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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Dec 2016 17:34:04 +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/t14820789509xwkjmwz1qc8n0r.htm/, Retrieved Thu, 09 May 2024 01:46:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301171, Retrieved Thu, 09 May 2024 01:46:57 +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] [N1030 ACF] [2016-12-18 16:34:04] [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=301171&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=301171&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301171&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	0.236614	1.5516	0.064046
2	0.348661	2.2863	0.013611
3	-0.079287	-0.5199	0.302892
4	-0.087765	-0.5755	0.283971
5	-0.058358	-0.3827	0.351922
6	-0.31202	-2.0461	0.023449
7	-0.232719	-1.526	0.067162
8	-0.344635	-2.2599	0.014474
9	-0.075767	-0.4968	0.310916
10	-0.271214	-1.7785	0.041199
11	-0.021867	-0.1434	0.443326
12	-0.158825	-1.0415	0.151736
13	0.201709	1.3227	0.096465
14	0.223807	1.4676	0.074745
15	0.24154	1.5839	0.060274
16	0.258012	1.6919	0.04895

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.236614 & 1.5516 & 0.064046 \tabularnewline
2 & 0.348661 & 2.2863 & 0.013611 \tabularnewline
3 & -0.079287 & -0.5199 & 0.302892 \tabularnewline
4 & -0.087765 & -0.5755 & 0.283971 \tabularnewline
5 & -0.058358 & -0.3827 & 0.351922 \tabularnewline
6 & -0.31202 & -2.0461 & 0.023449 \tabularnewline
7 & -0.232719 & -1.526 & 0.067162 \tabularnewline
8 & -0.344635 & -2.2599 & 0.014474 \tabularnewline
9 & -0.075767 & -0.4968 & 0.310916 \tabularnewline
10 & -0.271214 & -1.7785 & 0.041199 \tabularnewline
11 & -0.021867 & -0.1434 & 0.443326 \tabularnewline
12 & -0.158825 & -1.0415 & 0.151736 \tabularnewline
13 & 0.201709 & 1.3227 & 0.096465 \tabularnewline
14 & 0.223807 & 1.4676 & 0.074745 \tabularnewline
15 & 0.24154 & 1.5839 & 0.060274 \tabularnewline
16 & 0.258012 & 1.6919 & 0.04895 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301171&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]0.236614[/C][C]1.5516[/C][C]0.064046[/C][/ROW]
[ROW][C]2[/C][C]0.348661[/C][C]2.2863[/C][C]0.013611[/C][/ROW]
[ROW][C]3[/C][C]-0.079287[/C][C]-0.5199[/C][C]0.302892[/C][/ROW]
[ROW][C]4[/C][C]-0.087765[/C][C]-0.5755[/C][C]0.283971[/C][/ROW]
[ROW][C]5[/C][C]-0.058358[/C][C]-0.3827[/C][C]0.351922[/C][/ROW]
[ROW][C]6[/C][C]-0.31202[/C][C]-2.0461[/C][C]0.023449[/C][/ROW]
[ROW][C]7[/C][C]-0.232719[/C][C]-1.526[/C][C]0.067162[/C][/ROW]
[ROW][C]8[/C][C]-0.344635[/C][C]-2.2599[/C][C]0.014474[/C][/ROW]
[ROW][C]9[/C][C]-0.075767[/C][C]-0.4968[/C][C]0.310916[/C][/ROW]
[ROW][C]10[/C][C]-0.271214[/C][C]-1.7785[/C][C]0.041199[/C][/ROW]
[ROW][C]11[/C][C]-0.021867[/C][C]-0.1434[/C][C]0.443326[/C][/ROW]
[ROW][C]12[/C][C]-0.158825[/C][C]-1.0415[/C][C]0.151736[/C][/ROW]
[ROW][C]13[/C][C]0.201709[/C][C]1.3227[/C][C]0.096465[/C][/ROW]
[ROW][C]14[/C][C]0.223807[/C][C]1.4676[/C][C]0.074745[/C][/ROW]
[ROW][C]15[/C][C]0.24154[/C][C]1.5839[/C][C]0.060274[/C][/ROW]
[ROW][C]16[/C][C]0.258012[/C][C]1.6919[/C][C]0.04895[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301171&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301171&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	0.236614	1.5516	0.064046
2	0.348661	2.2863	0.013611
3	-0.079287	-0.5199	0.302892
4	-0.087765	-0.5755	0.283971
5	-0.058358	-0.3827	0.351922
6	-0.31202	-2.0461	0.023449
7	-0.232719	-1.526	0.067162
8	-0.344635	-2.2599	0.014474
9	-0.075767	-0.4968	0.310916
10	-0.271214	-1.7785	0.041199
11	-0.021867	-0.1434	0.443326
12	-0.158825	-1.0415	0.151736
13	0.201709	1.3227	0.096465
14	0.223807	1.4676	0.074745
15	0.24154	1.5839	0.060274
16	0.258012	1.6919	0.04895

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.236614	1.5516	0.064046
2	0.310033	2.033	0.024127
3	-0.245602	-1.6105	0.057301
4	-0.165561	-1.0857	0.141841
5	0.131347	0.8613	0.196925
6	-0.320725	-2.1031	0.020672
7	-0.229446	-1.5046	0.069871
8	-0.051954	-0.3407	0.367499
9	0.091441	0.5996	0.275953
10	-0.395909	-2.5961	0.006425
11	-0.0293	-0.1921	0.424272
12	-0.025999	-0.1705	0.432715
13	0.118762	0.7788	0.220188
14	0.020257	0.1328	0.447473
15	0.016926	0.111	0.456069
16	0.037803	0.2479	0.4027

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.236614 & 1.5516 & 0.064046 \tabularnewline
2 & 0.310033 & 2.033 & 0.024127 \tabularnewline
3 & -0.245602 & -1.6105 & 0.057301 \tabularnewline
4 & -0.165561 & -1.0857 & 0.141841 \tabularnewline
5 & 0.131347 & 0.8613 & 0.196925 \tabularnewline
6 & -0.320725 & -2.1031 & 0.020672 \tabularnewline
7 & -0.229446 & -1.5046 & 0.069871 \tabularnewline
8 & -0.051954 & -0.3407 & 0.367499 \tabularnewline
9 & 0.091441 & 0.5996 & 0.275953 \tabularnewline
10 & -0.395909 & -2.5961 & 0.006425 \tabularnewline
11 & -0.0293 & -0.1921 & 0.424272 \tabularnewline
12 & -0.025999 & -0.1705 & 0.432715 \tabularnewline
13 & 0.118762 & 0.7788 & 0.220188 \tabularnewline
14 & 0.020257 & 0.1328 & 0.447473 \tabularnewline
15 & 0.016926 & 0.111 & 0.456069 \tabularnewline
16 & 0.037803 & 0.2479 & 0.4027 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301171&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]0.236614[/C][C]1.5516[/C][C]0.064046[/C][/ROW]
[ROW][C]2[/C][C]0.310033[/C][C]2.033[/C][C]0.024127[/C][/ROW]
[ROW][C]3[/C][C]-0.245602[/C][C]-1.6105[/C][C]0.057301[/C][/ROW]
[ROW][C]4[/C][C]-0.165561[/C][C]-1.0857[/C][C]0.141841[/C][/ROW]
[ROW][C]5[/C][C]0.131347[/C][C]0.8613[/C][C]0.196925[/C][/ROW]
[ROW][C]6[/C][C]-0.320725[/C][C]-2.1031[/C][C]0.020672[/C][/ROW]
[ROW][C]7[/C][C]-0.229446[/C][C]-1.5046[/C][C]0.069871[/C][/ROW]
[ROW][C]8[/C][C]-0.051954[/C][C]-0.3407[/C][C]0.367499[/C][/ROW]
[ROW][C]9[/C][C]0.091441[/C][C]0.5996[/C][C]0.275953[/C][/ROW]
[ROW][C]10[/C][C]-0.395909[/C][C]-2.5961[/C][C]0.006425[/C][/ROW]
[ROW][C]11[/C][C]-0.0293[/C][C]-0.1921[/C][C]0.424272[/C][/ROW]
[ROW][C]12[/C][C]-0.025999[/C][C]-0.1705[/C][C]0.432715[/C][/ROW]
[ROW][C]13[/C][C]0.118762[/C][C]0.7788[/C][C]0.220188[/C][/ROW]
[ROW][C]14[/C][C]0.020257[/C][C]0.1328[/C][C]0.447473[/C][/ROW]
[ROW][C]15[/C][C]0.016926[/C][C]0.111[/C][C]0.456069[/C][/ROW]
[ROW][C]16[/C][C]0.037803[/C][C]0.2479[/C][C]0.4027[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301171&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301171&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	0.236614	1.5516	0.064046
2	0.310033	2.033	0.024127
3	-0.245602	-1.6105	0.057301
4	-0.165561	-1.0857	0.141841
5	0.131347	0.8613	0.196925
6	-0.320725	-2.1031	0.020672
7	-0.229446	-1.5046	0.069871
8	-0.051954	-0.3407	0.367499
9	0.091441	0.5996	0.275953
10	-0.395909	-2.5961	0.006425
11	-0.0293	-0.1921	0.424272
12	-0.025999	-0.1705	0.432715
13	0.118762	0.7788	0.220188
14	0.020257	0.1328	0.447473
15	0.016926	0.111	0.456069
16	0.037803	0.2479	0.4027

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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