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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 12:29:55 +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/16/t1481888973on19huv3uxnb9l8.htm/, Retrieved Fri, 03 May 2024 00:11:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300186, Retrieved Fri, 03 May 2024 00:11:53 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [] [2016-12-16 11:29:55] [edf5d828a362f128b5245bc1504a7130] [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=300186&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=300186&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300186&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	0.100548	0.4926	0.313392
2	-0.256822	-1.2582	0.110217
3	0.083129	0.4072	0.343718
4	0.538381	2.6375	0.007212
5	-0.024955	-0.1223	0.451857
6	-0.315206	-1.5442	0.067814
7	0.010331	0.0506	0.480028
8	0.45252	2.2169	0.018178
9	-0.091785	-0.4497	0.328497
10	-0.284357	-1.3931	0.088186
11	-0.015771	-0.0773	0.469528
12	0.243815	1.1944	0.121988
13	-0.132828	-0.6507	0.260703

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.100548 & 0.4926 & 0.313392 \tabularnewline
2 & -0.256822 & -1.2582 & 0.110217 \tabularnewline
3 & 0.083129 & 0.4072 & 0.343718 \tabularnewline
4 & 0.538381 & 2.6375 & 0.007212 \tabularnewline
5 & -0.024955 & -0.1223 & 0.451857 \tabularnewline
6 & -0.315206 & -1.5442 & 0.067814 \tabularnewline
7 & 0.010331 & 0.0506 & 0.480028 \tabularnewline
8 & 0.45252 & 2.2169 & 0.018178 \tabularnewline
9 & -0.091785 & -0.4497 & 0.328497 \tabularnewline
10 & -0.284357 & -1.3931 & 0.088186 \tabularnewline
11 & -0.015771 & -0.0773 & 0.469528 \tabularnewline
12 & 0.243815 & 1.1944 & 0.121988 \tabularnewline
13 & -0.132828 & -0.6507 & 0.260703 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300186&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]0.100548[/C][C]0.4926[/C][C]0.313392[/C][/ROW]
[ROW][C]2[/C][C]-0.256822[/C][C]-1.2582[/C][C]0.110217[/C][/ROW]
[ROW][C]3[/C][C]0.083129[/C][C]0.4072[/C][C]0.343718[/C][/ROW]
[ROW][C]4[/C][C]0.538381[/C][C]2.6375[/C][C]0.007212[/C][/ROW]
[ROW][C]5[/C][C]-0.024955[/C][C]-0.1223[/C][C]0.451857[/C][/ROW]
[ROW][C]6[/C][C]-0.315206[/C][C]-1.5442[/C][C]0.067814[/C][/ROW]
[ROW][C]7[/C][C]0.010331[/C][C]0.0506[/C][C]0.480028[/C][/ROW]
[ROW][C]8[/C][C]0.45252[/C][C]2.2169[/C][C]0.018178[/C][/ROW]
[ROW][C]9[/C][C]-0.091785[/C][C]-0.4497[/C][C]0.328497[/C][/ROW]
[ROW][C]10[/C][C]-0.284357[/C][C]-1.3931[/C][C]0.088186[/C][/ROW]
[ROW][C]11[/C][C]-0.015771[/C][C]-0.0773[/C][C]0.469528[/C][/ROW]
[ROW][C]12[/C][C]0.243815[/C][C]1.1944[/C][C]0.121988[/C][/ROW]
[ROW][C]13[/C][C]-0.132828[/C][C]-0.6507[/C][C]0.260703[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300186&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300186&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	0.100548	0.4926	0.313392
2	-0.256822	-1.2582	0.110217
3	0.083129	0.4072	0.343718
4	0.538381	2.6375	0.007212
5	-0.024955	-0.1223	0.451857
6	-0.315206	-1.5442	0.067814
7	0.010331	0.0506	0.480028
8	0.45252	2.2169	0.018178
9	-0.091785	-0.4497	0.328497
10	-0.284357	-1.3931	0.088186
11	-0.015771	-0.0773	0.469528
12	0.243815	1.1944	0.121988
13	-0.132828	-0.6507	0.260703

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.100548	0.4926	0.313392
2	-0.269658	-1.3211	0.099471
3	0.15582	0.7634	0.226344
4	0.484853	2.3753	0.012935
5	-0.13589	-0.6657	0.255968
6	-0.147596	-0.7231	0.238313
7	-0.051335	-0.2515	0.401789
8	0.230044	1.127	0.135446
9	-0.117469	-0.5755	0.285162
10	0.006104	0.0299	0.488196
11	-0.091372	-0.4476	0.329218
12	-0.112046	-0.5489	0.294069
13	-0.03532	-0.173	0.432038

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.100548 & 0.4926 & 0.313392 \tabularnewline
2 & -0.269658 & -1.3211 & 0.099471 \tabularnewline
3 & 0.15582 & 0.7634 & 0.226344 \tabularnewline
4 & 0.484853 & 2.3753 & 0.012935 \tabularnewline
5 & -0.13589 & -0.6657 & 0.255968 \tabularnewline
6 & -0.147596 & -0.7231 & 0.238313 \tabularnewline
7 & -0.051335 & -0.2515 & 0.401789 \tabularnewline
8 & 0.230044 & 1.127 & 0.135446 \tabularnewline
9 & -0.117469 & -0.5755 & 0.285162 \tabularnewline
10 & 0.006104 & 0.0299 & 0.488196 \tabularnewline
11 & -0.091372 & -0.4476 & 0.329218 \tabularnewline
12 & -0.112046 & -0.5489 & 0.294069 \tabularnewline
13 & -0.03532 & -0.173 & 0.432038 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300186&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]0.100548[/C][C]0.4926[/C][C]0.313392[/C][/ROW]
[ROW][C]2[/C][C]-0.269658[/C][C]-1.3211[/C][C]0.099471[/C][/ROW]
[ROW][C]3[/C][C]0.15582[/C][C]0.7634[/C][C]0.226344[/C][/ROW]
[ROW][C]4[/C][C]0.484853[/C][C]2.3753[/C][C]0.012935[/C][/ROW]
[ROW][C]5[/C][C]-0.13589[/C][C]-0.6657[/C][C]0.255968[/C][/ROW]
[ROW][C]6[/C][C]-0.147596[/C][C]-0.7231[/C][C]0.238313[/C][/ROW]
[ROW][C]7[/C][C]-0.051335[/C][C]-0.2515[/C][C]0.401789[/C][/ROW]
[ROW][C]8[/C][C]0.230044[/C][C]1.127[/C][C]0.135446[/C][/ROW]
[ROW][C]9[/C][C]-0.117469[/C][C]-0.5755[/C][C]0.285162[/C][/ROW]
[ROW][C]10[/C][C]0.006104[/C][C]0.0299[/C][C]0.488196[/C][/ROW]
[ROW][C]11[/C][C]-0.091372[/C][C]-0.4476[/C][C]0.329218[/C][/ROW]
[ROW][C]12[/C][C]-0.112046[/C][C]-0.5489[/C][C]0.294069[/C][/ROW]
[ROW][C]13[/C][C]-0.03532[/C][C]-0.173[/C][C]0.432038[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300186&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300186&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	0.100548	0.4926	0.313392
2	-0.269658	-1.3211	0.099471
3	0.15582	0.7634	0.226344
4	0.484853	2.3753	0.012935
5	-0.13589	-0.6657	0.255968
6	-0.147596	-0.7231	0.238313
7	-0.051335	-0.2515	0.401789
8	0.230044	1.127	0.135446
9	-0.117469	-0.5755	0.285162
10	0.006104	0.0299	0.488196
11	-0.091372	-0.4476	0.329218
12	-0.112046	-0.5489	0.294069
13	-0.03532	-0.173	0.432038

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 = 1 ; par2 = 0 ; par3 = 1 ; par4 = 4 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; 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