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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 03 Dec 2008 06:23:01 -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/2008/Dec/03/t12283106010fmb56ykplg1oht.htm/, Retrieved Sun, 19 May 2024 07:08:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28692, Retrieved Sun, 19 May 2024 07:08:17 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

182

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

F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
- RMPD  [Standard Deviation-Mean Plot] [q5] [2008-12-03 13:15:06] [3ffd109c9e040b1ae7e5dbe576d4698c]
- RMPD    [(Partial) Autocorrelation Function] [q8] [2008-12-03 13:16:51] [3ffd109c9e040b1ae7e5dbe576d4698c]
-   P         [(Partial) Autocorrelation Function] [q8] [2008-12-03 13:23:01] [962e6c9020896982bc8283b8971710a9] [Current]
-   P           [(Partial) Autocorrelation Function] [q8] [2008-12-03 13:25:43] [3ffd109c9e040b1ae7e5dbe576d4698c] 
- RMP             [Spectral Analysis] [q8] [2008-12-03 13:33:46] [3ffd109c9e040b1ae7e5dbe576d4698c] 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational 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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28692&T=0

[TABLE]
[ROW][C]Summary of computational 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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28692&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28692&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 computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.109039	0.8446	0.200841
2	-0.166477	-1.2895	0.101082
3	-0.230726	-1.7872	0.039479
4	-0.232809	-1.8033	0.038179
5	0.066944	0.5185	0.302993
6	0.17899	1.3865	0.085369
7	0.112688	0.8729	0.193105
8	-0.251955	-1.9516	0.027827
9	-0.209007	-1.619	0.05535
10	-0.15983	-1.238	0.110262
11	0.161154	1.2483	0.108387
12	0.677035	5.2443	1e-06
13	0.018582	0.1439	0.443017
14	-0.115114	-0.8917	0.188066
15	-0.213956	-1.6573	0.05134
16	-0.17807	-1.3793	0.086457
17	0.06455	0.5	0.309451

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.109039 & 0.8446 & 0.200841 \tabularnewline
2 & -0.166477 & -1.2895 & 0.101082 \tabularnewline
3 & -0.230726 & -1.7872 & 0.039479 \tabularnewline
4 & -0.232809 & -1.8033 & 0.038179 \tabularnewline
5 & 0.066944 & 0.5185 & 0.302993 \tabularnewline
6 & 0.17899 & 1.3865 & 0.085369 \tabularnewline
7 & 0.112688 & 0.8729 & 0.193105 \tabularnewline
8 & -0.251955 & -1.9516 & 0.027827 \tabularnewline
9 & -0.209007 & -1.619 & 0.05535 \tabularnewline
10 & -0.15983 & -1.238 & 0.110262 \tabularnewline
11 & 0.161154 & 1.2483 & 0.108387 \tabularnewline
12 & 0.677035 & 5.2443 & 1e-06 \tabularnewline
13 & 0.018582 & 0.1439 & 0.443017 \tabularnewline
14 & -0.115114 & -0.8917 & 0.188066 \tabularnewline
15 & -0.213956 & -1.6573 & 0.05134 \tabularnewline
16 & -0.17807 & -1.3793 & 0.086457 \tabularnewline
17 & 0.06455 & 0.5 & 0.309451 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28692&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]1[/C][C]0.109039[/C][C]0.8446[/C][C]0.200841[/C][/ROW]
[ROW][C]2[/C][C]-0.166477[/C][C]-1.2895[/C][C]0.101082[/C][/ROW]
[ROW][C]3[/C][C]-0.230726[/C][C]-1.7872[/C][C]0.039479[/C][/ROW]
[ROW][C]4[/C][C]-0.232809[/C][C]-1.8033[/C][C]0.038179[/C][/ROW]
[ROW][C]5[/C][C]0.066944[/C][C]0.5185[/C][C]0.302993[/C][/ROW]
[ROW][C]6[/C][C]0.17899[/C][C]1.3865[/C][C]0.085369[/C][/ROW]
[ROW][C]7[/C][C]0.112688[/C][C]0.8729[/C][C]0.193105[/C][/ROW]
[ROW][C]8[/C][C]-0.251955[/C][C]-1.9516[/C][C]0.027827[/C][/ROW]
[ROW][C]9[/C][C]-0.209007[/C][C]-1.619[/C][C]0.05535[/C][/ROW]
[ROW][C]10[/C][C]-0.15983[/C][C]-1.238[/C][C]0.110262[/C][/ROW]
[ROW][C]11[/C][C]0.161154[/C][C]1.2483[/C][C]0.108387[/C][/ROW]
[ROW][C]12[/C][C]0.677035[/C][C]5.2443[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.018582[/C][C]0.1439[/C][C]0.443017[/C][/ROW]
[ROW][C]14[/C][C]-0.115114[/C][C]-0.8917[/C][C]0.188066[/C][/ROW]
[ROW][C]15[/C][C]-0.213956[/C][C]-1.6573[/C][C]0.05134[/C][/ROW]
[ROW][C]16[/C][C]-0.17807[/C][C]-1.3793[/C][C]0.086457[/C][/ROW]
[ROW][C]17[/C][C]0.06455[/C][C]0.5[/C][C]0.309451[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28692&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28692&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
1	0.109039	0.8446	0.200841
2	-0.166477	-1.2895	0.101082
3	-0.230726	-1.7872	0.039479
4	-0.232809	-1.8033	0.038179
5	0.066944	0.5185	0.302993
6	0.17899	1.3865	0.085369
7	0.112688	0.8729	0.193105
8	-0.251955	-1.9516	0.027827
9	-0.209007	-1.619	0.05535
10	-0.15983	-1.238	0.110262
11	0.161154	1.2483	0.108387
12	0.677035	5.2443	1e-06
13	0.018582	0.1439	0.443017
14	-0.115114	-0.8917	0.188066
15	-0.213956	-1.6573	0.05134
16	-0.17807	-1.3793	0.086457
17	0.06455	0.5	0.309451

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.109039	0.8446	0.200841
2	-0.180513	-1.3982	0.083593
3	-0.198358	-1.5365	0.064839
4	-0.234718	-1.8181	0.037019
5	0.034329	0.2659	0.395611
6	0.057584	0.446	0.328587
7	0.028195	0.2184	0.413931
8	-0.293577	-2.274	0.013277
9	-0.118442	-0.9174	0.181291
10	-0.198341	-1.5363	0.064855
11	0.078168	0.6055	0.273569
12	0.574282	4.4484	1.9e-05
13	-0.13957	-1.0811	0.141989
14	0.06703	0.5192	0.302761
15	0.00805	0.0624	0.475243
16	0.016425	0.1272	0.449594
17	0.006363	0.0493	0.480428

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.109039 & 0.8446 & 0.200841 \tabularnewline
2 & -0.180513 & -1.3982 & 0.083593 \tabularnewline
3 & -0.198358 & -1.5365 & 0.064839 \tabularnewline
4 & -0.234718 & -1.8181 & 0.037019 \tabularnewline
5 & 0.034329 & 0.2659 & 0.395611 \tabularnewline
6 & 0.057584 & 0.446 & 0.328587 \tabularnewline
7 & 0.028195 & 0.2184 & 0.413931 \tabularnewline
8 & -0.293577 & -2.274 & 0.013277 \tabularnewline
9 & -0.118442 & -0.9174 & 0.181291 \tabularnewline
10 & -0.198341 & -1.5363 & 0.064855 \tabularnewline
11 & 0.078168 & 0.6055 & 0.273569 \tabularnewline
12 & 0.574282 & 4.4484 & 1.9e-05 \tabularnewline
13 & -0.13957 & -1.0811 & 0.141989 \tabularnewline
14 & 0.06703 & 0.5192 & 0.302761 \tabularnewline
15 & 0.00805 & 0.0624 & 0.475243 \tabularnewline
16 & 0.016425 & 0.1272 & 0.449594 \tabularnewline
17 & 0.006363 & 0.0493 & 0.480428 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28692&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]1[/C][C]0.109039[/C][C]0.8446[/C][C]0.200841[/C][/ROW]
[ROW][C]2[/C][C]-0.180513[/C][C]-1.3982[/C][C]0.083593[/C][/ROW]
[ROW][C]3[/C][C]-0.198358[/C][C]-1.5365[/C][C]0.064839[/C][/ROW]
[ROW][C]4[/C][C]-0.234718[/C][C]-1.8181[/C][C]0.037019[/C][/ROW]
[ROW][C]5[/C][C]0.034329[/C][C]0.2659[/C][C]0.395611[/C][/ROW]
[ROW][C]6[/C][C]0.057584[/C][C]0.446[/C][C]0.328587[/C][/ROW]
[ROW][C]7[/C][C]0.028195[/C][C]0.2184[/C][C]0.413931[/C][/ROW]
[ROW][C]8[/C][C]-0.293577[/C][C]-2.274[/C][C]0.013277[/C][/ROW]
[ROW][C]9[/C][C]-0.118442[/C][C]-0.9174[/C][C]0.181291[/C][/ROW]
[ROW][C]10[/C][C]-0.198341[/C][C]-1.5363[/C][C]0.064855[/C][/ROW]
[ROW][C]11[/C][C]0.078168[/C][C]0.6055[/C][C]0.273569[/C][/ROW]
[ROW][C]12[/C][C]0.574282[/C][C]4.4484[/C][C]1.9e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.13957[/C][C]-1.0811[/C][C]0.141989[/C][/ROW]
[ROW][C]14[/C][C]0.06703[/C][C]0.5192[/C][C]0.302761[/C][/ROW]
[ROW][C]15[/C][C]0.00805[/C][C]0.0624[/C][C]0.475243[/C][/ROW]
[ROW][C]16[/C][C]0.016425[/C][C]0.1272[/C][C]0.449594[/C][/ROW]
[ROW][C]17[/C][C]0.006363[/C][C]0.0493[/C][C]0.480428[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28692&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28692&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
1	0.109039	0.8446	0.200841
2	-0.180513	-1.3982	0.083593
3	-0.198358	-1.5365	0.064839
4	-0.234718	-1.8181	0.037019
5	0.034329	0.2659	0.395611
6	0.057584	0.446	0.328587
7	0.028195	0.2184	0.413931
8	-0.293577	-2.274	0.013277
9	-0.118442	-0.9174	0.181291
10	-0.198341	-1.5363	0.064855
11	0.078168	0.6055	0.273569
12	0.574282	4.4484	1.9e-05
13	-0.13957	-1.0811	0.141989
14	0.06703	0.5192	0.302761
15	0.00805	0.0624	0.475243
16	0.016425	0.1272	0.449594
17	0.006363	0.0493	0.480428

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 2:(par1+1)) {
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(abs(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,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(abs(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