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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 18 Aug 2010 08:34:33 +0000

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/2010/Aug/18/t12821204738a2ymx6dt2ssowp.htm/, Retrieved Thu, 16 May 2024 20:13:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79178, Retrieved Thu, 16 May 2024 20:13:00 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Patrick Fieremans

Estimated Impact

159

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

-       [(Partial) Autocorrelation Function] [Tijdreeks 1 - Sta...] [2010-08-18 08:34:33] [bffa0fb6afa860209dcefcd4361c2008] [Current]

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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=79178&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=79178&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79178&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	0.651875	7.1409	0
2	0.192148	2.1049	0.018694
3	-0.038566	-0.4225	0.336721
4	-0.116413	-1.2752	0.102344
5	-0.024828	-0.272	0.393053
6	0.052348	0.5734	0.283707
7	-0.000294	-0.0032	0.498718
8	-0.101691	-1.114	0.13376
9	-0.073257	-0.8025	0.211927
10	0.104197	1.1414	0.127985
11	0.478936	5.2465	0
12	0.763324	8.3618	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.651875 & 7.1409 & 0 \tabularnewline
2 & 0.192148 & 2.1049 & 0.018694 \tabularnewline
3 & -0.038566 & -0.4225 & 0.336721 \tabularnewline
4 & -0.116413 & -1.2752 & 0.102344 \tabularnewline
5 & -0.024828 & -0.272 & 0.393053 \tabularnewline
6 & 0.052348 & 0.5734 & 0.283707 \tabularnewline
7 & -0.000294 & -0.0032 & 0.498718 \tabularnewline
8 & -0.101691 & -1.114 & 0.13376 \tabularnewline
9 & -0.073257 & -0.8025 & 0.211927 \tabularnewline
10 & 0.104197 & 1.1414 & 0.127985 \tabularnewline
11 & 0.478936 & 5.2465 & 0 \tabularnewline
12 & 0.763324 & 8.3618 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79178&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]0.651875[/C][C]7.1409[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.192148[/C][C]2.1049[/C][C]0.018694[/C][/ROW]
[ROW][C]3[/C][C]-0.038566[/C][C]-0.4225[/C][C]0.336721[/C][/ROW]
[ROW][C]4[/C][C]-0.116413[/C][C]-1.2752[/C][C]0.102344[/C][/ROW]
[ROW][C]5[/C][C]-0.024828[/C][C]-0.272[/C][C]0.393053[/C][/ROW]
[ROW][C]6[/C][C]0.052348[/C][C]0.5734[/C][C]0.283707[/C][/ROW]
[ROW][C]7[/C][C]-0.000294[/C][C]-0.0032[/C][C]0.498718[/C][/ROW]
[ROW][C]8[/C][C]-0.101691[/C][C]-1.114[/C][C]0.13376[/C][/ROW]
[ROW][C]9[/C][C]-0.073257[/C][C]-0.8025[/C][C]0.211927[/C][/ROW]
[ROW][C]10[/C][C]0.104197[/C][C]1.1414[/C][C]0.127985[/C][/ROW]
[ROW][C]11[/C][C]0.478936[/C][C]5.2465[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.763324[/C][C]8.3618[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79178&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79178&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	0.651875	7.1409	0
2	0.192148	2.1049	0.018694
3	-0.038566	-0.4225	0.336721
4	-0.116413	-1.2752	0.102344
5	-0.024828	-0.272	0.393053
6	0.052348	0.5734	0.283707
7	-0.000294	-0.0032	0.498718
8	-0.101691	-1.114	0.13376
9	-0.073257	-0.8025	0.211927
10	0.104197	1.1414	0.127985
11	0.478936	5.2465	0
12	0.763324	8.3618	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.651875	7.1409	0
2	-0.404816	-4.4345	1e-05
3	0.102662	1.1246	0.131501
4	-0.106287	-1.1643	0.123302
5	0.205394	2.25	0.013136
6	-0.122524	-1.3422	0.091034
7	-0.056486	-0.6188	0.268618
8	-0.095103	-1.0418	0.149798
9	0.198641	2.176	0.015757
10	0.142038	1.5559	0.061177
11	0.605837	6.6366	0
12	0.24969	2.7352	0.00359

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.651875 & 7.1409 & 0 \tabularnewline
2 & -0.404816 & -4.4345 & 1e-05 \tabularnewline
3 & 0.102662 & 1.1246 & 0.131501 \tabularnewline
4 & -0.106287 & -1.1643 & 0.123302 \tabularnewline
5 & 0.205394 & 2.25 & 0.013136 \tabularnewline
6 & -0.122524 & -1.3422 & 0.091034 \tabularnewline
7 & -0.056486 & -0.6188 & 0.268618 \tabularnewline
8 & -0.095103 & -1.0418 & 0.149798 \tabularnewline
9 & 0.198641 & 2.176 & 0.015757 \tabularnewline
10 & 0.142038 & 1.5559 & 0.061177 \tabularnewline
11 & 0.605837 & 6.6366 & 0 \tabularnewline
12 & 0.24969 & 2.7352 & 0.00359 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79178&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]0.651875[/C][C]7.1409[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.404816[/C][C]-4.4345[/C][C]1e-05[/C][/ROW]
[ROW][C]3[/C][C]0.102662[/C][C]1.1246[/C][C]0.131501[/C][/ROW]
[ROW][C]4[/C][C]-0.106287[/C][C]-1.1643[/C][C]0.123302[/C][/ROW]
[ROW][C]5[/C][C]0.205394[/C][C]2.25[/C][C]0.013136[/C][/ROW]
[ROW][C]6[/C][C]-0.122524[/C][C]-1.3422[/C][C]0.091034[/C][/ROW]
[ROW][C]7[/C][C]-0.056486[/C][C]-0.6188[/C][C]0.268618[/C][/ROW]
[ROW][C]8[/C][C]-0.095103[/C][C]-1.0418[/C][C]0.149798[/C][/ROW]
[ROW][C]9[/C][C]0.198641[/C][C]2.176[/C][C]0.015757[/C][/ROW]
[ROW][C]10[/C][C]0.142038[/C][C]1.5559[/C][C]0.061177[/C][/ROW]
[ROW][C]11[/C][C]0.605837[/C][C]6.6366[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.24969[/C][C]2.7352[/C][C]0.00359[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79178&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79178&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	0.651875	7.1409	0
2	-0.404816	-4.4345	1e-05
3	0.102662	1.1246	0.131501
4	-0.106287	-1.1643	0.123302
5	0.205394	2.25	0.013136
6	-0.122524	-1.3422	0.091034
7	-0.056486	-0.6188	0.268618
8	-0.095103	-1.0418	0.149798
9	0.198641	2.176	0.015757
10	0.142038	1.5559	0.061177
11	0.605837	6.6366	0
12	0.24969	2.7352	0.00359

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 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code