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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Dec 2016 14:22:52 +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/18/t1482067451mqclstf0wdbd0s6.htm/, Retrieved Wed, 08 May 2024 21:37:30 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301066, Retrieved Wed, 08 May 2024 21:37:30 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-18 13:22:52] [94ac3c9a028ddd47e8862e80eac9f626] [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=301066&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=301066&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301066&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	-0.07996	-0.5057	0.307917
2	-0.267912	-1.6944	0.048979
3	-0.09143	-0.5783	0.283167
4	0.233837	1.4789	0.073497
5	-0.112177	-0.7095	0.241074
6	-0.107903	-0.6824	0.249447
7	0.094924	0.6004	0.275828
8	-0.055841	-0.3532	0.362909
9	-0.007714	-0.0488	0.480666
10	-0.028614	-0.181	0.428653
11	0.177036	1.1197	0.134765
12	-0.142077	-0.8986	0.187128
13	0.028126	0.1779	0.429856
14	0.116759	0.7384	0.232276
15	-0.050026	-0.3164	0.376675
16	-0.071436	-0.4518	0.326925

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.07996 & -0.5057 & 0.307917 \tabularnewline
2 & -0.267912 & -1.6944 & 0.048979 \tabularnewline
3 & -0.09143 & -0.5783 & 0.283167 \tabularnewline
4 & 0.233837 & 1.4789 & 0.073497 \tabularnewline
5 & -0.112177 & -0.7095 & 0.241074 \tabularnewline
6 & -0.107903 & -0.6824 & 0.249447 \tabularnewline
7 & 0.094924 & 0.6004 & 0.275828 \tabularnewline
8 & -0.055841 & -0.3532 & 0.362909 \tabularnewline
9 & -0.007714 & -0.0488 & 0.480666 \tabularnewline
10 & -0.028614 & -0.181 & 0.428653 \tabularnewline
11 & 0.177036 & 1.1197 & 0.134765 \tabularnewline
12 & -0.142077 & -0.8986 & 0.187128 \tabularnewline
13 & 0.028126 & 0.1779 & 0.429856 \tabularnewline
14 & 0.116759 & 0.7384 & 0.232276 \tabularnewline
15 & -0.050026 & -0.3164 & 0.376675 \tabularnewline
16 & -0.071436 & -0.4518 & 0.326925 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301066&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]-0.07996[/C][C]-0.5057[/C][C]0.307917[/C][/ROW]
[ROW][C]2[/C][C]-0.267912[/C][C]-1.6944[/C][C]0.048979[/C][/ROW]
[ROW][C]3[/C][C]-0.09143[/C][C]-0.5783[/C][C]0.283167[/C][/ROW]
[ROW][C]4[/C][C]0.233837[/C][C]1.4789[/C][C]0.073497[/C][/ROW]
[ROW][C]5[/C][C]-0.112177[/C][C]-0.7095[/C][C]0.241074[/C][/ROW]
[ROW][C]6[/C][C]-0.107903[/C][C]-0.6824[/C][C]0.249447[/C][/ROW]
[ROW][C]7[/C][C]0.094924[/C][C]0.6004[/C][C]0.275828[/C][/ROW]
[ROW][C]8[/C][C]-0.055841[/C][C]-0.3532[/C][C]0.362909[/C][/ROW]
[ROW][C]9[/C][C]-0.007714[/C][C]-0.0488[/C][C]0.480666[/C][/ROW]
[ROW][C]10[/C][C]-0.028614[/C][C]-0.181[/C][C]0.428653[/C][/ROW]
[ROW][C]11[/C][C]0.177036[/C][C]1.1197[/C][C]0.134765[/C][/ROW]
[ROW][C]12[/C][C]-0.142077[/C][C]-0.8986[/C][C]0.187128[/C][/ROW]
[ROW][C]13[/C][C]0.028126[/C][C]0.1779[/C][C]0.429856[/C][/ROW]
[ROW][C]14[/C][C]0.116759[/C][C]0.7384[/C][C]0.232276[/C][/ROW]
[ROW][C]15[/C][C]-0.050026[/C][C]-0.3164[/C][C]0.376675[/C][/ROW]
[ROW][C]16[/C][C]-0.071436[/C][C]-0.4518[/C][C]0.326925[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301066&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301066&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	-0.07996	-0.5057	0.307917
2	-0.267912	-1.6944	0.048979
3	-0.09143	-0.5783	0.283167
4	0.233837	1.4789	0.073497
5	-0.112177	-0.7095	0.241074
6	-0.107903	-0.6824	0.249447
7	0.094924	0.6004	0.275828
8	-0.055841	-0.3532	0.362909
9	-0.007714	-0.0488	0.480666
10	-0.028614	-0.181	0.428653
11	0.177036	1.1197	0.134765
12	-0.142077	-0.8986	0.187128
13	0.028126	0.1779	0.429856
14	0.116759	0.7384	0.232276
15	-0.050026	-0.3164	0.376675
16	-0.071436	-0.4518	0.326925

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.07996	-0.5057	0.307917
2	-0.27607	-1.746	0.044242
3	-0.153442	-0.9704	0.168827
4	0.145279	0.9188	0.181847
5	-0.148509	-0.9393	0.176619
6	-0.057788	-0.3655	0.358339
7	0.070119	0.4435	0.329907
8	-0.168308	-1.0645	0.146749
9	0.044279	0.28	0.390443
10	-0.051586	-0.3263	0.372964
11	0.117691	0.7443	0.230511
12	-0.091438	-0.5783	0.28315
13	0.061709	0.3903	0.349199
14	0.127844	0.8086	0.211777
15	-0.111698	-0.7064	0.242005
16	0.068303	0.432	0.334036

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.07996 & -0.5057 & 0.307917 \tabularnewline
2 & -0.27607 & -1.746 & 0.044242 \tabularnewline
3 & -0.153442 & -0.9704 & 0.168827 \tabularnewline
4 & 0.145279 & 0.9188 & 0.181847 \tabularnewline
5 & -0.148509 & -0.9393 & 0.176619 \tabularnewline
6 & -0.057788 & -0.3655 & 0.358339 \tabularnewline
7 & 0.070119 & 0.4435 & 0.329907 \tabularnewline
8 & -0.168308 & -1.0645 & 0.146749 \tabularnewline
9 & 0.044279 & 0.28 & 0.390443 \tabularnewline
10 & -0.051586 & -0.3263 & 0.372964 \tabularnewline
11 & 0.117691 & 0.7443 & 0.230511 \tabularnewline
12 & -0.091438 & -0.5783 & 0.28315 \tabularnewline
13 & 0.061709 & 0.3903 & 0.349199 \tabularnewline
14 & 0.127844 & 0.8086 & 0.211777 \tabularnewline
15 & -0.111698 & -0.7064 & 0.242005 \tabularnewline
16 & 0.068303 & 0.432 & 0.334036 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301066&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]-0.07996[/C][C]-0.5057[/C][C]0.307917[/C][/ROW]
[ROW][C]2[/C][C]-0.27607[/C][C]-1.746[/C][C]0.044242[/C][/ROW]
[ROW][C]3[/C][C]-0.153442[/C][C]-0.9704[/C][C]0.168827[/C][/ROW]
[ROW][C]4[/C][C]0.145279[/C][C]0.9188[/C][C]0.181847[/C][/ROW]
[ROW][C]5[/C][C]-0.148509[/C][C]-0.9393[/C][C]0.176619[/C][/ROW]
[ROW][C]6[/C][C]-0.057788[/C][C]-0.3655[/C][C]0.358339[/C][/ROW]
[ROW][C]7[/C][C]0.070119[/C][C]0.4435[/C][C]0.329907[/C][/ROW]
[ROW][C]8[/C][C]-0.168308[/C][C]-1.0645[/C][C]0.146749[/C][/ROW]
[ROW][C]9[/C][C]0.044279[/C][C]0.28[/C][C]0.390443[/C][/ROW]
[ROW][C]10[/C][C]-0.051586[/C][C]-0.3263[/C][C]0.372964[/C][/ROW]
[ROW][C]11[/C][C]0.117691[/C][C]0.7443[/C][C]0.230511[/C][/ROW]
[ROW][C]12[/C][C]-0.091438[/C][C]-0.5783[/C][C]0.28315[/C][/ROW]
[ROW][C]13[/C][C]0.061709[/C][C]0.3903[/C][C]0.349199[/C][/ROW]
[ROW][C]14[/C][C]0.127844[/C][C]0.8086[/C][C]0.211777[/C][/ROW]
[ROW][C]15[/C][C]-0.111698[/C][C]-0.7064[/C][C]0.242005[/C][/ROW]
[ROW][C]16[/C][C]0.068303[/C][C]0.432[/C][C]0.334036[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301066&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301066&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	-0.07996	-0.5057	0.307917
2	-0.27607	-1.746	0.044242
3	-0.153442	-0.9704	0.168827
4	0.145279	0.9188	0.181847
5	-0.148509	-0.9393	0.176619
6	-0.057788	-0.3655	0.358339
7	0.070119	0.4435	0.329907
8	-0.168308	-1.0645	0.146749
9	0.044279	0.28	0.390443
10	-0.051586	-0.3263	0.372964
11	0.117691	0.7443	0.230511
12	-0.091438	-0.5783	0.28315
13	0.061709	0.3903	0.349199
14	0.127844	0.8086	0.211777
15	-0.111698	-0.7064	0.242005
16	0.068303	0.432	0.334036

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 = 1 ; par3 = 0 ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.1 ; 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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