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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 25 Jul 2012 07:45:17 -0400

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/2012/Jul/25/t134321707136tw3vc2fcwhkwn.htm/, Retrieved Sat, 04 May 2024 05:28:49 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=168863, Retrieved Sat, 04 May 2024 05:28:49 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Van Maele Karen

Estimated Impact

160

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

-       [(Partial) Autocorrelation Function] [Autocorrelatie om...] [2012-07-25 11:45:17] [459538fe31c621d37110fb87514358a8] [Current]
- R P     [(Partial) Autocorrelation Function] [Autocorrelatie om...] [2012-07-25 11:52:34] [3651d3756f567419d1119fcc89fff080] 
-   P       [(Partial) Autocorrelation Function] [Gedifferentieerde...] [2012-07-25 12:05:33] [3651d3756f567419d1119fcc89fff080] 

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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	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168863&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168863&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168863&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	2 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.869396	9.5238	0
2	0.765539	8.3861	0
3	0.723451	7.925	0
4	0.686949	7.5252	0
5	0.704136	7.7134	0
6	0.723788	7.9287	0
7	0.677777	7.4247	0
8	0.627206	6.8707	0
9	0.627467	6.8736	0
10	0.613786	6.7237	0
11	0.664012	7.2739	0
12	0.722978	7.9198	0
13	0.600401	6.5771	0
14	0.494968	5.4221	0
15	0.447246	4.8993	2e-06
16	0.409724	4.4883	8e-06
17	0.423484	4.639	4e-06
18	0.448345	4.9114	1e-06
19	0.407335	4.4621	9e-06
20	0.348752	3.8204	0.000106

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.869396 & 9.5238 & 0 \tabularnewline
2 & 0.765539 & 8.3861 & 0 \tabularnewline
3 & 0.723451 & 7.925 & 0 \tabularnewline
4 & 0.686949 & 7.5252 & 0 \tabularnewline
5 & 0.704136 & 7.7134 & 0 \tabularnewline
6 & 0.723788 & 7.9287 & 0 \tabularnewline
7 & 0.677777 & 7.4247 & 0 \tabularnewline
8 & 0.627206 & 6.8707 & 0 \tabularnewline
9 & 0.627467 & 6.8736 & 0 \tabularnewline
10 & 0.613786 & 6.7237 & 0 \tabularnewline
11 & 0.664012 & 7.2739 & 0 \tabularnewline
12 & 0.722978 & 7.9198 & 0 \tabularnewline
13 & 0.600401 & 6.5771 & 0 \tabularnewline
14 & 0.494968 & 5.4221 & 0 \tabularnewline
15 & 0.447246 & 4.8993 & 2e-06 \tabularnewline
16 & 0.409724 & 4.4883 & 8e-06 \tabularnewline
17 & 0.423484 & 4.639 & 4e-06 \tabularnewline
18 & 0.448345 & 4.9114 & 1e-06 \tabularnewline
19 & 0.407335 & 4.4621 & 9e-06 \tabularnewline
20 & 0.348752 & 3.8204 & 0.000106 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168863&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]0.869396[/C][C]9.5238[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.765539[/C][C]8.3861[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.723451[/C][C]7.925[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.686949[/C][C]7.5252[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.704136[/C][C]7.7134[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.723788[/C][C]7.9287[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.677777[/C][C]7.4247[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.627206[/C][C]6.8707[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.627467[/C][C]6.8736[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.613786[/C][C]6.7237[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.664012[/C][C]7.2739[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.722978[/C][C]7.9198[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.600401[/C][C]6.5771[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.494968[/C][C]5.4221[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.447246[/C][C]4.8993[/C][C]2e-06[/C][/ROW]
[ROW][C]16[/C][C]0.409724[/C][C]4.4883[/C][C]8e-06[/C][/ROW]
[ROW][C]17[/C][C]0.423484[/C][C]4.639[/C][C]4e-06[/C][/ROW]
[ROW][C]18[/C][C]0.448345[/C][C]4.9114[/C][C]1e-06[/C][/ROW]
[ROW][C]19[/C][C]0.407335[/C][C]4.4621[/C][C]9e-06[/C][/ROW]
[ROW][C]20[/C][C]0.348752[/C][C]3.8204[/C][C]0.000106[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168863&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168863&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	0.869396	9.5238	0
2	0.765539	8.3861	0
3	0.723451	7.925	0
4	0.686949	7.5252	0
5	0.704136	7.7134	0
6	0.723788	7.9287	0
7	0.677777	7.4247	0
8	0.627206	6.8707	0
9	0.627467	6.8736	0
10	0.613786	6.7237	0
11	0.664012	7.2739	0
12	0.722978	7.9198	0
13	0.600401	6.5771	0
14	0.494968	5.4221	0
15	0.447246	4.8993	2e-06
16	0.409724	4.4883	8e-06
17	0.423484	4.639	4e-06
18	0.448345	4.9114	1e-06
19	0.407335	4.4621	9e-06
20	0.348752	3.8204	0.000106

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.869396	9.5238	0
2	0.039685	0.4347	0.332271
3	0.204313	2.2381	0.013528
4	0.048745	0.534	0.297172
5	0.279621	3.0631	0.001352
6	0.120375	1.3186	0.094901
7	-0.114178	-1.2508	0.106729
8	-0.02916	-0.3194	0.374977
9	0.167294	1.8326	0.034669
10	-0.022763	-0.2494	0.401755
11	0.294578	3.2269	0.000807
12	0.151091	1.6551	0.050256
13	-0.593769	-6.5044	0
14	-0.118956	-1.3031	0.097518
15	-0.003852	-0.0422	0.483205
16	-0.027315	-0.2992	0.382645
17	0.010667	0.1169	0.453585
18	0.048608	0.5325	0.297691
19	0.022846	0.2503	0.401406
20	-0.089413	-0.9795	0.164659

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.869396 & 9.5238 & 0 \tabularnewline
2 & 0.039685 & 0.4347 & 0.332271 \tabularnewline
3 & 0.204313 & 2.2381 & 0.013528 \tabularnewline
4 & 0.048745 & 0.534 & 0.297172 \tabularnewline
5 & 0.279621 & 3.0631 & 0.001352 \tabularnewline
6 & 0.120375 & 1.3186 & 0.094901 \tabularnewline
7 & -0.114178 & -1.2508 & 0.106729 \tabularnewline
8 & -0.02916 & -0.3194 & 0.374977 \tabularnewline
9 & 0.167294 & 1.8326 & 0.034669 \tabularnewline
10 & -0.022763 & -0.2494 & 0.401755 \tabularnewline
11 & 0.294578 & 3.2269 & 0.000807 \tabularnewline
12 & 0.151091 & 1.6551 & 0.050256 \tabularnewline
13 & -0.593769 & -6.5044 & 0 \tabularnewline
14 & -0.118956 & -1.3031 & 0.097518 \tabularnewline
15 & -0.003852 & -0.0422 & 0.483205 \tabularnewline
16 & -0.027315 & -0.2992 & 0.382645 \tabularnewline
17 & 0.010667 & 0.1169 & 0.453585 \tabularnewline
18 & 0.048608 & 0.5325 & 0.297691 \tabularnewline
19 & 0.022846 & 0.2503 & 0.401406 \tabularnewline
20 & -0.089413 & -0.9795 & 0.164659 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=168863&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]0.869396[/C][C]9.5238[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.039685[/C][C]0.4347[/C][C]0.332271[/C][/ROW]
[ROW][C]3[/C][C]0.204313[/C][C]2.2381[/C][C]0.013528[/C][/ROW]
[ROW][C]4[/C][C]0.048745[/C][C]0.534[/C][C]0.297172[/C][/ROW]
[ROW][C]5[/C][C]0.279621[/C][C]3.0631[/C][C]0.001352[/C][/ROW]
[ROW][C]6[/C][C]0.120375[/C][C]1.3186[/C][C]0.094901[/C][/ROW]
[ROW][C]7[/C][C]-0.114178[/C][C]-1.2508[/C][C]0.106729[/C][/ROW]
[ROW][C]8[/C][C]-0.02916[/C][C]-0.3194[/C][C]0.374977[/C][/ROW]
[ROW][C]9[/C][C]0.167294[/C][C]1.8326[/C][C]0.034669[/C][/ROW]
[ROW][C]10[/C][C]-0.022763[/C][C]-0.2494[/C][C]0.401755[/C][/ROW]
[ROW][C]11[/C][C]0.294578[/C][C]3.2269[/C][C]0.000807[/C][/ROW]
[ROW][C]12[/C][C]0.151091[/C][C]1.6551[/C][C]0.050256[/C][/ROW]
[ROW][C]13[/C][C]-0.593769[/C][C]-6.5044[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]-0.118956[/C][C]-1.3031[/C][C]0.097518[/C][/ROW]
[ROW][C]15[/C][C]-0.003852[/C][C]-0.0422[/C][C]0.483205[/C][/ROW]
[ROW][C]16[/C][C]-0.027315[/C][C]-0.2992[/C][C]0.382645[/C][/ROW]
[ROW][C]17[/C][C]0.010667[/C][C]0.1169[/C][C]0.453585[/C][/ROW]
[ROW][C]18[/C][C]0.048608[/C][C]0.5325[/C][C]0.297691[/C][/ROW]
[ROW][C]19[/C][C]0.022846[/C][C]0.2503[/C][C]0.401406[/C][/ROW]
[ROW][C]20[/C][C]-0.089413[/C][C]-0.9795[/C][C]0.164659[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=168863&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=168863&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	0.869396	9.5238	0
2	0.039685	0.4347	0.332271
3	0.204313	2.2381	0.013528
4	0.048745	0.534	0.297172
5	0.279621	3.0631	0.001352
6	0.120375	1.3186	0.094901
7	-0.114178	-1.2508	0.106729
8	-0.02916	-0.3194	0.374977
9	0.167294	1.8326	0.034669
10	-0.022763	-0.2494	0.401755
11	0.294578	3.2269	0.000807
12	0.151091	1.6551	0.050256
13	-0.593769	-6.5044	0
14	-0.118956	-1.3031	0.097518
15	-0.003852	-0.0422	0.483205
16	-0.027315	-0.2992	0.382645
17	0.010667	0.1169	0.453585
18	0.048608	0.5325	0.297691
19	0.022846	0.2503	0.401406
20	-0.089413	-0.9795	0.164659

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

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 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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