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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Dec 2010 20:40:03 +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/19/t1292793702hqnjyvjbkvwvewd.htm/, Retrieved Sun, 05 May 2024 05:41:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112753, Retrieved Sun, 05 May 2024 05:41:28 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

184

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]
-   PD  [Variance Reduction Matrix] [WS 9 Variance Red...] [2010-12-03 17:46:28] [8081b8996d5947580de3eb171e82db4f]
-    D    [Variance Reduction Matrix] [Workshop 9, VRM] [2010-12-05 18:42:47] [3635fb7041b1998c5a1332cf9de22bce]
- R  D      [Variance Reduction Matrix] [Paper VRM] [2010-12-19 14:36:42] [3635fb7041b1998c5a1332cf9de22bce]
- RM D          [(Partial) Autocorrelation Function] [Paper VRM 2] [2010-12-19 20:40:03] [23a9b79f355c69a75648521a893cf584] [Current]
-   P             [(Partial) Autocorrelation Function] [Variance Reductio...] [2010-12-22 08:43:47] [8081b8996d5947580de3eb171e82db4f] 
-   P             [(Partial) Autocorrelation Function] [Paper Variance Re...] [2010-12-22 09:01:18] [d946de7cca328fbcf207448a112523ab] 

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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=112753&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=112753&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112753&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	0.198041	1.8042	0.037411
2	0.166609	1.5179	0.066423
3	-0.009068	-0.0826	0.467178
4	-0.145599	-1.3265	0.094161
5	-0.246847	-2.2489	0.013584
6	-0.335866	-3.0599	0.001491
7	-0.209911	-1.9124	0.029639
8	-0.158753	-1.4463	0.075928
9	-0.105412	-0.9604	0.169834
10	0.083727	0.7628	0.223877
11	0.295299	2.6903	0.004315
12	0.458044	4.173	3.7e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.198041 & 1.8042 & 0.037411 \tabularnewline
2 & 0.166609 & 1.5179 & 0.066423 \tabularnewline
3 & -0.009068 & -0.0826 & 0.467178 \tabularnewline
4 & -0.145599 & -1.3265 & 0.094161 \tabularnewline
5 & -0.246847 & -2.2489 & 0.013584 \tabularnewline
6 & -0.335866 & -3.0599 & 0.001491 \tabularnewline
7 & -0.209911 & -1.9124 & 0.029639 \tabularnewline
8 & -0.158753 & -1.4463 & 0.075928 \tabularnewline
9 & -0.105412 & -0.9604 & 0.169834 \tabularnewline
10 & 0.083727 & 0.7628 & 0.223877 \tabularnewline
11 & 0.295299 & 2.6903 & 0.004315 \tabularnewline
12 & 0.458044 & 4.173 & 3.7e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112753&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]0.198041[/C][C]1.8042[/C][C]0.037411[/C][/ROW]
[ROW][C]2[/C][C]0.166609[/C][C]1.5179[/C][C]0.066423[/C][/ROW]
[ROW][C]3[/C][C]-0.009068[/C][C]-0.0826[/C][C]0.467178[/C][/ROW]
[ROW][C]4[/C][C]-0.145599[/C][C]-1.3265[/C][C]0.094161[/C][/ROW]
[ROW][C]5[/C][C]-0.246847[/C][C]-2.2489[/C][C]0.013584[/C][/ROW]
[ROW][C]6[/C][C]-0.335866[/C][C]-3.0599[/C][C]0.001491[/C][/ROW]
[ROW][C]7[/C][C]-0.209911[/C][C]-1.9124[/C][C]0.029639[/C][/ROW]
[ROW][C]8[/C][C]-0.158753[/C][C]-1.4463[/C][C]0.075928[/C][/ROW]
[ROW][C]9[/C][C]-0.105412[/C][C]-0.9604[/C][C]0.169834[/C][/ROW]
[ROW][C]10[/C][C]0.083727[/C][C]0.7628[/C][C]0.223877[/C][/ROW]
[ROW][C]11[/C][C]0.295299[/C][C]2.6903[/C][C]0.004315[/C][/ROW]
[ROW][C]12[/C][C]0.458044[/C][C]4.173[/C][C]3.7e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112753&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112753&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	0.198041	1.8042	0.037411
2	0.166609	1.5179	0.066423
3	-0.009068	-0.0826	0.467178
4	-0.145599	-1.3265	0.094161
5	-0.246847	-2.2489	0.013584
6	-0.335866	-3.0599	0.001491
7	-0.209911	-1.9124	0.029639
8	-0.158753	-1.4463	0.075928
9	-0.105412	-0.9604	0.169834
10	0.083727	0.7628	0.223877
11	0.295299	2.6903	0.004315
12	0.458044	4.173	3.7e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.198041	1.8042	0.037411
2	0.132589	1.2079	0.115251
3	-0.067748	-0.6172	0.269391
4	-0.164516	-1.4988	0.068858
5	-0.198784	-1.811	0.036879
6	-0.247831	-2.2578	0.01329
7	-0.089796	-0.8181	0.207828
8	-0.082471	-0.7513	0.227285
9	-0.128337	-1.1692	0.122835
10	0.015015	0.1368	0.445762
11	0.20264	1.8461	0.034218
12	0.339395	3.092	0.001354

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.198041 & 1.8042 & 0.037411 \tabularnewline
2 & 0.132589 & 1.2079 & 0.115251 \tabularnewline
3 & -0.067748 & -0.6172 & 0.269391 \tabularnewline
4 & -0.164516 & -1.4988 & 0.068858 \tabularnewline
5 & -0.198784 & -1.811 & 0.036879 \tabularnewline
6 & -0.247831 & -2.2578 & 0.01329 \tabularnewline
7 & -0.089796 & -0.8181 & 0.207828 \tabularnewline
8 & -0.082471 & -0.7513 & 0.227285 \tabularnewline
9 & -0.128337 & -1.1692 & 0.122835 \tabularnewline
10 & 0.015015 & 0.1368 & 0.445762 \tabularnewline
11 & 0.20264 & 1.8461 & 0.034218 \tabularnewline
12 & 0.339395 & 3.092 & 0.001354 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112753&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]0.198041[/C][C]1.8042[/C][C]0.037411[/C][/ROW]
[ROW][C]2[/C][C]0.132589[/C][C]1.2079[/C][C]0.115251[/C][/ROW]
[ROW][C]3[/C][C]-0.067748[/C][C]-0.6172[/C][C]0.269391[/C][/ROW]
[ROW][C]4[/C][C]-0.164516[/C][C]-1.4988[/C][C]0.068858[/C][/ROW]
[ROW][C]5[/C][C]-0.198784[/C][C]-1.811[/C][C]0.036879[/C][/ROW]
[ROW][C]6[/C][C]-0.247831[/C][C]-2.2578[/C][C]0.01329[/C][/ROW]
[ROW][C]7[/C][C]-0.089796[/C][C]-0.8181[/C][C]0.207828[/C][/ROW]
[ROW][C]8[/C][C]-0.082471[/C][C]-0.7513[/C][C]0.227285[/C][/ROW]
[ROW][C]9[/C][C]-0.128337[/C][C]-1.1692[/C][C]0.122835[/C][/ROW]
[ROW][C]10[/C][C]0.015015[/C][C]0.1368[/C][C]0.445762[/C][/ROW]
[ROW][C]11[/C][C]0.20264[/C][C]1.8461[/C][C]0.034218[/C][/ROW]
[ROW][C]12[/C][C]0.339395[/C][C]3.092[/C][C]0.001354[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112753&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112753&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	0.198041	1.8042	0.037411
2	0.132589	1.2079	0.115251
3	-0.067748	-0.6172	0.269391
4	-0.164516	-1.4988	0.068858
5	-0.198784	-1.811	0.036879
6	-0.247831	-2.2578	0.01329
7	-0.089796	-0.8181	0.207828
8	-0.082471	-0.7513	0.227285
9	-0.128337	-1.1692	0.122835
10	0.015015	0.1368	0.445762
11	0.20264	1.8461	0.034218
12	0.339395	3.092	0.001354

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 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; 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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Input Parameters & R Code