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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 30 Nov 2008 11:03:25 -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/Nov/30/t12280682233y115j3qjh4ubwe.htm/, Retrieved Fri, 24 May 2024 10:11:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26657, Retrieved Fri, 24 May 2024 10:11:41 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

224

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] [2008-11-29 20:10:39] [57fa5e3679c393aa19449b2f1be9928b]
-   P     [Standard Deviation-Mean Plot] [Q5] [2008-11-29 20:18:39] [57fa5e3679c393aa19449b2f1be9928b]
- RM        [Variance Reduction Matrix] [Q6 Variance] [2008-11-29 20:25:29] [57fa5e3679c393aa19449b2f1be9928b]
- RM          [(Partial) Autocorrelation Function] [Q6 ACF] [2008-11-29 20:35:57] [57fa5e3679c393aa19449b2f1be9928b]
-   P           [(Partial) Autocorrelation Function] [] [2008-11-30 11:08:30] [a4ee3bef49b119f4bd2e925060c84f5e]
F                   [(Partial) Autocorrelation Function] [] [2008-11-30 18:03:25] [6912578025c824de531bc660dd61b996] [Current]
F                     [(Partial) Autocorrelation Function] [] [2008-12-01 17:22:25] [29747f79f5beb5b2516e1271770ecb47] 
F                     [(Partial) Autocorrelation Function] [] [2008-12-01 17:24:04] [4ddbf81f78ea7c738951638c7e93f6ee] 
-                     [(Partial) Autocorrelation Function] [q6 taak 7] [2008-12-01 17:29:03] [7506b5e9e41ec66c6657f4234f97306e] 
F                     [(Partial) Autocorrelation Function] [Q 6 ACF] [2008-12-01 17:40:17] [491a70d26f8c977398d8a0c1c87d3dd4] 
-                       [(Partial) Autocorrelation Function] [Q6] [2008-12-01 21:21:38] [82d201ca7b4e7cd2c6f885d29b5b6937] 
-   P                   [(Partial) Autocorrelation Function] [autocorrelation] [2008-12-07 10:15:03] [ed2ba3b6182103c15c0ab511ae4e6284] 
-                     [(Partial) Autocorrelation Function] [Q6] [2008-12-01 18:33:00] [4ad596f10399a71ad29b7d76e6ab90ac] 
-                     [(Partial) Autocorrelation Function] [Non Stationary Ti...] [2008-12-01 18:45:23] [79c17183721a40a589db5f9f561947d8] 
-                     [(Partial) Autocorrelation Function] [] [2008-12-01 18:55:51] [c5e27150943bc3d623392efb0d98f8d3] 
-                     [(Partial) Autocorrelation Function] [Q6] [2008-12-01 18:58:21] [b47fceb71c9525e79a89b5fc6d023d0e] 
F                     [(Partial) Autocorrelation Function] [Non Stationary Ti...] [2008-12-01 19:37:23] [db72903d7941c8279d5ce0e4e873d517] 
-                     [(Partial) Autocorrelation Function] [] [2008-12-01 23:14:26] [fad8a251ac01c156a8ae23a83577546f] 

Feedback Forum

2008-12-08 16:29:41 [Lindsay Heyndrickx] [reply] 
Bij de autocorrolatie voegen we 36 lags in zodat we voldoende terug kunnen gaan.  Bji de Variance Reduction Matrix: krijgen we de kleinste variantie bij d=1 en D=1. Dit hebben we nodig om de tijdreeks stationair te maken. 
Bij de spectrum analyse zien we de frequentie gecumuleerd. Dit wordt geschat tussen 0 en 1. Hier kunnen we zeggen dat het hier significant is daar de grafiek niet tussen de twee stippellijnen ligt.  
Nadat we de seizonaliteit er hebben uitgehaald en de tijdreeks stationair hebben gemaakt door D=1 en d=1 te doen krijgen we een grafiek die beter tussen de stippelijnen valt. 

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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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26657&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26657&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26657&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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.948047	11.3766	0
2	0.875575	10.5069	0
3	0.806681	9.6802	0
4	0.752625	9.0315	0
5	0.71377	8.5652	0
6	0.681734	8.1808	0
7	0.662904	7.9549	0
8	0.65561	7.8673	0
9	0.670948	8.0514	0
10	0.70272	8.4326	0
11	0.74324	8.9189	0
12	0.760395	9.1247	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.948047 & 11.3766 & 0 \tabularnewline
2 & 0.875575 & 10.5069 & 0 \tabularnewline
3 & 0.806681 & 9.6802 & 0 \tabularnewline
4 & 0.752625 & 9.0315 & 0 \tabularnewline
5 & 0.71377 & 8.5652 & 0 \tabularnewline
6 & 0.681734 & 8.1808 & 0 \tabularnewline
7 & 0.662904 & 7.9549 & 0 \tabularnewline
8 & 0.65561 & 7.8673 & 0 \tabularnewline
9 & 0.670948 & 8.0514 & 0 \tabularnewline
10 & 0.70272 & 8.4326 & 0 \tabularnewline
11 & 0.74324 & 8.9189 & 0 \tabularnewline
12 & 0.760395 & 9.1247 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26657&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]0.948047[/C][C]11.3766[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.875575[/C][C]10.5069[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.806681[/C][C]9.6802[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.752625[/C][C]9.0315[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.71377[/C][C]8.5652[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.681734[/C][C]8.1808[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.662904[/C][C]7.9549[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.65561[/C][C]7.8673[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.670948[/C][C]8.0514[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.70272[/C][C]8.4326[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.74324[/C][C]8.9189[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.760395[/C][C]9.1247[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26657&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26657&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	0.948047	11.3766	0
2	0.875575	10.5069	0
3	0.806681	9.6802	0
4	0.752625	9.0315	0
5	0.71377	8.5652	0
6	0.681734	8.1808	0
7	0.662904	7.9549	0
8	0.65561	7.8673	0
9	0.670948	8.0514	0
10	0.70272	8.4326	0
11	0.74324	8.9189	0
12	0.760395	9.1247	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.948047	11.3766	0
2	-0.229422	-2.7531	0.003332
3	0.038148	0.4578	0.323903
4	0.093785	1.1254	0.131141
5	0.073607	0.8833	0.189279
6	0.007728	0.0927	0.463123
7	0.125597	1.5072	0.066979
8	0.089951	1.0794	0.141103
9	0.232489	2.7899	0.002994
10	0.166051	1.9926	0.024097
11	0.171274	2.0553	0.020829
12	-0.135431	-1.6252	0.053156

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.948047 & 11.3766 & 0 \tabularnewline
2 & -0.229422 & -2.7531 & 0.003332 \tabularnewline
3 & 0.038148 & 0.4578 & 0.323903 \tabularnewline
4 & 0.093785 & 1.1254 & 0.131141 \tabularnewline
5 & 0.073607 & 0.8833 & 0.189279 \tabularnewline
6 & 0.007728 & 0.0927 & 0.463123 \tabularnewline
7 & 0.125597 & 1.5072 & 0.066979 \tabularnewline
8 & 0.089951 & 1.0794 & 0.141103 \tabularnewline
9 & 0.232489 & 2.7899 & 0.002994 \tabularnewline
10 & 0.166051 & 1.9926 & 0.024097 \tabularnewline
11 & 0.171274 & 2.0553 & 0.020829 \tabularnewline
12 & -0.135431 & -1.6252 & 0.053156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26657&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]0.948047[/C][C]11.3766[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.229422[/C][C]-2.7531[/C][C]0.003332[/C][/ROW]
[ROW][C]3[/C][C]0.038148[/C][C]0.4578[/C][C]0.323903[/C][/ROW]
[ROW][C]4[/C][C]0.093785[/C][C]1.1254[/C][C]0.131141[/C][/ROW]
[ROW][C]5[/C][C]0.073607[/C][C]0.8833[/C][C]0.189279[/C][/ROW]
[ROW][C]6[/C][C]0.007728[/C][C]0.0927[/C][C]0.463123[/C][/ROW]
[ROW][C]7[/C][C]0.125597[/C][C]1.5072[/C][C]0.066979[/C][/ROW]
[ROW][C]8[/C][C]0.089951[/C][C]1.0794[/C][C]0.141103[/C][/ROW]
[ROW][C]9[/C][C]0.232489[/C][C]2.7899[/C][C]0.002994[/C][/ROW]
[ROW][C]10[/C][C]0.166051[/C][C]1.9926[/C][C]0.024097[/C][/ROW]
[ROW][C]11[/C][C]0.171274[/C][C]2.0553[/C][C]0.020829[/C][/ROW]
[ROW][C]12[/C][C]-0.135431[/C][C]-1.6252[/C][C]0.053156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26657&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26657&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	0.948047	11.3766	0
2	-0.229422	-2.7531	0.003332
3	0.038148	0.4578	0.323903
4	0.093785	1.1254	0.131141
5	0.073607	0.8833	0.189279
6	0.007728	0.0927	0.463123
7	0.125597	1.5072	0.066979
8	0.089951	1.0794	0.141103
9	0.232489	2.7899	0.002994
10	0.166051	1.9926	0.024097
11	0.171274	2.0553	0.020829
12	-0.135431	-1.6252	0.053156

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = 12 ; 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 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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code