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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 29 Dec 2010 20:05:52 +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/29/t129365305143cnii925786cwz.htm/, Retrieved Fri, 03 May 2024 10:51:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117093, Retrieved Fri, 03 May 2024 10:51:58 +0000

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Original text written by user:

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No (this computation is public)

User-defined keywords

Estimated Impact

143

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D    [(Partial) Autocorrelation Function] [Workshop 6 'Aanta...] [2010-12-14 16:26:00] [40c8b935cbad1b0be3c22a481f9723f7]
-           [(Partial) Autocorrelation Function] [] [2010-12-16 00:41:10] [bcc4ad4a6c0f95d5b548de29638ac6c2]
-   P         [(Partial) Autocorrelation Function] [] [2010-12-16 01:31:32] [bcc4ad4a6c0f95d5b548de29638ac6c2]
-               [(Partial) Autocorrelation Function] [ACF] [2010-12-16 17:57:21] [f1aa04283d83c25edc8ae3bb0d0fb93e]
-    D            [(Partial) Autocorrelation Function] [autocorrelatie] [2010-12-27 14:52:24] [f1aa04283d83c25edc8ae3bb0d0fb93e]
- R P                 [(Partial) Autocorrelation Function] [autocorrelatie] [2010-12-29 20:05:52] [b90a48a1f8ff99465eedb4ebbc8930ab] [Current]
-   P                   [(Partial) Autocorrelation Function] [ACF met alleen D=0] [2011-01-06 12:52:41] [96348ef82925ade81ab3c243141d80f1] 

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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	'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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117093&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117093&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117093&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.944801	7.3184	0
2	0.889427	6.8895	0
3	0.827109	6.4068	0
4	0.739387	5.7273	0
5	0.662083	5.1285	2e-06
6	0.573183	4.4399	2e-05
7	0.482718	3.7391	0.000207
8	0.38627	2.992	0.002009
9	0.295925	2.2922	0.012708
10	0.213388	1.6529	0.051788
11	0.142264	1.102	0.137438
12	0.075807	0.5872	0.279637
13	0.006147	0.0476	0.481092
14	-0.072132	-0.5587	0.289212
15	-0.149141	-1.1552	0.126286
16	-0.213024	-1.6501	0.052076
17	-0.274886	-2.1293	0.018673

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.944801 & 7.3184 & 0 \tabularnewline
2 & 0.889427 & 6.8895 & 0 \tabularnewline
3 & 0.827109 & 6.4068 & 0 \tabularnewline
4 & 0.739387 & 5.7273 & 0 \tabularnewline
5 & 0.662083 & 5.1285 & 2e-06 \tabularnewline
6 & 0.573183 & 4.4399 & 2e-05 \tabularnewline
7 & 0.482718 & 3.7391 & 0.000207 \tabularnewline
8 & 0.38627 & 2.992 & 0.002009 \tabularnewline
9 & 0.295925 & 2.2922 & 0.012708 \tabularnewline
10 & 0.213388 & 1.6529 & 0.051788 \tabularnewline
11 & 0.142264 & 1.102 & 0.137438 \tabularnewline
12 & 0.075807 & 0.5872 & 0.279637 \tabularnewline
13 & 0.006147 & 0.0476 & 0.481092 \tabularnewline
14 & -0.072132 & -0.5587 & 0.289212 \tabularnewline
15 & -0.149141 & -1.1552 & 0.126286 \tabularnewline
16 & -0.213024 & -1.6501 & 0.052076 \tabularnewline
17 & -0.274886 & -2.1293 & 0.018673 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117093&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]0.944801[/C][C]7.3184[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.889427[/C][C]6.8895[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.827109[/C][C]6.4068[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.739387[/C][C]5.7273[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.662083[/C][C]5.1285[/C][C]2e-06[/C][/ROW]
[ROW][C]6[/C][C]0.573183[/C][C]4.4399[/C][C]2e-05[/C][/ROW]
[ROW][C]7[/C][C]0.482718[/C][C]3.7391[/C][C]0.000207[/C][/ROW]
[ROW][C]8[/C][C]0.38627[/C][C]2.992[/C][C]0.002009[/C][/ROW]
[ROW][C]9[/C][C]0.295925[/C][C]2.2922[/C][C]0.012708[/C][/ROW]
[ROW][C]10[/C][C]0.213388[/C][C]1.6529[/C][C]0.051788[/C][/ROW]
[ROW][C]11[/C][C]0.142264[/C][C]1.102[/C][C]0.137438[/C][/ROW]
[ROW][C]12[/C][C]0.075807[/C][C]0.5872[/C][C]0.279637[/C][/ROW]
[ROW][C]13[/C][C]0.006147[/C][C]0.0476[/C][C]0.481092[/C][/ROW]
[ROW][C]14[/C][C]-0.072132[/C][C]-0.5587[/C][C]0.289212[/C][/ROW]
[ROW][C]15[/C][C]-0.149141[/C][C]-1.1552[/C][C]0.126286[/C][/ROW]
[ROW][C]16[/C][C]-0.213024[/C][C]-1.6501[/C][C]0.052076[/C][/ROW]
[ROW][C]17[/C][C]-0.274886[/C][C]-2.1293[/C][C]0.018673[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117093&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117093&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	0.944801	7.3184	0
2	0.889427	6.8895	0
3	0.827109	6.4068	0
4	0.739387	5.7273	0
5	0.662083	5.1285	2e-06
6	0.573183	4.4399	2e-05
7	0.482718	3.7391	0.000207
8	0.38627	2.992	0.002009
9	0.295925	2.2922	0.012708
10	0.213388	1.6529	0.051788
11	0.142264	1.102	0.137438
12	0.075807	0.5872	0.279637
13	0.006147	0.0476	0.481092
14	-0.072132	-0.5587	0.289212
15	-0.149141	-1.1552	0.126286
16	-0.213024	-1.6501	0.052076
17	-0.274886	-2.1293	0.018673

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.944801	7.3184	0
2	-0.030017	-0.2325	0.408467
3	-0.094049	-0.7285	0.234571
4	-0.273149	-2.1158	0.01926
5	0.049134	0.3806	0.352425
6	-0.135241	-1.0476	0.149518
7	-0.029978	-0.2322	0.408584
8	-0.164176	-1.2717	0.104194
9	0.047829	0.3705	0.356163
10	-0.010325	-0.08	0.468261
11	0.097497	0.7552	0.226538
12	-0.083343	-0.6456	0.260508
13	-0.09677	-0.7496	0.22822
14	-0.238728	-1.8492	0.03468
15	-0.052337	-0.4054	0.343313
16	0.032585	0.2524	0.400797
17	-0.006828	-0.0529	0.478998

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.944801 & 7.3184 & 0 \tabularnewline
2 & -0.030017 & -0.2325 & 0.408467 \tabularnewline
3 & -0.094049 & -0.7285 & 0.234571 \tabularnewline
4 & -0.273149 & -2.1158 & 0.01926 \tabularnewline
5 & 0.049134 & 0.3806 & 0.352425 \tabularnewline
6 & -0.135241 & -1.0476 & 0.149518 \tabularnewline
7 & -0.029978 & -0.2322 & 0.408584 \tabularnewline
8 & -0.164176 & -1.2717 & 0.104194 \tabularnewline
9 & 0.047829 & 0.3705 & 0.356163 \tabularnewline
10 & -0.010325 & -0.08 & 0.468261 \tabularnewline
11 & 0.097497 & 0.7552 & 0.226538 \tabularnewline
12 & -0.083343 & -0.6456 & 0.260508 \tabularnewline
13 & -0.09677 & -0.7496 & 0.22822 \tabularnewline
14 & -0.238728 & -1.8492 & 0.03468 \tabularnewline
15 & -0.052337 & -0.4054 & 0.343313 \tabularnewline
16 & 0.032585 & 0.2524 & 0.400797 \tabularnewline
17 & -0.006828 & -0.0529 & 0.478998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117093&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]0.944801[/C][C]7.3184[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.030017[/C][C]-0.2325[/C][C]0.408467[/C][/ROW]
[ROW][C]3[/C][C]-0.094049[/C][C]-0.7285[/C][C]0.234571[/C][/ROW]
[ROW][C]4[/C][C]-0.273149[/C][C]-2.1158[/C][C]0.01926[/C][/ROW]
[ROW][C]5[/C][C]0.049134[/C][C]0.3806[/C][C]0.352425[/C][/ROW]
[ROW][C]6[/C][C]-0.135241[/C][C]-1.0476[/C][C]0.149518[/C][/ROW]
[ROW][C]7[/C][C]-0.029978[/C][C]-0.2322[/C][C]0.408584[/C][/ROW]
[ROW][C]8[/C][C]-0.164176[/C][C]-1.2717[/C][C]0.104194[/C][/ROW]
[ROW][C]9[/C][C]0.047829[/C][C]0.3705[/C][C]0.356163[/C][/ROW]
[ROW][C]10[/C][C]-0.010325[/C][C]-0.08[/C][C]0.468261[/C][/ROW]
[ROW][C]11[/C][C]0.097497[/C][C]0.7552[/C][C]0.226538[/C][/ROW]
[ROW][C]12[/C][C]-0.083343[/C][C]-0.6456[/C][C]0.260508[/C][/ROW]
[ROW][C]13[/C][C]-0.09677[/C][C]-0.7496[/C][C]0.22822[/C][/ROW]
[ROW][C]14[/C][C]-0.238728[/C][C]-1.8492[/C][C]0.03468[/C][/ROW]
[ROW][C]15[/C][C]-0.052337[/C][C]-0.4054[/C][C]0.343313[/C][/ROW]
[ROW][C]16[/C][C]0.032585[/C][C]0.2524[/C][C]0.400797[/C][/ROW]
[ROW][C]17[/C][C]-0.006828[/C][C]-0.0529[/C][C]0.478998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117093&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117093&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	0.944801	7.3184	0
2	-0.030017	-0.2325	0.408467
3	-0.094049	-0.7285	0.234571
4	-0.273149	-2.1158	0.01926
5	0.049134	0.3806	0.352425
6	-0.135241	-1.0476	0.149518
7	-0.029978	-0.2322	0.408584
8	-0.164176	-1.2717	0.104194
9	0.047829	0.3705	0.356163
10	-0.010325	-0.08	0.468261
11	0.097497	0.7552	0.226538
12	-0.083343	-0.6456	0.260508
13	-0.09677	-0.7496	0.22822
14	-0.238728	-1.8492	0.03468
15	-0.052337	-0.4054	0.343313
16	0.032585	0.2524	0.400797
17	-0.006828	-0.0529	0.478998

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

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')

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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code