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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Dec 2016 20:42:28 +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/22/t1482436458d2dg8b2i55n30x5.htm/, Retrieved Sun, 28 Apr 2024 20:12:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302660, Retrieved Sun, 28 Apr 2024 20:12:33 +0000

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-     [(Partial) Autocorrelation Function] [ACF1] [2016-12-22 17:08:50] [267314984f6394bb93cd815224aa34ba]
- R  D    [(Partial) Autocorrelation Function] [ACF3] [2016-12-22 19:42:28] [636d0f72197ac5e1dae4a755427db02a] [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
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302660&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] [ROW]

R Framework error message[/C][C]

Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302660&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302660&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
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.170199	-1.2155	0.114893
2	0.131915	0.9421	0.175301
3	-0.048957	-0.3496	0.364031
4	-0.074218	-0.53	0.299199
5	-0.145204	-1.037	0.152322
6	0.015293	0.1092	0.45673
7	0.124948	0.8923	0.188209
8	-0.141372	-1.0096	0.158727
9	0.057157	0.4082	0.342423
10	0.102886	0.7348	0.232928
11	-0.019759	-0.1411	0.44417
12	-0.03579	-0.2556	0.399648
13	0.007802	0.0557	0.477892
14	-0.083952	-0.5995	0.275735
15	-0.071606	-0.5114	0.305649
16	0.107619	0.7686	0.222851
17	0.098584	0.704	0.242308

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.170199 & -1.2155 & 0.114893 \tabularnewline
2 & 0.131915 & 0.9421 & 0.175301 \tabularnewline
3 & -0.048957 & -0.3496 & 0.364031 \tabularnewline
4 & -0.074218 & -0.53 & 0.299199 \tabularnewline
5 & -0.145204 & -1.037 & 0.152322 \tabularnewline
6 & 0.015293 & 0.1092 & 0.45673 \tabularnewline
7 & 0.124948 & 0.8923 & 0.188209 \tabularnewline
8 & -0.141372 & -1.0096 & 0.158727 \tabularnewline
9 & 0.057157 & 0.4082 & 0.342423 \tabularnewline
10 & 0.102886 & 0.7348 & 0.232928 \tabularnewline
11 & -0.019759 & -0.1411 & 0.44417 \tabularnewline
12 & -0.03579 & -0.2556 & 0.399648 \tabularnewline
13 & 0.007802 & 0.0557 & 0.477892 \tabularnewline
14 & -0.083952 & -0.5995 & 0.275735 \tabularnewline
15 & -0.071606 & -0.5114 & 0.305649 \tabularnewline
16 & 0.107619 & 0.7686 & 0.222851 \tabularnewline
17 & 0.098584 & 0.704 & 0.242308 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302660&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]-0.170199[/C][C]-1.2155[/C][C]0.114893[/C][/ROW]
[ROW][C]2[/C][C]0.131915[/C][C]0.9421[/C][C]0.175301[/C][/ROW]
[ROW][C]3[/C][C]-0.048957[/C][C]-0.3496[/C][C]0.364031[/C][/ROW]
[ROW][C]4[/C][C]-0.074218[/C][C]-0.53[/C][C]0.299199[/C][/ROW]
[ROW][C]5[/C][C]-0.145204[/C][C]-1.037[/C][C]0.152322[/C][/ROW]
[ROW][C]6[/C][C]0.015293[/C][C]0.1092[/C][C]0.45673[/C][/ROW]
[ROW][C]7[/C][C]0.124948[/C][C]0.8923[/C][C]0.188209[/C][/ROW]
[ROW][C]8[/C][C]-0.141372[/C][C]-1.0096[/C][C]0.158727[/C][/ROW]
[ROW][C]9[/C][C]0.057157[/C][C]0.4082[/C][C]0.342423[/C][/ROW]
[ROW][C]10[/C][C]0.102886[/C][C]0.7348[/C][C]0.232928[/C][/ROW]
[ROW][C]11[/C][C]-0.019759[/C][C]-0.1411[/C][C]0.44417[/C][/ROW]
[ROW][C]12[/C][C]-0.03579[/C][C]-0.2556[/C][C]0.399648[/C][/ROW]
[ROW][C]13[/C][C]0.007802[/C][C]0.0557[/C][C]0.477892[/C][/ROW]
[ROW][C]14[/C][C]-0.083952[/C][C]-0.5995[/C][C]0.275735[/C][/ROW]
[ROW][C]15[/C][C]-0.071606[/C][C]-0.5114[/C][C]0.305649[/C][/ROW]
[ROW][C]16[/C][C]0.107619[/C][C]0.7686[/C][C]0.222851[/C][/ROW]
[ROW][C]17[/C][C]0.098584[/C][C]0.704[/C][C]0.242308[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302660&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302660&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	-0.170199	-1.2155	0.114893
2	0.131915	0.9421	0.175301
3	-0.048957	-0.3496	0.364031
4	-0.074218	-0.53	0.299199
5	-0.145204	-1.037	0.152322
6	0.015293	0.1092	0.45673
7	0.124948	0.8923	0.188209
8	-0.141372	-1.0096	0.158727
9	0.057157	0.4082	0.342423
10	0.102886	0.7348	0.232928
11	-0.019759	-0.1411	0.44417
12	-0.03579	-0.2556	0.399648
13	0.007802	0.0557	0.477892
14	-0.083952	-0.5995	0.275735
15	-0.071606	-0.5114	0.305649
16	0.107619	0.7686	0.222851
17	0.098584	0.704	0.242308

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.170199	-1.2155	0.114893
2	0.106019	0.7571	0.22623
3	-0.011291	-0.0806	0.468023
4	-0.101343	-0.7237	0.236268
5	-0.173249	-1.2372	0.110831
6	-0.01533	-0.1095	0.456627
7	0.170637	1.2186	0.114302
8	-0.12491	-0.892	0.188281
9	-0.062789	-0.4484	0.327882
10	0.141417	1.0099	0.15865
11	0.052388	0.3741	0.354932
12	-0.067397	-0.4813	0.316177
13	-0.061034	-0.4359	0.332386
14	-0.058397	-0.417	0.339201
15	-0.009067	-0.0647	0.474314
16	0.087043	0.6216	0.268483
17	0.097737	0.698	0.244179

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.170199 & -1.2155 & 0.114893 \tabularnewline
2 & 0.106019 & 0.7571 & 0.22623 \tabularnewline
3 & -0.011291 & -0.0806 & 0.468023 \tabularnewline
4 & -0.101343 & -0.7237 & 0.236268 \tabularnewline
5 & -0.173249 & -1.2372 & 0.110831 \tabularnewline
6 & -0.01533 & -0.1095 & 0.456627 \tabularnewline
7 & 0.170637 & 1.2186 & 0.114302 \tabularnewline
8 & -0.12491 & -0.892 & 0.188281 \tabularnewline
9 & -0.062789 & -0.4484 & 0.327882 \tabularnewline
10 & 0.141417 & 1.0099 & 0.15865 \tabularnewline
11 & 0.052388 & 0.3741 & 0.354932 \tabularnewline
12 & -0.067397 & -0.4813 & 0.316177 \tabularnewline
13 & -0.061034 & -0.4359 & 0.332386 \tabularnewline
14 & -0.058397 & -0.417 & 0.339201 \tabularnewline
15 & -0.009067 & -0.0647 & 0.474314 \tabularnewline
16 & 0.087043 & 0.6216 & 0.268483 \tabularnewline
17 & 0.097737 & 0.698 & 0.244179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302660&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]-0.170199[/C][C]-1.2155[/C][C]0.114893[/C][/ROW]
[ROW][C]2[/C][C]0.106019[/C][C]0.7571[/C][C]0.22623[/C][/ROW]
[ROW][C]3[/C][C]-0.011291[/C][C]-0.0806[/C][C]0.468023[/C][/ROW]
[ROW][C]4[/C][C]-0.101343[/C][C]-0.7237[/C][C]0.236268[/C][/ROW]
[ROW][C]5[/C][C]-0.173249[/C][C]-1.2372[/C][C]0.110831[/C][/ROW]
[ROW][C]6[/C][C]-0.01533[/C][C]-0.1095[/C][C]0.456627[/C][/ROW]
[ROW][C]7[/C][C]0.170637[/C][C]1.2186[/C][C]0.114302[/C][/ROW]
[ROW][C]8[/C][C]-0.12491[/C][C]-0.892[/C][C]0.188281[/C][/ROW]
[ROW][C]9[/C][C]-0.062789[/C][C]-0.4484[/C][C]0.327882[/C][/ROW]
[ROW][C]10[/C][C]0.141417[/C][C]1.0099[/C][C]0.15865[/C][/ROW]
[ROW][C]11[/C][C]0.052388[/C][C]0.3741[/C][C]0.354932[/C][/ROW]
[ROW][C]12[/C][C]-0.067397[/C][C]-0.4813[/C][C]0.316177[/C][/ROW]
[ROW][C]13[/C][C]-0.061034[/C][C]-0.4359[/C][C]0.332386[/C][/ROW]
[ROW][C]14[/C][C]-0.058397[/C][C]-0.417[/C][C]0.339201[/C][/ROW]
[ROW][C]15[/C][C]-0.009067[/C][C]-0.0647[/C][C]0.474314[/C][/ROW]
[ROW][C]16[/C][C]0.087043[/C][C]0.6216[/C][C]0.268483[/C][/ROW]
[ROW][C]17[/C][C]0.097737[/C][C]0.698[/C][C]0.244179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302660&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302660&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	-0.170199	-1.2155	0.114893
2	0.106019	0.7571	0.22623
3	-0.011291	-0.0806	0.468023
4	-0.101343	-0.7237	0.236268
5	-0.173249	-1.2372	0.110831
6	-0.01533	-0.1095	0.456627
7	0.170637	1.2186	0.114302
8	-0.12491	-0.892	0.188281
9	-0.062789	-0.4484	0.327882
10	0.141417	1.0099	0.15865
11	0.052388	0.3741	0.354932
12	-0.067397	-0.4813	0.316177
13	-0.061034	-0.4359	0.332386
14	-0.058397	-0.417	0.339201
15	-0.009067	-0.0647	0.474314
16	0.087043	0.6216	0.268483
17	0.097737	0.698	0.244179

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 = 12 ; par2 = -0.3 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ; par10 = FALSE ;

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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Dataset

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Figures (Output of Computation)

Input Parameters & R Code