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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, 26 Dec 2010 11:26:44 +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/Dec/26/t1293362687yxtnj82bjzd274m.htm/, Retrieved Mon, 06 May 2024 13:56:08 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115529, Retrieved Mon, 06 May 2024 13:56:08 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Autocorrelatie functie met D=d=1

Estimated Impact

153

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

-     [Variance Reduction Matrix] [Unemployment] [2010-11-29 09:29:57] [b98453cac15ba1066b407e146608df68]
- RMPD  [(Partial) Autocorrelation Function] [Workshop 9 (ACF p=0)] [2010-12-15 13:59:06] [845827b7f02503df17c96f445745fee7]
-         [(Partial) Autocorrelation Function] [] [2010-12-16 16:02:02] [24bb5b06bd1854f48aebec8f44957ed0]
-   PD        [(Partial) Autocorrelation Function] [Paper] [2010-12-26 11:26:44] [e247a0a17f1c9a5b89239760575ef468] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115529&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115529&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115529&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.177423	1.2292	0.11249
2	0.273771	1.8967	0.031944
3	0.35698	2.4732	0.008491
4	0.161643	1.1199	0.134166
5	0.100506	0.6963	0.244791
6	0.205981	1.4271	0.080015
7	-0.013541	-0.0938	0.462824
8	0.062612	0.4338	0.333193
9	0.014524	0.1006	0.460133
10	-0.161139	-1.1164	0.134904
11	0.104638	0.725	0.236001
12	-0.20817	-1.4422	0.077864
13	-0.131549	-0.9114	0.183319
14	-0.017053	-0.1182	0.453221
15	-0.093983	-0.6511	0.259033
16	-0.131727	-0.9126	0.182998
17	-0.026399	-0.1829	0.427824

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.177423 & 1.2292 & 0.11249 \tabularnewline
2 & 0.273771 & 1.8967 & 0.031944 \tabularnewline
3 & 0.35698 & 2.4732 & 0.008491 \tabularnewline
4 & 0.161643 & 1.1199 & 0.134166 \tabularnewline
5 & 0.100506 & 0.6963 & 0.244791 \tabularnewline
6 & 0.205981 & 1.4271 & 0.080015 \tabularnewline
7 & -0.013541 & -0.0938 & 0.462824 \tabularnewline
8 & 0.062612 & 0.4338 & 0.333193 \tabularnewline
9 & 0.014524 & 0.1006 & 0.460133 \tabularnewline
10 & -0.161139 & -1.1164 & 0.134904 \tabularnewline
11 & 0.104638 & 0.725 & 0.236001 \tabularnewline
12 & -0.20817 & -1.4422 & 0.077864 \tabularnewline
13 & -0.131549 & -0.9114 & 0.183319 \tabularnewline
14 & -0.017053 & -0.1182 & 0.453221 \tabularnewline
15 & -0.093983 & -0.6511 & 0.259033 \tabularnewline
16 & -0.131727 & -0.9126 & 0.182998 \tabularnewline
17 & -0.026399 & -0.1829 & 0.427824 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115529&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]0.177423[/C][C]1.2292[/C][C]0.11249[/C][/ROW]
[ROW][C]2[/C][C]0.273771[/C][C]1.8967[/C][C]0.031944[/C][/ROW]
[ROW][C]3[/C][C]0.35698[/C][C]2.4732[/C][C]0.008491[/C][/ROW]
[ROW][C]4[/C][C]0.161643[/C][C]1.1199[/C][C]0.134166[/C][/ROW]
[ROW][C]5[/C][C]0.100506[/C][C]0.6963[/C][C]0.244791[/C][/ROW]
[ROW][C]6[/C][C]0.205981[/C][C]1.4271[/C][C]0.080015[/C][/ROW]
[ROW][C]7[/C][C]-0.013541[/C][C]-0.0938[/C][C]0.462824[/C][/ROW]
[ROW][C]8[/C][C]0.062612[/C][C]0.4338[/C][C]0.333193[/C][/ROW]
[ROW][C]9[/C][C]0.014524[/C][C]0.1006[/C][C]0.460133[/C][/ROW]
[ROW][C]10[/C][C]-0.161139[/C][C]-1.1164[/C][C]0.134904[/C][/ROW]
[ROW][C]11[/C][C]0.104638[/C][C]0.725[/C][C]0.236001[/C][/ROW]
[ROW][C]12[/C][C]-0.20817[/C][C]-1.4422[/C][C]0.077864[/C][/ROW]
[ROW][C]13[/C][C]-0.131549[/C][C]-0.9114[/C][C]0.183319[/C][/ROW]
[ROW][C]14[/C][C]-0.017053[/C][C]-0.1182[/C][C]0.453221[/C][/ROW]
[ROW][C]15[/C][C]-0.093983[/C][C]-0.6511[/C][C]0.259033[/C][/ROW]
[ROW][C]16[/C][C]-0.131727[/C][C]-0.9126[/C][C]0.182998[/C][/ROW]
[ROW][C]17[/C][C]-0.026399[/C][C]-0.1829[/C][C]0.427824[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115529&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115529&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	0.177423	1.2292	0.11249
2	0.273771	1.8967	0.031944
3	0.35698	2.4732	0.008491
4	0.161643	1.1199	0.134166
5	0.100506	0.6963	0.244791
6	0.205981	1.4271	0.080015
7	-0.013541	-0.0938	0.462824
8	0.062612	0.4338	0.333193
9	0.014524	0.1006	0.460133
10	-0.161139	-1.1164	0.134904
11	0.104638	0.725	0.236001
12	-0.20817	-1.4422	0.077864
13	-0.131549	-0.9114	0.183319
14	-0.017053	-0.1182	0.453221
15	-0.093983	-0.6511	0.259033
16	-0.131727	-0.9126	0.182998
17	-0.026399	-0.1829	0.427824

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.177423	1.2292	0.11249
2	0.250167	1.7332	0.04474
3	0.304186	2.1075	0.020163
4	0.036336	0.2517	0.401158
5	-0.082895	-0.5743	0.284218
6	0.066379	0.4599	0.323836
7	-0.113783	-0.7883	0.217196
8	0.001812	0.0126	0.495018
9	-0.048978	-0.3393	0.367921
10	-0.182789	-1.2664	0.105741
11	0.171505	1.1882	0.120296
12	-0.212144	-1.4698	0.074073
13	-0.0284	-0.1968	0.422422
14	0.039506	0.2737	0.392742
15	0.039766	0.2755	0.392054
16	0.010952	0.0759	0.469915
17	-0.079122	-0.5482	0.293056

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.177423 & 1.2292 & 0.11249 \tabularnewline
2 & 0.250167 & 1.7332 & 0.04474 \tabularnewline
3 & 0.304186 & 2.1075 & 0.020163 \tabularnewline
4 & 0.036336 & 0.2517 & 0.401158 \tabularnewline
5 & -0.082895 & -0.5743 & 0.284218 \tabularnewline
6 & 0.066379 & 0.4599 & 0.323836 \tabularnewline
7 & -0.113783 & -0.7883 & 0.217196 \tabularnewline
8 & 0.001812 & 0.0126 & 0.495018 \tabularnewline
9 & -0.048978 & -0.3393 & 0.367921 \tabularnewline
10 & -0.182789 & -1.2664 & 0.105741 \tabularnewline
11 & 0.171505 & 1.1882 & 0.120296 \tabularnewline
12 & -0.212144 & -1.4698 & 0.074073 \tabularnewline
13 & -0.0284 & -0.1968 & 0.422422 \tabularnewline
14 & 0.039506 & 0.2737 & 0.392742 \tabularnewline
15 & 0.039766 & 0.2755 & 0.392054 \tabularnewline
16 & 0.010952 & 0.0759 & 0.469915 \tabularnewline
17 & -0.079122 & -0.5482 & 0.293056 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115529&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]0.177423[/C][C]1.2292[/C][C]0.11249[/C][/ROW]
[ROW][C]2[/C][C]0.250167[/C][C]1.7332[/C][C]0.04474[/C][/ROW]
[ROW][C]3[/C][C]0.304186[/C][C]2.1075[/C][C]0.020163[/C][/ROW]
[ROW][C]4[/C][C]0.036336[/C][C]0.2517[/C][C]0.401158[/C][/ROW]
[ROW][C]5[/C][C]-0.082895[/C][C]-0.5743[/C][C]0.284218[/C][/ROW]
[ROW][C]6[/C][C]0.066379[/C][C]0.4599[/C][C]0.323836[/C][/ROW]
[ROW][C]7[/C][C]-0.113783[/C][C]-0.7883[/C][C]0.217196[/C][/ROW]
[ROW][C]8[/C][C]0.001812[/C][C]0.0126[/C][C]0.495018[/C][/ROW]
[ROW][C]9[/C][C]-0.048978[/C][C]-0.3393[/C][C]0.367921[/C][/ROW]
[ROW][C]10[/C][C]-0.182789[/C][C]-1.2664[/C][C]0.105741[/C][/ROW]
[ROW][C]11[/C][C]0.171505[/C][C]1.1882[/C][C]0.120296[/C][/ROW]
[ROW][C]12[/C][C]-0.212144[/C][C]-1.4698[/C][C]0.074073[/C][/ROW]
[ROW][C]13[/C][C]-0.0284[/C][C]-0.1968[/C][C]0.422422[/C][/ROW]
[ROW][C]14[/C][C]0.039506[/C][C]0.2737[/C][C]0.392742[/C][/ROW]
[ROW][C]15[/C][C]0.039766[/C][C]0.2755[/C][C]0.392054[/C][/ROW]
[ROW][C]16[/C][C]0.010952[/C][C]0.0759[/C][C]0.469915[/C][/ROW]
[ROW][C]17[/C][C]-0.079122[/C][C]-0.5482[/C][C]0.293056[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115529&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115529&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	0.177423	1.2292	0.11249
2	0.250167	1.7332	0.04474
3	0.304186	2.1075	0.020163
4	0.036336	0.2517	0.401158
5	-0.082895	-0.5743	0.284218
6	0.066379	0.4599	0.323836
7	-0.113783	-0.7883	0.217196
8	0.001812	0.0126	0.495018
9	-0.048978	-0.3393	0.367921
10	-0.182789	-1.2664	0.105741
11	0.171505	1.1882	0.120296
12	-0.212144	-1.4698	0.074073
13	-0.0284	-0.1968	0.422422
14	0.039506	0.2737	0.392742
15	0.039766	0.2755	0.392054
16	0.010952	0.0759	0.469915
17	-0.079122	-0.5482	0.293056

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 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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')

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Input Parameters & R Code