0.401212
7	-0.011212	-0.0861	0.53417
8	-0.103217	-0.7928	0.784472
9	0.074243	0.5703	0.285328
10	-0.157584	-1.2104	0.884529
11	-0.02886	-0.2217	0.587336
12	0.110654	0.85	0.199394
13	-0.062744	-0.4819	0.684185
14	0.030879	0.2372	0.406667
15	-0.1001	-0.7689	0.777484
16	0.14336	1.1012	0.137648

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.362524 & 2.7846 & 0.003596 \tabularnewline
1 & 0.314102 & 2.4127 & 0.009481 \tabularnewline
2 & 0.296182 & 2.275 & 0.013277 \tabularnewline
3 & 0.022091 & 0.1697 & 0.43292 \tabularnewline
4 & 0.081827 & 0.6285 & 0.266043 \tabularnewline
5 & -0.060105 & -0.4617 & 0.676994 \tabularnewline
6 & 0.032722 & 0.2513 & 0.401212 \tabularnewline
7 & -0.011212 & -0.0861 & 0.53417 \tabularnewline
8 & -0.103217 & -0.7928 & 0.784472 \tabularnewline
9 & 0.074243 & 0.5703 & 0.285328 \tabularnewline
10 & -0.157584 & -1.2104 & 0.884529 \tabularnewline
11 & -0.02886 & -0.2217 & 0.587336 \tabularnewline
12 & 0.110654 & 0.85 & 0.199394 \tabularnewline
13 & -0.062744 & -0.4819 & 0.684185 \tabularnewline
14 & 0.030879 & 0.2372 & 0.406667 \tabularnewline
15 & -0.1001 & -0.7689 & 0.777484 \tabularnewline
16 & 0.14336 & 1.1012 & 0.137648 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3332&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]0.362524[/C][C]2.7846[/C][C]0.003596[/C][/ROW]
[ROW][C]1[/C][C]0.314102[/C][C]2.4127[/C][C]0.009481[/C][/ROW]
[ROW][C]2[/C][C]0.296182[/C][C]2.275[/C][C]0.013277[/C][/ROW]
[ROW][C]3[/C][C]0.022091[/C][C]0.1697[/C][C]0.43292[/C][/ROW]
[ROW][C]4[/C][C]0.081827[/C][C]0.6285[/C][C]0.266043[/C][/ROW]
[ROW][C]5[/C][C]-0.060105[/C][C]-0.4617[/C][C]0.676994[/C][/ROW]
[ROW][C]6[/C][C]0.032722[/C][C]0.2513[/C][C]0.401212[/C][/ROW]
[ROW][C]7[/C][C]-0.011212[/C][C]-0.0861[/C][C]0.53417[/C][/ROW]
[ROW][C]8[/C][C]-0.103217[/C][C]-0.7928[/C][C]0.784472[/C][/ROW]
[ROW][C]9[/C][C]0.074243[/C][C]0.5703[/C][C]0.285328[/C][/ROW]
[ROW][C]10[/C][C]-0.157584[/C][C]-1.2104[/C][C]0.884529[/C][/ROW]
[ROW][C]11[/C][C]-0.02886[/C][C]-0.2217[/C][C]0.587336[/C][/ROW]
[ROW][C]12[/C][C]0.110654[/C][C]0.85[/C][C]0.199394[/C][/ROW]
[ROW][C]13[/C][C]-0.062744[/C][C]-0.4819[/C][C]0.684185[/C][/ROW]
[ROW][C]14[/C][C]0.030879[/C][C]0.2372[/C][C]0.406667[/C][/ROW]
[ROW][C]15[/C][C]-0.1001[/C][C]-0.7689[/C][C]0.777484[/C][/ROW]
[ROW][C]16[/C][C]0.14336[/C][C]1.1012[/C][C]0.137648[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3332&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3332&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	0.362524	2.7846	0.003596
1	0.314102	2.4127	0.009481
2	0.296182	2.275	0.013277
3	0.022091	0.1697	0.43292
4	0.081827	0.6285	0.266043
5	-0.060105	-0.4617	0.676994
6	0.032722	0.2513	0.401212
7	-0.011212	-0.0861	0.53417
8	-0.103217	-0.7928	0.784472
9	0.074243	0.5703	0.285328
10	-0.157584	-1.2104	0.884529
11	-0.02886	-0.2217	0.587336
12	0.110654	0.85	0.199394
13	-0.062744	-0.4819	0.684185
14	0.030879	0.2372	0.406667
15	-0.1001	-0.7689	0.777484
16	0.14336	1.1012	0.137648

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 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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Input Parameters & R Code