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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2016 17:02:21 +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/20/t1482249825dk5csjixnqg7lor.htm/, Retrieved Sat, 27 Apr 2024 13:34:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301728, Retrieved Sat, 27 Apr 2024 13:34:40 +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] [] [2016-12-20 16:02:21] [b7216e4bc5ee29192acbe9c506cee18c] [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=301728&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=301728&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301728&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	-0.55268	-5.2722	0
2	-0.064323	-0.6136	0.270504
3	0.264748	2.5255	0.006641
4	-0.229208	-2.1865	0.015672
5	0.054364	0.5186	0.302649
6	0.119674	1.1416	0.128304
7	-0.143721	-1.371	0.086872
8	0.06823	0.6509	0.258383
9	0.027089	0.2584	0.398335
10	-0.164251	-1.5669	0.06031
11	0.393964	3.7582	0.000151
12	-0.410469	-3.9156	8.7e-05
13	0.015893	0.1516	0.439915
14	0.201241	1.9197	0.029013
15	-0.022996	-0.2194	0.413429
16	-0.125181	-1.1941	0.117762
17	0.103784	0.99	0.16239
18	0.015849	0.1512	0.440079
19	-0.184723	-1.7621	0.040701
20	0.209456	1.9981	0.024346

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.55268 & -5.2722 & 0 \tabularnewline
2 & -0.064323 & -0.6136 & 0.270504 \tabularnewline
3 & 0.264748 & 2.5255 & 0.006641 \tabularnewline
4 & -0.229208 & -2.1865 & 0.015672 \tabularnewline
5 & 0.054364 & 0.5186 & 0.302649 \tabularnewline
6 & 0.119674 & 1.1416 & 0.128304 \tabularnewline
7 & -0.143721 & -1.371 & 0.086872 \tabularnewline
8 & 0.06823 & 0.6509 & 0.258383 \tabularnewline
9 & 0.027089 & 0.2584 & 0.398335 \tabularnewline
10 & -0.164251 & -1.5669 & 0.06031 \tabularnewline
11 & 0.393964 & 3.7582 & 0.000151 \tabularnewline
12 & -0.410469 & -3.9156 & 8.7e-05 \tabularnewline
13 & 0.015893 & 0.1516 & 0.439915 \tabularnewline
14 & 0.201241 & 1.9197 & 0.029013 \tabularnewline
15 & -0.022996 & -0.2194 & 0.413429 \tabularnewline
16 & -0.125181 & -1.1941 & 0.117762 \tabularnewline
17 & 0.103784 & 0.99 & 0.16239 \tabularnewline
18 & 0.015849 & 0.1512 & 0.440079 \tabularnewline
19 & -0.184723 & -1.7621 & 0.040701 \tabularnewline
20 & 0.209456 & 1.9981 & 0.024346 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301728&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]-0.55268[/C][C]-5.2722[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.064323[/C][C]-0.6136[/C][C]0.270504[/C][/ROW]
[ROW][C]3[/C][C]0.264748[/C][C]2.5255[/C][C]0.006641[/C][/ROW]
[ROW][C]4[/C][C]-0.229208[/C][C]-2.1865[/C][C]0.015672[/C][/ROW]
[ROW][C]5[/C][C]0.054364[/C][C]0.5186[/C][C]0.302649[/C][/ROW]
[ROW][C]6[/C][C]0.119674[/C][C]1.1416[/C][C]0.128304[/C][/ROW]
[ROW][C]7[/C][C]-0.143721[/C][C]-1.371[/C][C]0.086872[/C][/ROW]
[ROW][C]8[/C][C]0.06823[/C][C]0.6509[/C][C]0.258383[/C][/ROW]
[ROW][C]9[/C][C]0.027089[/C][C]0.2584[/C][C]0.398335[/C][/ROW]
[ROW][C]10[/C][C]-0.164251[/C][C]-1.5669[/C][C]0.06031[/C][/ROW]
[ROW][C]11[/C][C]0.393964[/C][C]3.7582[/C][C]0.000151[/C][/ROW]
[ROW][C]12[/C][C]-0.410469[/C][C]-3.9156[/C][C]8.7e-05[/C][/ROW]
[ROW][C]13[/C][C]0.015893[/C][C]0.1516[/C][C]0.439915[/C][/ROW]
[ROW][C]14[/C][C]0.201241[/C][C]1.9197[/C][C]0.029013[/C][/ROW]
[ROW][C]15[/C][C]-0.022996[/C][C]-0.2194[/C][C]0.413429[/C][/ROW]
[ROW][C]16[/C][C]-0.125181[/C][C]-1.1941[/C][C]0.117762[/C][/ROW]
[ROW][C]17[/C][C]0.103784[/C][C]0.99[/C][C]0.16239[/C][/ROW]
[ROW][C]18[/C][C]0.015849[/C][C]0.1512[/C][C]0.440079[/C][/ROW]
[ROW][C]19[/C][C]-0.184723[/C][C]-1.7621[/C][C]0.040701[/C][/ROW]
[ROW][C]20[/C][C]0.209456[/C][C]1.9981[/C][C]0.024346[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301728&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301728&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	-0.55268	-5.2722	0
2	-0.064323	-0.6136	0.270504
3	0.264748	2.5255	0.006641
4	-0.229208	-2.1865	0.015672
5	0.054364	0.5186	0.302649
6	0.119674	1.1416	0.128304
7	-0.143721	-1.371	0.086872
8	0.06823	0.6509	0.258383
9	0.027089	0.2584	0.398335
10	-0.164251	-1.5669	0.06031
11	0.393964	3.7582	0.000151
12	-0.410469	-3.9156	8.7e-05
13	0.015893	0.1516	0.439915
14	0.201241	1.9197	0.029013
15	-0.022996	-0.2194	0.413429
16	-0.125181	-1.1941	0.117762
17	0.103784	0.99	0.16239
18	0.015849	0.1512	0.440079
19	-0.184723	-1.7621	0.040701
20	0.209456	1.9981	0.024346

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.55268	-5.2722	0
2	-0.532404	-5.0788	1e-06
3	-0.168743	-1.6097	0.055463
4	-0.243845	-2.3261	0.011116
5	-0.236858	-2.2595	0.01312
6	-0.097344	-0.9286	0.177776
7	-0.092265	-0.8801	0.190549
8	-0.046534	-0.4439	0.329083
9	-0.000671	-0.0064	0.497453
10	-0.208286	-1.9869	0.024969
11	0.38528	3.6753	0.000201
12	0.095519	0.9112	0.182302
13	-0.181835	-1.7346	0.043099
14	-0.384904	-3.6718	0.000203
15	0.077198	0.7364	0.231685
16	0.021155	0.2018	0.42026
17	-0.17223	-1.643	0.05192
18	-0.002751	-0.0262	0.48956
19	-0.092515	-0.8825	0.189906
20	-0.047602	-0.4541	0.325421

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.55268 & -5.2722 & 0 \tabularnewline
2 & -0.532404 & -5.0788 & 1e-06 \tabularnewline
3 & -0.168743 & -1.6097 & 0.055463 \tabularnewline
4 & -0.243845 & -2.3261 & 0.011116 \tabularnewline
5 & -0.236858 & -2.2595 & 0.01312 \tabularnewline
6 & -0.097344 & -0.9286 & 0.177776 \tabularnewline
7 & -0.092265 & -0.8801 & 0.190549 \tabularnewline
8 & -0.046534 & -0.4439 & 0.329083 \tabularnewline
9 & -0.000671 & -0.0064 & 0.497453 \tabularnewline
10 & -0.208286 & -1.9869 & 0.024969 \tabularnewline
11 & 0.38528 & 3.6753 & 0.000201 \tabularnewline
12 & 0.095519 & 0.9112 & 0.182302 \tabularnewline
13 & -0.181835 & -1.7346 & 0.043099 \tabularnewline
14 & -0.384904 & -3.6718 & 0.000203 \tabularnewline
15 & 0.077198 & 0.7364 & 0.231685 \tabularnewline
16 & 0.021155 & 0.2018 & 0.42026 \tabularnewline
17 & -0.17223 & -1.643 & 0.05192 \tabularnewline
18 & -0.002751 & -0.0262 & 0.48956 \tabularnewline
19 & -0.092515 & -0.8825 & 0.189906 \tabularnewline
20 & -0.047602 & -0.4541 & 0.325421 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301728&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]-0.55268[/C][C]-5.2722[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.532404[/C][C]-5.0788[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.168743[/C][C]-1.6097[/C][C]0.055463[/C][/ROW]
[ROW][C]4[/C][C]-0.243845[/C][C]-2.3261[/C][C]0.011116[/C][/ROW]
[ROW][C]5[/C][C]-0.236858[/C][C]-2.2595[/C][C]0.01312[/C][/ROW]
[ROW][C]6[/C][C]-0.097344[/C][C]-0.9286[/C][C]0.177776[/C][/ROW]
[ROW][C]7[/C][C]-0.092265[/C][C]-0.8801[/C][C]0.190549[/C][/ROW]
[ROW][C]8[/C][C]-0.046534[/C][C]-0.4439[/C][C]0.329083[/C][/ROW]
[ROW][C]9[/C][C]-0.000671[/C][C]-0.0064[/C][C]0.497453[/C][/ROW]
[ROW][C]10[/C][C]-0.208286[/C][C]-1.9869[/C][C]0.024969[/C][/ROW]
[ROW][C]11[/C][C]0.38528[/C][C]3.6753[/C][C]0.000201[/C][/ROW]
[ROW][C]12[/C][C]0.095519[/C][C]0.9112[/C][C]0.182302[/C][/ROW]
[ROW][C]13[/C][C]-0.181835[/C][C]-1.7346[/C][C]0.043099[/C][/ROW]
[ROW][C]14[/C][C]-0.384904[/C][C]-3.6718[/C][C]0.000203[/C][/ROW]
[ROW][C]15[/C][C]0.077198[/C][C]0.7364[/C][C]0.231685[/C][/ROW]
[ROW][C]16[/C][C]0.021155[/C][C]0.2018[/C][C]0.42026[/C][/ROW]
[ROW][C]17[/C][C]-0.17223[/C][C]-1.643[/C][C]0.05192[/C][/ROW]
[ROW][C]18[/C][C]-0.002751[/C][C]-0.0262[/C][C]0.48956[/C][/ROW]
[ROW][C]19[/C][C]-0.092515[/C][C]-0.8825[/C][C]0.189906[/C][/ROW]
[ROW][C]20[/C][C]-0.047602[/C][C]-0.4541[/C][C]0.325421[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301728&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301728&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	-0.55268	-5.2722	0
2	-0.532404	-5.0788	1e-06
3	-0.168743	-1.6097	0.055463
4	-0.243845	-2.3261	0.011116
5	-0.236858	-2.2595	0.01312
6	-0.097344	-0.9286	0.177776
7	-0.092265	-0.8801	0.190549
8	-0.046534	-0.4439	0.329083
9	-0.000671	-0.0064	0.497453
10	-0.208286	-1.9869	0.024969
11	0.38528	3.6753	0.000201
12	0.095519	0.9112	0.182302
13	-0.181835	-1.7346	0.043099
14	-0.384904	-3.6718	0.000203
15	0.077198	0.7364	0.231685
16	0.021155	0.2018	0.42026
17	-0.17223	-1.643	0.05192
18	-0.002751	-0.0262	0.48956
19	-0.092515	-0.8825	0.189906
20	-0.047602	-0.4541	0.325421

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

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Parameters (Session):

par1 = Default ; par2 = -0.4 ; par3 = 1 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = -0.4 ; par3 = 1 ; par4 = 2 ; 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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code