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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 26 Dec 2010 15:17:47 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/26/t1293376561o2x50prgm6f2u8q.htm/, Retrieved Mon, 06 May 2024 22:37:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115655, Retrieved Mon, 06 May 2024 22:37:43 +0000

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126

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-       [(Partial) Autocorrelation Function] [paper statistiek 1] [2010-12-26 15:17:47] [f3d6336ce664ba129edd250394d444d3] [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=115655&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=115655&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115655&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	0.917339	7.1057	0
2	0.842738	6.5278	0
3	0.790225	6.1211	0
4	0.76739	5.9442	0
5	0.678015	5.2519	1e-06
6	0.593392	4.5964	1.1e-05
7	0.539659	4.1802	4.8e-05
8	0.522544	4.0476	7.5e-05
9	0.44126	3.418	0.000569
10	0.386486	2.9937	0.001999
11	0.350401	2.7142	0.004331
12	0.344758	2.6705	0.004866
13	0.24272	1.8801	0.032476
14	0.153343	1.1878	0.119798
15	0.093653	0.7254	0.235504
16	0.06657	0.5156	0.303997
17	-0.010505	-0.0814	0.46771

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.917339 & 7.1057 & 0 \tabularnewline
2 & 0.842738 & 6.5278 & 0 \tabularnewline
3 & 0.790225 & 6.1211 & 0 \tabularnewline
4 & 0.76739 & 5.9442 & 0 \tabularnewline
5 & 0.678015 & 5.2519 & 1e-06 \tabularnewline
6 & 0.593392 & 4.5964 & 1.1e-05 \tabularnewline
7 & 0.539659 & 4.1802 & 4.8e-05 \tabularnewline
8 & 0.522544 & 4.0476 & 7.5e-05 \tabularnewline
9 & 0.44126 & 3.418 & 0.000569 \tabularnewline
10 & 0.386486 & 2.9937 & 0.001999 \tabularnewline
11 & 0.350401 & 2.7142 & 0.004331 \tabularnewline
12 & 0.344758 & 2.6705 & 0.004866 \tabularnewline
13 & 0.24272 & 1.8801 & 0.032476 \tabularnewline
14 & 0.153343 & 1.1878 & 0.119798 \tabularnewline
15 & 0.093653 & 0.7254 & 0.235504 \tabularnewline
16 & 0.06657 & 0.5156 & 0.303997 \tabularnewline
17 & -0.010505 & -0.0814 & 0.46771 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115655&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]0.917339[/C][C]7.1057[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.842738[/C][C]6.5278[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.790225[/C][C]6.1211[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.76739[/C][C]5.9442[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.678015[/C][C]5.2519[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.593392[/C][C]4.5964[/C][C]1.1e-05[/C][/ROW]
[ROW][C]7[/C][C]0.539659[/C][C]4.1802[/C][C]4.8e-05[/C][/ROW]
[ROW][C]8[/C][C]0.522544[/C][C]4.0476[/C][C]7.5e-05[/C][/ROW]
[ROW][C]9[/C][C]0.44126[/C][C]3.418[/C][C]0.000569[/C][/ROW]
[ROW][C]10[/C][C]0.386486[/C][C]2.9937[/C][C]0.001999[/C][/ROW]
[ROW][C]11[/C][C]0.350401[/C][C]2.7142[/C][C]0.004331[/C][/ROW]
[ROW][C]12[/C][C]0.344758[/C][C]2.6705[/C][C]0.004866[/C][/ROW]
[ROW][C]13[/C][C]0.24272[/C][C]1.8801[/C][C]0.032476[/C][/ROW]
[ROW][C]14[/C][C]0.153343[/C][C]1.1878[/C][C]0.119798[/C][/ROW]
[ROW][C]15[/C][C]0.093653[/C][C]0.7254[/C][C]0.235504[/C][/ROW]
[ROW][C]16[/C][C]0.06657[/C][C]0.5156[/C][C]0.303997[/C][/ROW]
[ROW][C]17[/C][C]-0.010505[/C][C]-0.0814[/C][C]0.46771[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115655&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115655&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	0.917339	7.1057	0
2	0.842738	6.5278	0
3	0.790225	6.1211	0
4	0.76739	5.9442	0
5	0.678015	5.2519	1e-06
6	0.593392	4.5964	1.1e-05
7	0.539659	4.1802	4.8e-05
8	0.522544	4.0476	7.5e-05
9	0.44126	3.418	0.000569
10	0.386486	2.9937	0.001999
11	0.350401	2.7142	0.004331
12	0.344758	2.6705	0.004866
13	0.24272	1.8801	0.032476
14	0.153343	1.1878	0.119798
15	0.093653	0.7254	0.235504
16	0.06657	0.5156	0.303997
17	-0.010505	-0.0814	0.46771

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.917339	7.1057	0
2	0.007743	0.06	0.476188
3	0.101161	0.7836	0.218182
4	0.172082	1.3329	0.093795
5	-0.411097	-3.1843	0.001151
6	0.008781	0.068	0.473
7	0.120271	0.9316	0.177635
8	0.085081	0.659	0.256197
9	-0.29258	-2.2663	0.013526
10	0.252843	1.9585	0.027411
11	-0.028689	-0.2222	0.412446
12	-0.038995	-0.3021	0.381828
13	-0.478496	-3.7064	0.00023
14	0.120825	0.9359	0.176536
15	0.007408	0.0574	0.477216
16	-0.097034	-0.7516	0.227607
17	0.087476	0.6776	0.250318

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.917339 & 7.1057 & 0 \tabularnewline
2 & 0.007743 & 0.06 & 0.476188 \tabularnewline
3 & 0.101161 & 0.7836 & 0.218182 \tabularnewline
4 & 0.172082 & 1.3329 & 0.093795 \tabularnewline
5 & -0.411097 & -3.1843 & 0.001151 \tabularnewline
6 & 0.008781 & 0.068 & 0.473 \tabularnewline
7 & 0.120271 & 0.9316 & 0.177635 \tabularnewline
8 & 0.085081 & 0.659 & 0.256197 \tabularnewline
9 & -0.29258 & -2.2663 & 0.013526 \tabularnewline
10 & 0.252843 & 1.9585 & 0.027411 \tabularnewline
11 & -0.028689 & -0.2222 & 0.412446 \tabularnewline
12 & -0.038995 & -0.3021 & 0.381828 \tabularnewline
13 & -0.478496 & -3.7064 & 0.00023 \tabularnewline
14 & 0.120825 & 0.9359 & 0.176536 \tabularnewline
15 & 0.007408 & 0.0574 & 0.477216 \tabularnewline
16 & -0.097034 & -0.7516 & 0.227607 \tabularnewline
17 & 0.087476 & 0.6776 & 0.250318 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115655&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]0.917339[/C][C]7.1057[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.007743[/C][C]0.06[/C][C]0.476188[/C][/ROW]
[ROW][C]3[/C][C]0.101161[/C][C]0.7836[/C][C]0.218182[/C][/ROW]
[ROW][C]4[/C][C]0.172082[/C][C]1.3329[/C][C]0.093795[/C][/ROW]
[ROW][C]5[/C][C]-0.411097[/C][C]-3.1843[/C][C]0.001151[/C][/ROW]
[ROW][C]6[/C][C]0.008781[/C][C]0.068[/C][C]0.473[/C][/ROW]
[ROW][C]7[/C][C]0.120271[/C][C]0.9316[/C][C]0.177635[/C][/ROW]
[ROW][C]8[/C][C]0.085081[/C][C]0.659[/C][C]0.256197[/C][/ROW]
[ROW][C]9[/C][C]-0.29258[/C][C]-2.2663[/C][C]0.013526[/C][/ROW]
[ROW][C]10[/C][C]0.252843[/C][C]1.9585[/C][C]0.027411[/C][/ROW]
[ROW][C]11[/C][C]-0.028689[/C][C]-0.2222[/C][C]0.412446[/C][/ROW]
[ROW][C]12[/C][C]-0.038995[/C][C]-0.3021[/C][C]0.381828[/C][/ROW]
[ROW][C]13[/C][C]-0.478496[/C][C]-3.7064[/C][C]0.00023[/C][/ROW]
[ROW][C]14[/C][C]0.120825[/C][C]0.9359[/C][C]0.176536[/C][/ROW]
[ROW][C]15[/C][C]0.007408[/C][C]0.0574[/C][C]0.477216[/C][/ROW]
[ROW][C]16[/C][C]-0.097034[/C][C]-0.7516[/C][C]0.227607[/C][/ROW]
[ROW][C]17[/C][C]0.087476[/C][C]0.6776[/C][C]0.250318[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115655&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115655&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	0.917339	7.1057	0
2	0.007743	0.06	0.476188
3	0.101161	0.7836	0.218182
4	0.172082	1.3329	0.093795
5	-0.411097	-3.1843	0.001151
6	0.008781	0.068	0.473
7	0.120271	0.9316	0.177635
8	0.085081	0.659	0.256197
9	-0.29258	-2.2663	0.013526
10	0.252843	1.9585	0.027411
11	-0.028689	-0.2222	0.412446
12	-0.038995	-0.3021	0.381828
13	-0.478496	-3.7064	0.00023
14	0.120825	0.9359	0.176536
15	0.007408	0.0574	0.477216
16	-0.097034	-0.7516	0.227607
17	0.087476	0.6776	0.250318

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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