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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2016 12:54:12 +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/23/t14824940654kjw1yy27r2ymh1.htm/, Retrieved Wed, 08 May 2024 03:20:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302885, Retrieved Wed, 08 May 2024 03:20:56 +0000

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-       [(Partial) Autocorrelation Function] [N1023] [2016-12-23 11:54:12] [8e56909c70ba580a071e942d9a393c42] [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=302885&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=302885&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302885&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	-0.443619	-2.909	0.002859
2	-0.045376	-0.2976	0.383739
3	0.182499	1.1967	0.118985
4	-0.153664	-1.0076	0.159631
5	-0.044464	-0.2916	0.386008
6	0.257749	1.6902	0.049116
7	-0.163491	-1.0721	0.144832
8	-0.06415	-0.4207	0.33805
9	0.178031	1.1674	0.124736
10	-0.173727	-1.1392	0.130463
11	0.033795	0.2216	0.412834
12	-0.006425	-0.0421	0.483295
13	-0.112162	-0.7355	0.233015
14	0.146028	0.9576	0.171817
15	0.01693	0.111	0.456061
16	-0.022917	-0.1503	0.440624

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.443619 & -2.909 & 0.002859 \tabularnewline
2 & -0.045376 & -0.2976 & 0.383739 \tabularnewline
3 & 0.182499 & 1.1967 & 0.118985 \tabularnewline
4 & -0.153664 & -1.0076 & 0.159631 \tabularnewline
5 & -0.044464 & -0.2916 & 0.386008 \tabularnewline
6 & 0.257749 & 1.6902 & 0.049116 \tabularnewline
7 & -0.163491 & -1.0721 & 0.144832 \tabularnewline
8 & -0.06415 & -0.4207 & 0.33805 \tabularnewline
9 & 0.178031 & 1.1674 & 0.124736 \tabularnewline
10 & -0.173727 & -1.1392 & 0.130463 \tabularnewline
11 & 0.033795 & 0.2216 & 0.412834 \tabularnewline
12 & -0.006425 & -0.0421 & 0.483295 \tabularnewline
13 & -0.112162 & -0.7355 & 0.233015 \tabularnewline
14 & 0.146028 & 0.9576 & 0.171817 \tabularnewline
15 & 0.01693 & 0.111 & 0.456061 \tabularnewline
16 & -0.022917 & -0.1503 & 0.440624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302885&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]-0.443619[/C][C]-2.909[/C][C]0.002859[/C][/ROW]
[ROW][C]2[/C][C]-0.045376[/C][C]-0.2976[/C][C]0.383739[/C][/ROW]
[ROW][C]3[/C][C]0.182499[/C][C]1.1967[/C][C]0.118985[/C][/ROW]
[ROW][C]4[/C][C]-0.153664[/C][C]-1.0076[/C][C]0.159631[/C][/ROW]
[ROW][C]5[/C][C]-0.044464[/C][C]-0.2916[/C][C]0.386008[/C][/ROW]
[ROW][C]6[/C][C]0.257749[/C][C]1.6902[/C][C]0.049116[/C][/ROW]
[ROW][C]7[/C][C]-0.163491[/C][C]-1.0721[/C][C]0.144832[/C][/ROW]
[ROW][C]8[/C][C]-0.06415[/C][C]-0.4207[/C][C]0.33805[/C][/ROW]
[ROW][C]9[/C][C]0.178031[/C][C]1.1674[/C][C]0.124736[/C][/ROW]
[ROW][C]10[/C][C]-0.173727[/C][C]-1.1392[/C][C]0.130463[/C][/ROW]
[ROW][C]11[/C][C]0.033795[/C][C]0.2216[/C][C]0.412834[/C][/ROW]
[ROW][C]12[/C][C]-0.006425[/C][C]-0.0421[/C][C]0.483295[/C][/ROW]
[ROW][C]13[/C][C]-0.112162[/C][C]-0.7355[/C][C]0.233015[/C][/ROW]
[ROW][C]14[/C][C]0.146028[/C][C]0.9576[/C][C]0.171817[/C][/ROW]
[ROW][C]15[/C][C]0.01693[/C][C]0.111[/C][C]0.456061[/C][/ROW]
[ROW][C]16[/C][C]-0.022917[/C][C]-0.1503[/C][C]0.440624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302885&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302885&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	-0.443619	-2.909	0.002859
2	-0.045376	-0.2976	0.383739
3	0.182499	1.1967	0.118985
4	-0.153664	-1.0076	0.159631
5	-0.044464	-0.2916	0.386008
6	0.257749	1.6902	0.049116
7	-0.163491	-1.0721	0.144832
8	-0.06415	-0.4207	0.33805
9	0.178031	1.1674	0.124736
10	-0.173727	-1.1392	0.130463
11	0.033795	0.2216	0.412834
12	-0.006425	-0.0421	0.483295
13	-0.112162	-0.7355	0.233015
14	0.146028	0.9576	0.171817
15	0.01693	0.111	0.456061
16	-0.022917	-0.1503	0.440624

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.443619	-2.909	0.002859
2	-0.301511	-1.9771	0.02723
3	0.030874	0.2025	0.420258
4	-0.067402	-0.442	0.330358
5	-0.146537	-0.9609	0.170985
6	0.173195	1.1357	0.131183
7	0.075446	0.4947	0.311653
8	-0.078419	-0.5142	0.304863
9	0.047365	0.3106	0.378804
10	-0.049746	-0.3262	0.372925
11	-0.031399	-0.2059	0.418921
12	-0.162386	-1.0648	0.146446
13	-0.198562	-1.3021	0.099914
14	0.046625	0.3057	0.380638
15	0.077294	0.5069	0.307424
16	0.133828	0.8776	0.192527

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.443619 & -2.909 & 0.002859 \tabularnewline
2 & -0.301511 & -1.9771 & 0.02723 \tabularnewline
3 & 0.030874 & 0.2025 & 0.420258 \tabularnewline
4 & -0.067402 & -0.442 & 0.330358 \tabularnewline
5 & -0.146537 & -0.9609 & 0.170985 \tabularnewline
6 & 0.173195 & 1.1357 & 0.131183 \tabularnewline
7 & 0.075446 & 0.4947 & 0.311653 \tabularnewline
8 & -0.078419 & -0.5142 & 0.304863 \tabularnewline
9 & 0.047365 & 0.3106 & 0.378804 \tabularnewline
10 & -0.049746 & -0.3262 & 0.372925 \tabularnewline
11 & -0.031399 & -0.2059 & 0.418921 \tabularnewline
12 & -0.162386 & -1.0648 & 0.146446 \tabularnewline
13 & -0.198562 & -1.3021 & 0.099914 \tabularnewline
14 & 0.046625 & 0.3057 & 0.380638 \tabularnewline
15 & 0.077294 & 0.5069 & 0.307424 \tabularnewline
16 & 0.133828 & 0.8776 & 0.192527 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302885&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]-0.443619[/C][C]-2.909[/C][C]0.002859[/C][/ROW]
[ROW][C]2[/C][C]-0.301511[/C][C]-1.9771[/C][C]0.02723[/C][/ROW]
[ROW][C]3[/C][C]0.030874[/C][C]0.2025[/C][C]0.420258[/C][/ROW]
[ROW][C]4[/C][C]-0.067402[/C][C]-0.442[/C][C]0.330358[/C][/ROW]
[ROW][C]5[/C][C]-0.146537[/C][C]-0.9609[/C][C]0.170985[/C][/ROW]
[ROW][C]6[/C][C]0.173195[/C][C]1.1357[/C][C]0.131183[/C][/ROW]
[ROW][C]7[/C][C]0.075446[/C][C]0.4947[/C][C]0.311653[/C][/ROW]
[ROW][C]8[/C][C]-0.078419[/C][C]-0.5142[/C][C]0.304863[/C][/ROW]
[ROW][C]9[/C][C]0.047365[/C][C]0.3106[/C][C]0.378804[/C][/ROW]
[ROW][C]10[/C][C]-0.049746[/C][C]-0.3262[/C][C]0.372925[/C][/ROW]
[ROW][C]11[/C][C]-0.031399[/C][C]-0.2059[/C][C]0.418921[/C][/ROW]
[ROW][C]12[/C][C]-0.162386[/C][C]-1.0648[/C][C]0.146446[/C][/ROW]
[ROW][C]13[/C][C]-0.198562[/C][C]-1.3021[/C][C]0.099914[/C][/ROW]
[ROW][C]14[/C][C]0.046625[/C][C]0.3057[/C][C]0.380638[/C][/ROW]
[ROW][C]15[/C][C]0.077294[/C][C]0.5069[/C][C]0.307424[/C][/ROW]
[ROW][C]16[/C][C]0.133828[/C][C]0.8776[/C][C]0.192527[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302885&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302885&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	-0.443619	-2.909	0.002859
2	-0.301511	-1.9771	0.02723
3	0.030874	0.2025	0.420258
4	-0.067402	-0.442	0.330358
5	-0.146537	-0.9609	0.170985
6	0.173195	1.1357	0.131183
7	0.075446	0.4947	0.311653
8	-0.078419	-0.5142	0.304863
9	0.047365	0.3106	0.378804
10	-0.049746	-0.3262	0.372925
11	-0.031399	-0.2059	0.418921
12	-0.162386	-1.0648	0.146446
13	-0.198562	-1.3021	0.099914
14	0.046625	0.3057	0.380638
15	0.077294	0.5069	0.307424
16	0.133828	0.8776	0.192527

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = additive ; par2 = 12 ;

Parameters (R input):

par1 = Default ; 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)
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