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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 18 Dec 2009 04:29:14 -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/2009/Dec/18/t12611357822nqwp3s5tkv82aa.htm/, Retrieved Sat, 27 Apr 2024 11:35:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69243, Retrieved Sat, 27 Apr 2024 11:35:58 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

114

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

-       [(Partial) Autocorrelation Function] [] [2009-12-18 11:29:14] [02cb93c9d037d32bf77dfc632a3a9fbe] [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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69243&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69243&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69243&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.852946	6.6617	0
2	0.634231	4.9535	3e-06
3	0.518338	4.0483	7.4e-05
4	0.542175	4.2345	3.9e-05
5	0.631933	4.9356	3e-06
6	0.67582	5.2783	1e-06
7	0.597725	4.6684	9e-06
8	0.45116	3.5237	0.000407
9	0.34236	2.6739	0.004804
10	0.315562	2.4646	0.008274
11	0.363267	2.8372	0.003085
12	0.371012	2.8977	0.002608
13	0.288164	2.2506	0.014012
14	0.189428	1.4795	0.072079
15	0.130799	1.0216	0.155509
16	0.098566	0.7698	0.222187
17	0.075219	0.5875	0.279525

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.852946 & 6.6617 & 0 \tabularnewline
2 & 0.634231 & 4.9535 & 3e-06 \tabularnewline
3 & 0.518338 & 4.0483 & 7.4e-05 \tabularnewline
4 & 0.542175 & 4.2345 & 3.9e-05 \tabularnewline
5 & 0.631933 & 4.9356 & 3e-06 \tabularnewline
6 & 0.67582 & 5.2783 & 1e-06 \tabularnewline
7 & 0.597725 & 4.6684 & 9e-06 \tabularnewline
8 & 0.45116 & 3.5237 & 0.000407 \tabularnewline
9 & 0.34236 & 2.6739 & 0.004804 \tabularnewline
10 & 0.315562 & 2.4646 & 0.008274 \tabularnewline
11 & 0.363267 & 2.8372 & 0.003085 \tabularnewline
12 & 0.371012 & 2.8977 & 0.002608 \tabularnewline
13 & 0.288164 & 2.2506 & 0.014012 \tabularnewline
14 & 0.189428 & 1.4795 & 0.072079 \tabularnewline
15 & 0.130799 & 1.0216 & 0.155509 \tabularnewline
16 & 0.098566 & 0.7698 & 0.222187 \tabularnewline
17 & 0.075219 & 0.5875 & 0.279525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69243&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]0.852946[/C][C]6.6617[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.634231[/C][C]4.9535[/C][C]3e-06[/C][/ROW]
[ROW][C]3[/C][C]0.518338[/C][C]4.0483[/C][C]7.4e-05[/C][/ROW]
[ROW][C]4[/C][C]0.542175[/C][C]4.2345[/C][C]3.9e-05[/C][/ROW]
[ROW][C]5[/C][C]0.631933[/C][C]4.9356[/C][C]3e-06[/C][/ROW]
[ROW][C]6[/C][C]0.67582[/C][C]5.2783[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.597725[/C][C]4.6684[/C][C]9e-06[/C][/ROW]
[ROW][C]8[/C][C]0.45116[/C][C]3.5237[/C][C]0.000407[/C][/ROW]
[ROW][C]9[/C][C]0.34236[/C][C]2.6739[/C][C]0.004804[/C][/ROW]
[ROW][C]10[/C][C]0.315562[/C][C]2.4646[/C][C]0.008274[/C][/ROW]
[ROW][C]11[/C][C]0.363267[/C][C]2.8372[/C][C]0.003085[/C][/ROW]
[ROW][C]12[/C][C]0.371012[/C][C]2.8977[/C][C]0.002608[/C][/ROW]
[ROW][C]13[/C][C]0.288164[/C][C]2.2506[/C][C]0.014012[/C][/ROW]
[ROW][C]14[/C][C]0.189428[/C][C]1.4795[/C][C]0.072079[/C][/ROW]
[ROW][C]15[/C][C]0.130799[/C][C]1.0216[/C][C]0.155509[/C][/ROW]
[ROW][C]16[/C][C]0.098566[/C][C]0.7698[/C][C]0.222187[/C][/ROW]
[ROW][C]17[/C][C]0.075219[/C][C]0.5875[/C][C]0.279525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69243&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69243&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	0.852946	6.6617	0
2	0.634231	4.9535	3e-06
3	0.518338	4.0483	7.4e-05
4	0.542175	4.2345	3.9e-05
5	0.631933	4.9356	3e-06
6	0.67582	5.2783	1e-06
7	0.597725	4.6684	9e-06
8	0.45116	3.5237	0.000407
9	0.34236	2.6739	0.004804
10	0.315562	2.4646	0.008274
11	0.363267	2.8372	0.003085
12	0.371012	2.8977	0.002608
13	0.288164	2.2506	0.014012
14	0.189428	1.4795	0.072079
15	0.130799	1.0216	0.155509
16	0.098566	0.7698	0.222187
17	0.075219	0.5875	0.279525

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.852946	6.6617	0
2	-0.342352	-2.6739	0.004805
3	0.349952	2.7332	0.004098
4	0.281235	2.1965	0.015933
5	0.206603	1.6136	0.055886
6	0.045275	0.3536	0.362426
7	-0.17432	-1.3615	0.089184
8	-0.090474	-0.7066	0.241244
9	-0.05115	-0.3995	0.345463
10	-0.072101	-0.5631	0.287705
11	0.092914	0.7257	0.235404
12	-0.200204	-1.5636	0.061538
13	-0.076853	-0.6002	0.275284
14	0.115081	0.8988	0.186144
15	-0.0414	-0.3233	0.373772
16	-0.138483	-1.0816	0.141847
17	-0.081391	-0.6357	0.263681

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.852946 & 6.6617 & 0 \tabularnewline
2 & -0.342352 & -2.6739 & 0.004805 \tabularnewline
3 & 0.349952 & 2.7332 & 0.004098 \tabularnewline
4 & 0.281235 & 2.1965 & 0.015933 \tabularnewline
5 & 0.206603 & 1.6136 & 0.055886 \tabularnewline
6 & 0.045275 & 0.3536 & 0.362426 \tabularnewline
7 & -0.17432 & -1.3615 & 0.089184 \tabularnewline
8 & -0.090474 & -0.7066 & 0.241244 \tabularnewline
9 & -0.05115 & -0.3995 & 0.345463 \tabularnewline
10 & -0.072101 & -0.5631 & 0.287705 \tabularnewline
11 & 0.092914 & 0.7257 & 0.235404 \tabularnewline
12 & -0.200204 & -1.5636 & 0.061538 \tabularnewline
13 & -0.076853 & -0.6002 & 0.275284 \tabularnewline
14 & 0.115081 & 0.8988 & 0.186144 \tabularnewline
15 & -0.0414 & -0.3233 & 0.373772 \tabularnewline
16 & -0.138483 & -1.0816 & 0.141847 \tabularnewline
17 & -0.081391 & -0.6357 & 0.263681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69243&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]0.852946[/C][C]6.6617[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.342352[/C][C]-2.6739[/C][C]0.004805[/C][/ROW]
[ROW][C]3[/C][C]0.349952[/C][C]2.7332[/C][C]0.004098[/C][/ROW]
[ROW][C]4[/C][C]0.281235[/C][C]2.1965[/C][C]0.015933[/C][/ROW]
[ROW][C]5[/C][C]0.206603[/C][C]1.6136[/C][C]0.055886[/C][/ROW]
[ROW][C]6[/C][C]0.045275[/C][C]0.3536[/C][C]0.362426[/C][/ROW]
[ROW][C]7[/C][C]-0.17432[/C][C]-1.3615[/C][C]0.089184[/C][/ROW]
[ROW][C]8[/C][C]-0.090474[/C][C]-0.7066[/C][C]0.241244[/C][/ROW]
[ROW][C]9[/C][C]-0.05115[/C][C]-0.3995[/C][C]0.345463[/C][/ROW]
[ROW][C]10[/C][C]-0.072101[/C][C]-0.5631[/C][C]0.287705[/C][/ROW]
[ROW][C]11[/C][C]0.092914[/C][C]0.7257[/C][C]0.235404[/C][/ROW]
[ROW][C]12[/C][C]-0.200204[/C][C]-1.5636[/C][C]0.061538[/C][/ROW]
[ROW][C]13[/C][C]-0.076853[/C][C]-0.6002[/C][C]0.275284[/C][/ROW]
[ROW][C]14[/C][C]0.115081[/C][C]0.8988[/C][C]0.186144[/C][/ROW]
[ROW][C]15[/C][C]-0.0414[/C][C]-0.3233[/C][C]0.373772[/C][/ROW]
[ROW][C]16[/C][C]-0.138483[/C][C]-1.0816[/C][C]0.141847[/C][/ROW]
[ROW][C]17[/C][C]-0.081391[/C][C]-0.6357[/C][C]0.263681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69243&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69243&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	0.852946	6.6617	0
2	-0.342352	-2.6739	0.004805
3	0.349952	2.7332	0.004098
4	0.281235	2.1965	0.015933
5	0.206603	1.6136	0.055886
6	0.045275	0.3536	0.362426
7	-0.17432	-1.3615	0.089184
8	-0.090474	-0.7066	0.241244
9	-0.05115	-0.3995	0.345463
10	-0.072101	-0.5631	0.287705
11	0.092914	0.7257	0.235404
12	-0.200204	-1.5636	0.061538
13	-0.076853	-0.6002	0.275284
14	0.115081	0.8988	0.186144
15	-0.0414	-0.3233	0.373772
16	-0.138483	-1.0816	0.141847
17	-0.081391	-0.6357	0.263681

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; 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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code