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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 15 Dec 2016 16:33:25 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/15/t1481816059otnupp1t4eewx6k.htm/, Retrieved Fri, 03 May 2024 10:07:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299921, Retrieved Fri, 03 May 2024 10:07:16 +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] [N324- ACF] [2016-12-15 15:33:25] [86c7fb9c8a0af864c0a27e2f433e80d7] [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=299921&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=299921&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299921&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	0.759513	3.1316	0.00304
2	0.531588	2.1918	0.021303
3	0.361924	1.4923	0.076979
4	0.304042	1.2536	0.113478
5	0.24792	1.0222	0.160506
6	0.089165	0.3676	0.358841
7	-0.068892	-0.284	0.389902
8	-0.235773	-0.9721	0.172311
9	-0.354934	-1.4634	0.080797
10	-0.365385	-1.5065	0.075145
11	-0.348454	-1.4367	0.084474
12	-0.282386	-1.1643	0.13019

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.759513 & 3.1316 & 0.00304 \tabularnewline
2 & 0.531588 & 2.1918 & 0.021303 \tabularnewline
3 & 0.361924 & 1.4923 & 0.076979 \tabularnewline
4 & 0.304042 & 1.2536 & 0.113478 \tabularnewline
5 & 0.24792 & 1.0222 & 0.160506 \tabularnewline
6 & 0.089165 & 0.3676 & 0.358841 \tabularnewline
7 & -0.068892 & -0.284 & 0.389902 \tabularnewline
8 & -0.235773 & -0.9721 & 0.172311 \tabularnewline
9 & -0.354934 & -1.4634 & 0.080797 \tabularnewline
10 & -0.365385 & -1.5065 & 0.075145 \tabularnewline
11 & -0.348454 & -1.4367 & 0.084474 \tabularnewline
12 & -0.282386 & -1.1643 & 0.13019 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299921&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]0.759513[/C][C]3.1316[/C][C]0.00304[/C][/ROW]
[ROW][C]2[/C][C]0.531588[/C][C]2.1918[/C][C]0.021303[/C][/ROW]
[ROW][C]3[/C][C]0.361924[/C][C]1.4923[/C][C]0.076979[/C][/ROW]
[ROW][C]4[/C][C]0.304042[/C][C]1.2536[/C][C]0.113478[/C][/ROW]
[ROW][C]5[/C][C]0.24792[/C][C]1.0222[/C][C]0.160506[/C][/ROW]
[ROW][C]6[/C][C]0.089165[/C][C]0.3676[/C][C]0.358841[/C][/ROW]
[ROW][C]7[/C][C]-0.068892[/C][C]-0.284[/C][C]0.389902[/C][/ROW]
[ROW][C]8[/C][C]-0.235773[/C][C]-0.9721[/C][C]0.172311[/C][/ROW]
[ROW][C]9[/C][C]-0.354934[/C][C]-1.4634[/C][C]0.080797[/C][/ROW]
[ROW][C]10[/C][C]-0.365385[/C][C]-1.5065[/C][C]0.075145[/C][/ROW]
[ROW][C]11[/C][C]-0.348454[/C][C]-1.4367[/C][C]0.084474[/C][/ROW]
[ROW][C]12[/C][C]-0.282386[/C][C]-1.1643[/C][C]0.13019[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299921&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299921&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	0.759513	3.1316	0.00304
2	0.531588	2.1918	0.021303
3	0.361924	1.4923	0.076979
4	0.304042	1.2536	0.113478
5	0.24792	1.0222	0.160506
6	0.089165	0.3676	0.358841
7	-0.068892	-0.284	0.389902
8	-0.235773	-0.9721	0.172311
9	-0.354934	-1.4634	0.080797
10	-0.365385	-1.5065	0.075145
11	-0.348454	-1.4367	0.084474
12	-0.282386	-1.1643	0.13019

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.759513	3.1316	0.00304
2	-0.10699	-0.4411	0.332338
3	-0.00899	-0.0371	0.485433
4	0.142921	0.5893	0.281713
5	-0.041325	-0.1704	0.433359
6	-0.264998	-1.0926	0.144903
7	-0.087792	-0.362	0.360915
8	-0.205987	-0.8493	0.203756
9	-0.173304	-0.7146	0.242292
10	0.08416	0.347	0.366425
11	-0.002398	-0.0099	0.496113
12	0.106544	0.4393	0.332991

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.759513 & 3.1316 & 0.00304 \tabularnewline
2 & -0.10699 & -0.4411 & 0.332338 \tabularnewline
3 & -0.00899 & -0.0371 & 0.485433 \tabularnewline
4 & 0.142921 & 0.5893 & 0.281713 \tabularnewline
5 & -0.041325 & -0.1704 & 0.433359 \tabularnewline
6 & -0.264998 & -1.0926 & 0.144903 \tabularnewline
7 & -0.087792 & -0.362 & 0.360915 \tabularnewline
8 & -0.205987 & -0.8493 & 0.203756 \tabularnewline
9 & -0.173304 & -0.7146 & 0.242292 \tabularnewline
10 & 0.08416 & 0.347 & 0.366425 \tabularnewline
11 & -0.002398 & -0.0099 & 0.496113 \tabularnewline
12 & 0.106544 & 0.4393 & 0.332991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299921&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]0.759513[/C][C]3.1316[/C][C]0.00304[/C][/ROW]
[ROW][C]2[/C][C]-0.10699[/C][C]-0.4411[/C][C]0.332338[/C][/ROW]
[ROW][C]3[/C][C]-0.00899[/C][C]-0.0371[/C][C]0.485433[/C][/ROW]
[ROW][C]4[/C][C]0.142921[/C][C]0.5893[/C][C]0.281713[/C][/ROW]
[ROW][C]5[/C][C]-0.041325[/C][C]-0.1704[/C][C]0.433359[/C][/ROW]
[ROW][C]6[/C][C]-0.264998[/C][C]-1.0926[/C][C]0.144903[/C][/ROW]
[ROW][C]7[/C][C]-0.087792[/C][C]-0.362[/C][C]0.360915[/C][/ROW]
[ROW][C]8[/C][C]-0.205987[/C][C]-0.8493[/C][C]0.203756[/C][/ROW]
[ROW][C]9[/C][C]-0.173304[/C][C]-0.7146[/C][C]0.242292[/C][/ROW]
[ROW][C]10[/C][C]0.08416[/C][C]0.347[/C][C]0.366425[/C][/ROW]
[ROW][C]11[/C][C]-0.002398[/C][C]-0.0099[/C][C]0.496113[/C][/ROW]
[ROW][C]12[/C][C]0.106544[/C][C]0.4393[/C][C]0.332991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299921&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299921&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	0.759513	3.1316	0.00304
2	-0.10699	-0.4411	0.332338
3	-0.00899	-0.0371	0.485433
4	0.142921	0.5893	0.281713
5	-0.041325	-0.1704	0.433359
6	-0.264998	-1.0926	0.144903
7	-0.087792	-0.362	0.360915
8	-0.205987	-0.8493	0.203756
9	-0.173304	-0.7146	0.242292
10	0.08416	0.347	0.366425
11	-0.002398	-0.0099	0.496113
12	0.106544	0.4393	0.332991

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 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; 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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Input Parameters & R Code