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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 12 Dec 2016 18:55:05 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/12/t1481565364b3j8t5otwt1ko1n.htm/, Retrieved Sat, 04 May 2024 03:47:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298950, Retrieved Sat, 04 May 2024 03:47:50 +0000

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-       [(Partial) Autocorrelation Function] [(Partial) Autocor...] [2016-12-12 17:55:05] [59384cc4294cbecf8e09b453c4247580] [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	1 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298950&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=298950&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298950&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	1 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.94638	6.8898	0
2	0.893829	6.5072	0
3	0.843547	6.1411	0
4	0.789003	5.744	0
5	0.736226	5.3598	1e-06
6	0.679253	4.945	4e-06
7	0.619177	4.5077	1.8e-05
8	0.558804	4.0682	7.9e-05
9	0.499393	3.6356	0.000314
10	0.439216	3.1975	0.001169
11	0.380284	2.7685	0.003871
12	0.325909	2.3727	0.010661
13	0.270993	1.9729	0.026869
14	0.218892	1.5936	0.058491
15	0.167495	1.2194	0.11405
16	0.119294	0.8685	0.194526
17	0.078642	0.5725	0.284693

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.94638 & 6.8898 & 0 \tabularnewline
2 & 0.893829 & 6.5072 & 0 \tabularnewline
3 & 0.843547 & 6.1411 & 0 \tabularnewline
4 & 0.789003 & 5.744 & 0 \tabularnewline
5 & 0.736226 & 5.3598 & 1e-06 \tabularnewline
6 & 0.679253 & 4.945 & 4e-06 \tabularnewline
7 & 0.619177 & 4.5077 & 1.8e-05 \tabularnewline
8 & 0.558804 & 4.0682 & 7.9e-05 \tabularnewline
9 & 0.499393 & 3.6356 & 0.000314 \tabularnewline
10 & 0.439216 & 3.1975 & 0.001169 \tabularnewline
11 & 0.380284 & 2.7685 & 0.003871 \tabularnewline
12 & 0.325909 & 2.3727 & 0.010661 \tabularnewline
13 & 0.270993 & 1.9729 & 0.026869 \tabularnewline
14 & 0.218892 & 1.5936 & 0.058491 \tabularnewline
15 & 0.167495 & 1.2194 & 0.11405 \tabularnewline
16 & 0.119294 & 0.8685 & 0.194526 \tabularnewline
17 & 0.078642 & 0.5725 & 0.284693 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298950&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]0.94638[/C][C]6.8898[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.893829[/C][C]6.5072[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.843547[/C][C]6.1411[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.789003[/C][C]5.744[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.736226[/C][C]5.3598[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.679253[/C][C]4.945[/C][C]4e-06[/C][/ROW]
[ROW][C]7[/C][C]0.619177[/C][C]4.5077[/C][C]1.8e-05[/C][/ROW]
[ROW][C]8[/C][C]0.558804[/C][C]4.0682[/C][C]7.9e-05[/C][/ROW]
[ROW][C]9[/C][C]0.499393[/C][C]3.6356[/C][C]0.000314[/C][/ROW]
[ROW][C]10[/C][C]0.439216[/C][C]3.1975[/C][C]0.001169[/C][/ROW]
[ROW][C]11[/C][C]0.380284[/C][C]2.7685[/C][C]0.003871[/C][/ROW]
[ROW][C]12[/C][C]0.325909[/C][C]2.3727[/C][C]0.010661[/C][/ROW]
[ROW][C]13[/C][C]0.270993[/C][C]1.9729[/C][C]0.026869[/C][/ROW]
[ROW][C]14[/C][C]0.218892[/C][C]1.5936[/C][C]0.058491[/C][/ROW]
[ROW][C]15[/C][C]0.167495[/C][C]1.2194[/C][C]0.11405[/C][/ROW]
[ROW][C]16[/C][C]0.119294[/C][C]0.8685[/C][C]0.194526[/C][/ROW]
[ROW][C]17[/C][C]0.078642[/C][C]0.5725[/C][C]0.284693[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298950&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298950&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	0.94638	6.8898	0
2	0.893829	6.5072	0
3	0.843547	6.1411	0
4	0.789003	5.744	0
5	0.736226	5.3598	1e-06
6	0.679253	4.945	4e-06
7	0.619177	4.5077	1.8e-05
8	0.558804	4.0682	7.9e-05
9	0.499393	3.6356	0.000314
10	0.439216	3.1975	0.001169
11	0.380284	2.7685	0.003871
12	0.325909	2.3727	0.010661
13	0.270993	1.9729	0.026869
14	0.218892	1.5936	0.058491
15	0.167495	1.2194	0.11405
16	0.119294	0.8685	0.194526
17	0.078642	0.5725	0.284693

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.94638	6.8898	0
2	-0.017302	-0.126	0.450119
3	-0.005907	-0.043	0.482931
4	-0.067747	-0.4932	0.311952
5	-0.013773	-0.1003	0.460255
6	-0.072208	-0.5257	0.300651
7	-0.062492	-0.455	0.325501
8	-0.043908	-0.3197	0.375243
9	-0.027778	-0.2022	0.420257
10	-0.046475	-0.3383	0.36822
11	-0.028593	-0.2082	0.41795
12	0.002982	0.0217	0.49138
13	-0.042645	-0.3105	0.378714
14	-0.015053	-0.1096	0.456575
15	-0.038171	-0.2779	0.391088
16	-0.01012	-0.0737	0.470772
17	0.025546	0.186	0.426587

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.94638 & 6.8898 & 0 \tabularnewline
2 & -0.017302 & -0.126 & 0.450119 \tabularnewline
3 & -0.005907 & -0.043 & 0.482931 \tabularnewline
4 & -0.067747 & -0.4932 & 0.311952 \tabularnewline
5 & -0.013773 & -0.1003 & 0.460255 \tabularnewline
6 & -0.072208 & -0.5257 & 0.300651 \tabularnewline
7 & -0.062492 & -0.455 & 0.325501 \tabularnewline
8 & -0.043908 & -0.3197 & 0.375243 \tabularnewline
9 & -0.027778 & -0.2022 & 0.420257 \tabularnewline
10 & -0.046475 & -0.3383 & 0.36822 \tabularnewline
11 & -0.028593 & -0.2082 & 0.41795 \tabularnewline
12 & 0.002982 & 0.0217 & 0.49138 \tabularnewline
13 & -0.042645 & -0.3105 & 0.378714 \tabularnewline
14 & -0.015053 & -0.1096 & 0.456575 \tabularnewline
15 & -0.038171 & -0.2779 & 0.391088 \tabularnewline
16 & -0.01012 & -0.0737 & 0.470772 \tabularnewline
17 & 0.025546 & 0.186 & 0.426587 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298950&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]0.94638[/C][C]6.8898[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.017302[/C][C]-0.126[/C][C]0.450119[/C][/ROW]
[ROW][C]3[/C][C]-0.005907[/C][C]-0.043[/C][C]0.482931[/C][/ROW]
[ROW][C]4[/C][C]-0.067747[/C][C]-0.4932[/C][C]0.311952[/C][/ROW]
[ROW][C]5[/C][C]-0.013773[/C][C]-0.1003[/C][C]0.460255[/C][/ROW]
[ROW][C]6[/C][C]-0.072208[/C][C]-0.5257[/C][C]0.300651[/C][/ROW]
[ROW][C]7[/C][C]-0.062492[/C][C]-0.455[/C][C]0.325501[/C][/ROW]
[ROW][C]8[/C][C]-0.043908[/C][C]-0.3197[/C][C]0.375243[/C][/ROW]
[ROW][C]9[/C][C]-0.027778[/C][C]-0.2022[/C][C]0.420257[/C][/ROW]
[ROW][C]10[/C][C]-0.046475[/C][C]-0.3383[/C][C]0.36822[/C][/ROW]
[ROW][C]11[/C][C]-0.028593[/C][C]-0.2082[/C][C]0.41795[/C][/ROW]
[ROW][C]12[/C][C]0.002982[/C][C]0.0217[/C][C]0.49138[/C][/ROW]
[ROW][C]13[/C][C]-0.042645[/C][C]-0.3105[/C][C]0.378714[/C][/ROW]
[ROW][C]14[/C][C]-0.015053[/C][C]-0.1096[/C][C]0.456575[/C][/ROW]
[ROW][C]15[/C][C]-0.038171[/C][C]-0.2779[/C][C]0.391088[/C][/ROW]
[ROW][C]16[/C][C]-0.01012[/C][C]-0.0737[/C][C]0.470772[/C][/ROW]
[ROW][C]17[/C][C]0.025546[/C][C]0.186[/C][C]0.426587[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298950&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298950&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	0.94638	6.8898	0
2	-0.017302	-0.126	0.450119
3	-0.005907	-0.043	0.482931
4	-0.067747	-0.4932	0.311952
5	-0.013773	-0.1003	0.460255
6	-0.072208	-0.5257	0.300651
7	-0.062492	-0.455	0.325501
8	-0.043908	-0.3197	0.375243
9	-0.027778	-0.2022	0.420257
10	-0.046475	-0.3383	0.36822
11	-0.028593	-0.2082	0.41795
12	0.002982	0.0217	0.49138
13	-0.042645	-0.3105	0.378714
14	-0.015053	-0.1096	0.456575
15	-0.038171	-0.2779	0.391088
16	-0.01012	-0.0737	0.470772
17	0.025546	0.186	0.426587

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 = 6 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 6 ; 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)
x <- na.omit(x)
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,'ACF(k)',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,'PACF(k)',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