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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 22:26:10 +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/19/t1482182810wd96ad7hh3frwy0.htm/, Retrieved Fri, 01 Nov 2024 03:37:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301526, Retrieved Fri, 01 Nov 2024 03:37:00 +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] [] [2016-12-19 21:26:10] [2e11ca31a00cf8de75c33c1af2d59434] [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	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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301526&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301526&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301526&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.851492	5.6482	1e-06
2	0.757152	5.0224	4e-06
3	0.706613	4.6871	1.3e-05
4	0.717768	4.7611	1.1e-05
5	0.583402	3.8699	0.000178
6	0.501428	3.3261	0.000892
7	0.45722	3.0329	0.002027
8	0.467461	3.1008	0.001681
9	0.345863	2.2942	0.013305
10	0.270782	1.7962	0.039668
11	0.237403	1.5748	0.061239
12	0.252947	1.6779	0.050232
13	0.14168	0.9398	0.176225
14	0.074152	0.4919	0.31263
15	0.04606	0.3055	0.380702
16	0.066585	0.4417	0.330443

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.851492 & 5.6482 & 1e-06 \tabularnewline
2 & 0.757152 & 5.0224 & 4e-06 \tabularnewline
3 & 0.706613 & 4.6871 & 1.3e-05 \tabularnewline
4 & 0.717768 & 4.7611 & 1.1e-05 \tabularnewline
5 & 0.583402 & 3.8699 & 0.000178 \tabularnewline
6 & 0.501428 & 3.3261 & 0.000892 \tabularnewline
7 & 0.45722 & 3.0329 & 0.002027 \tabularnewline
8 & 0.467461 & 3.1008 & 0.001681 \tabularnewline
9 & 0.345863 & 2.2942 & 0.013305 \tabularnewline
10 & 0.270782 & 1.7962 & 0.039668 \tabularnewline
11 & 0.237403 & 1.5748 & 0.061239 \tabularnewline
12 & 0.252947 & 1.6779 & 0.050232 \tabularnewline
13 & 0.14168 & 0.9398 & 0.176225 \tabularnewline
14 & 0.074152 & 0.4919 & 0.31263 \tabularnewline
15 & 0.04606 & 0.3055 & 0.380702 \tabularnewline
16 & 0.066585 & 0.4417 & 0.330443 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301526&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]0.851492[/C][C]5.6482[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.757152[/C][C]5.0224[/C][C]4e-06[/C][/ROW]
[ROW][C]3[/C][C]0.706613[/C][C]4.6871[/C][C]1.3e-05[/C][/ROW]
[ROW][C]4[/C][C]0.717768[/C][C]4.7611[/C][C]1.1e-05[/C][/ROW]
[ROW][C]5[/C][C]0.583402[/C][C]3.8699[/C][C]0.000178[/C][/ROW]
[ROW][C]6[/C][C]0.501428[/C][C]3.3261[/C][C]0.000892[/C][/ROW]
[ROW][C]7[/C][C]0.45722[/C][C]3.0329[/C][C]0.002027[/C][/ROW]
[ROW][C]8[/C][C]0.467461[/C][C]3.1008[/C][C]0.001681[/C][/ROW]
[ROW][C]9[/C][C]0.345863[/C][C]2.2942[/C][C]0.013305[/C][/ROW]
[ROW][C]10[/C][C]0.270782[/C][C]1.7962[/C][C]0.039668[/C][/ROW]
[ROW][C]11[/C][C]0.237403[/C][C]1.5748[/C][C]0.061239[/C][/ROW]
[ROW][C]12[/C][C]0.252947[/C][C]1.6779[/C][C]0.050232[/C][/ROW]
[ROW][C]13[/C][C]0.14168[/C][C]0.9398[/C][C]0.176225[/C][/ROW]
[ROW][C]14[/C][C]0.074152[/C][C]0.4919[/C][C]0.31263[/C][/ROW]
[ROW][C]15[/C][C]0.04606[/C][C]0.3055[/C][C]0.380702[/C][/ROW]
[ROW][C]16[/C][C]0.066585[/C][C]0.4417[/C][C]0.330443[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301526&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301526&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	0.851492	5.6482	1e-06
2	0.757152	5.0224	4e-06
3	0.706613	4.6871	1.3e-05
4	0.717768	4.7611	1.1e-05
5	0.583402	3.8699	0.000178
6	0.501428	3.3261	0.000892
7	0.45722	3.0329	0.002027
8	0.467461	3.1008	0.001681
9	0.345863	2.2942	0.013305
10	0.270782	1.7962	0.039668
11	0.237403	1.5748	0.061239
12	0.252947	1.6779	0.050232
13	0.14168	0.9398	0.176225
14	0.074152	0.4919	0.31263
15	0.04606	0.3055	0.380702
16	0.066585	0.4417	0.330443

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.851492	5.6482	1e-06
2	0.116791	0.7747	0.221329
3	0.139206	0.9234	0.180421
4	0.263787	1.7498	0.043565
5	-0.43531	-2.8875	0.003
6	0.069419	0.4605	0.323721
7	0.05451	0.3616	0.359699
8	0.069354	0.46	0.323876
9	-0.237346	-1.5744	0.061282
10	0.014954	0.0992	0.460718
11	0.05471	0.3629	0.359207
12	0.019678	0.1305	0.448372
13	-0.177895	-1.18	0.122166
14	0.004163	0.0276	0.489048
15	0.013383	0.0888	0.464832
16	0.011686	0.0775	0.469283

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.851492 & 5.6482 & 1e-06 \tabularnewline
2 & 0.116791 & 0.7747 & 0.221329 \tabularnewline
3 & 0.139206 & 0.9234 & 0.180421 \tabularnewline
4 & 0.263787 & 1.7498 & 0.043565 \tabularnewline
5 & -0.43531 & -2.8875 & 0.003 \tabularnewline
6 & 0.069419 & 0.4605 & 0.323721 \tabularnewline
7 & 0.05451 & 0.3616 & 0.359699 \tabularnewline
8 & 0.069354 & 0.46 & 0.323876 \tabularnewline
9 & -0.237346 & -1.5744 & 0.061282 \tabularnewline
10 & 0.014954 & 0.0992 & 0.460718 \tabularnewline
11 & 0.05471 & 0.3629 & 0.359207 \tabularnewline
12 & 0.019678 & 0.1305 & 0.448372 \tabularnewline
13 & -0.177895 & -1.18 & 0.122166 \tabularnewline
14 & 0.004163 & 0.0276 & 0.489048 \tabularnewline
15 & 0.013383 & 0.0888 & 0.464832 \tabularnewline
16 & 0.011686 & 0.0775 & 0.469283 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301526&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]0.851492[/C][C]5.6482[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.116791[/C][C]0.7747[/C][C]0.221329[/C][/ROW]
[ROW][C]3[/C][C]0.139206[/C][C]0.9234[/C][C]0.180421[/C][/ROW]
[ROW][C]4[/C][C]0.263787[/C][C]1.7498[/C][C]0.043565[/C][/ROW]
[ROW][C]5[/C][C]-0.43531[/C][C]-2.8875[/C][C]0.003[/C][/ROW]
[ROW][C]6[/C][C]0.069419[/C][C]0.4605[/C][C]0.323721[/C][/ROW]
[ROW][C]7[/C][C]0.05451[/C][C]0.3616[/C][C]0.359699[/C][/ROW]
[ROW][C]8[/C][C]0.069354[/C][C]0.46[/C][C]0.323876[/C][/ROW]
[ROW][C]9[/C][C]-0.237346[/C][C]-1.5744[/C][C]0.061282[/C][/ROW]
[ROW][C]10[/C][C]0.014954[/C][C]0.0992[/C][C]0.460718[/C][/ROW]
[ROW][C]11[/C][C]0.05471[/C][C]0.3629[/C][C]0.359207[/C][/ROW]
[ROW][C]12[/C][C]0.019678[/C][C]0.1305[/C][C]0.448372[/C][/ROW]
[ROW][C]13[/C][C]-0.177895[/C][C]-1.18[/C][C]0.122166[/C][/ROW]
[ROW][C]14[/C][C]0.004163[/C][C]0.0276[/C][C]0.489048[/C][/ROW]
[ROW][C]15[/C][C]0.013383[/C][C]0.0888[/C][C]0.464832[/C][/ROW]
[ROW][C]16[/C][C]0.011686[/C][C]0.0775[/C][C]0.469283[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301526&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301526&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	0.851492	5.6482	1e-06
2	0.116791	0.7747	0.221329
3	0.139206	0.9234	0.180421
4	0.263787	1.7498	0.043565
5	-0.43531	-2.8875	0.003
6	0.069419	0.4605	0.323721
7	0.05451	0.3616	0.359699
8	0.069354	0.46	0.323876
9	-0.237346	-1.5744	0.061282
10	0.014954	0.0992	0.460718
11	0.05471	0.3629	0.359207
12	0.019678	0.1305	0.448372
13	-0.177895	-1.18	0.122166
14	0.004163	0.0276	0.489048
15	0.013383	0.0888	0.464832
16	0.011686	0.0775	0.469283

Figure 1

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Postscript link

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Figure 2

PNG link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

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)
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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Figures (Output of Computation)

Input Parameters & R Code