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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 19 Mar 2013 16:16:24 -0400

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Mar/19/t13637242138qagfbbiuv68q43.htm/, Retrieved Tue, 30 Apr 2024 07:05:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207937, Retrieved Tue, 30 Apr 2024 07:05:58 +0000

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-       [(Partial) Autocorrelation Function] [] [2013-03-19 20:16:24] [4d26c4233714d8e4ecf99606d744931b] [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	'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=207937&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=207937&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207937&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	0.967229	8.2072	0
2	0.93184	7.9069	0
3	0.896077	7.6035	0
4	0.860591	7.3024	0
5	0.82683	7.0159	0
6	0.789405	6.6983	0
7	0.749464	6.3594	0
8	0.706724	5.9968	0
9	0.662772	5.6238	0
10	0.620679	5.2666	1e-06
11	0.578481	4.9086	3e-06
12	0.536538	4.5527	1.1e-05
13	0.494276	4.1941	3.8e-05
14	0.452181	3.8369	0.000132
15	0.409667	3.4761	0.000433
16	0.367122	3.1151	0.00132
17	0.326198	2.7679	0.003584
18	0.284406	2.4133	0.009178

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.967229 & 8.2072 & 0 \tabularnewline
2 & 0.93184 & 7.9069 & 0 \tabularnewline
3 & 0.896077 & 7.6035 & 0 \tabularnewline
4 & 0.860591 & 7.3024 & 0 \tabularnewline
5 & 0.82683 & 7.0159 & 0 \tabularnewline
6 & 0.789405 & 6.6983 & 0 \tabularnewline
7 & 0.749464 & 6.3594 & 0 \tabularnewline
8 & 0.706724 & 5.9968 & 0 \tabularnewline
9 & 0.662772 & 5.6238 & 0 \tabularnewline
10 & 0.620679 & 5.2666 & 1e-06 \tabularnewline
11 & 0.578481 & 4.9086 & 3e-06 \tabularnewline
12 & 0.536538 & 4.5527 & 1.1e-05 \tabularnewline
13 & 0.494276 & 4.1941 & 3.8e-05 \tabularnewline
14 & 0.452181 & 3.8369 & 0.000132 \tabularnewline
15 & 0.409667 & 3.4761 & 0.000433 \tabularnewline
16 & 0.367122 & 3.1151 & 0.00132 \tabularnewline
17 & 0.326198 & 2.7679 & 0.003584 \tabularnewline
18 & 0.284406 & 2.4133 & 0.009178 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207937&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]0.967229[/C][C]8.2072[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.93184[/C][C]7.9069[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.896077[/C][C]7.6035[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.860591[/C][C]7.3024[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.82683[/C][C]7.0159[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.789405[/C][C]6.6983[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.749464[/C][C]6.3594[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.706724[/C][C]5.9968[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.662772[/C][C]5.6238[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.620679[/C][C]5.2666[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.578481[/C][C]4.9086[/C][C]3e-06[/C][/ROW]
[ROW][C]12[/C][C]0.536538[/C][C]4.5527[/C][C]1.1e-05[/C][/ROW]
[ROW][C]13[/C][C]0.494276[/C][C]4.1941[/C][C]3.8e-05[/C][/ROW]
[ROW][C]14[/C][C]0.452181[/C][C]3.8369[/C][C]0.000132[/C][/ROW]
[ROW][C]15[/C][C]0.409667[/C][C]3.4761[/C][C]0.000433[/C][/ROW]
[ROW][C]16[/C][C]0.367122[/C][C]3.1151[/C][C]0.00132[/C][/ROW]
[ROW][C]17[/C][C]0.326198[/C][C]2.7679[/C][C]0.003584[/C][/ROW]
[ROW][C]18[/C][C]0.284406[/C][C]2.4133[/C][C]0.009178[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207937&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207937&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	0.967229	8.2072	0
2	0.93184	7.9069	0
3	0.896077	7.6035	0
4	0.860591	7.3024	0
5	0.82683	7.0159	0
6	0.789405	6.6983	0
7	0.749464	6.3594	0
8	0.706724	5.9968	0
9	0.662772	5.6238	0
10	0.620679	5.2666	1e-06
11	0.578481	4.9086	3e-06
12	0.536538	4.5527	1.1e-05
13	0.494276	4.1941	3.8e-05
14	0.452181	3.8369	0.000132
15	0.409667	3.4761	0.000433
16	0.367122	3.1151	0.00132
17	0.326198	2.7679	0.003584
18	0.284406	2.4133	0.009178

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.967229	8.2072	0
2	-0.057276	-0.486	0.314221
3	-0.022565	-0.1915	0.424348
4	-0.01418	-0.1203	0.452281
5	0.007491	0.0636	0.474749
6	-0.077667	-0.659	0.25599
7	-0.056091	-0.476	0.317775
8	-0.06332	-0.5373	0.296363
9	-0.040831	-0.3465	0.365002
10	0.000457	0.0039	0.498457
11	-0.029163	-0.2475	0.402629
12	-0.021629	-0.1835	0.427451
13	-0.027872	-0.2365	0.406856
14	-0.019278	-0.1636	0.43526
15	-0.036283	-0.3079	0.379534
16	-0.030258	-0.2568	0.399052
17	-0.007804	-0.0662	0.473695
18	-0.046855	-0.3976	0.346058

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.967229 & 8.2072 & 0 \tabularnewline
2 & -0.057276 & -0.486 & 0.314221 \tabularnewline
3 & -0.022565 & -0.1915 & 0.424348 \tabularnewline
4 & -0.01418 & -0.1203 & 0.452281 \tabularnewline
5 & 0.007491 & 0.0636 & 0.474749 \tabularnewline
6 & -0.077667 & -0.659 & 0.25599 \tabularnewline
7 & -0.056091 & -0.476 & 0.317775 \tabularnewline
8 & -0.06332 & -0.5373 & 0.296363 \tabularnewline
9 & -0.040831 & -0.3465 & 0.365002 \tabularnewline
10 & 0.000457 & 0.0039 & 0.498457 \tabularnewline
11 & -0.029163 & -0.2475 & 0.402629 \tabularnewline
12 & -0.021629 & -0.1835 & 0.427451 \tabularnewline
13 & -0.027872 & -0.2365 & 0.406856 \tabularnewline
14 & -0.019278 & -0.1636 & 0.43526 \tabularnewline
15 & -0.036283 & -0.3079 & 0.379534 \tabularnewline
16 & -0.030258 & -0.2568 & 0.399052 \tabularnewline
17 & -0.007804 & -0.0662 & 0.473695 \tabularnewline
18 & -0.046855 & -0.3976 & 0.346058 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207937&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]0.967229[/C][C]8.2072[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.057276[/C][C]-0.486[/C][C]0.314221[/C][/ROW]
[ROW][C]3[/C][C]-0.022565[/C][C]-0.1915[/C][C]0.424348[/C][/ROW]
[ROW][C]4[/C][C]-0.01418[/C][C]-0.1203[/C][C]0.452281[/C][/ROW]
[ROW][C]5[/C][C]0.007491[/C][C]0.0636[/C][C]0.474749[/C][/ROW]
[ROW][C]6[/C][C]-0.077667[/C][C]-0.659[/C][C]0.25599[/C][/ROW]
[ROW][C]7[/C][C]-0.056091[/C][C]-0.476[/C][C]0.317775[/C][/ROW]
[ROW][C]8[/C][C]-0.06332[/C][C]-0.5373[/C][C]0.296363[/C][/ROW]
[ROW][C]9[/C][C]-0.040831[/C][C]-0.3465[/C][C]0.365002[/C][/ROW]
[ROW][C]10[/C][C]0.000457[/C][C]0.0039[/C][C]0.498457[/C][/ROW]
[ROW][C]11[/C][C]-0.029163[/C][C]-0.2475[/C][C]0.402629[/C][/ROW]
[ROW][C]12[/C][C]-0.021629[/C][C]-0.1835[/C][C]0.427451[/C][/ROW]
[ROW][C]13[/C][C]-0.027872[/C][C]-0.2365[/C][C]0.406856[/C][/ROW]
[ROW][C]14[/C][C]-0.019278[/C][C]-0.1636[/C][C]0.43526[/C][/ROW]
[ROW][C]15[/C][C]-0.036283[/C][C]-0.3079[/C][C]0.379534[/C][/ROW]
[ROW][C]16[/C][C]-0.030258[/C][C]-0.2568[/C][C]0.399052[/C][/ROW]
[ROW][C]17[/C][C]-0.007804[/C][C]-0.0662[/C][C]0.473695[/C][/ROW]
[ROW][C]18[/C][C]-0.046855[/C][C]-0.3976[/C][C]0.346058[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207937&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207937&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	0.967229	8.2072	0
2	-0.057276	-0.486	0.314221
3	-0.022565	-0.1915	0.424348
4	-0.01418	-0.1203	0.452281
5	0.007491	0.0636	0.474749
6	-0.077667	-0.659	0.25599
7	-0.056091	-0.476	0.317775
8	-0.06332	-0.5373	0.296363
9	-0.040831	-0.3465	0.365002
10	0.000457	0.0039	0.498457
11	-0.029163	-0.2475	0.402629
12	-0.021629	-0.1835	0.427451
13	-0.027872	-0.2365	0.406856
14	-0.019278	-0.1636	0.43526
15	-0.036283	-0.3079	0.379534
16	-0.030258	-0.2568	0.399052
17	-0.007804	-0.0662	0.473695
18	-0.046855	-0.3976	0.346058

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')

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