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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Dec 2016 16:54:19 +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/t148207648454yd9klawrcydoq.htm/, Retrieved Wed, 08 May 2024 22:50:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301153, Retrieved Wed, 08 May 2024 22:50:48 +0000

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-       [(Partial) Autocorrelation Function] [autocorrelation f...] [2016-12-18 15:54:19] [84a79156fb687334cf7dc390d7b82d5a] [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=301153&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=301153&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301153&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	-0.325191	-2.1324	0.019362
2	0.007389	0.0485	0.48079
3	-0.355473	-2.331	0.012256
4	0.558722	3.6638	0.000339
5	-0.20665	-1.3551	0.091231
6	-0.007518	-0.0493	0.480456
7	-0.167903	-1.101	0.138508
8	0.301334	1.976	0.027298
9	-0.164303	-1.0774	0.143653
10	-0.088003	-0.5771	0.283449
11	-0.122009	-0.8001	0.214034
12	0.247357	1.622	0.056054
13	-0.093746	-0.6147	0.270985
14	-0.047521	-0.3116	0.378418
15	-0.072433	-0.475	0.318603
16	0.096742	0.6344	0.264597

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.325191 & -2.1324 & 0.019362 \tabularnewline
2 & 0.007389 & 0.0485 & 0.48079 \tabularnewline
3 & -0.355473 & -2.331 & 0.012256 \tabularnewline
4 & 0.558722 & 3.6638 & 0.000339 \tabularnewline
5 & -0.20665 & -1.3551 & 0.091231 \tabularnewline
6 & -0.007518 & -0.0493 & 0.480456 \tabularnewline
7 & -0.167903 & -1.101 & 0.138508 \tabularnewline
8 & 0.301334 & 1.976 & 0.027298 \tabularnewline
9 & -0.164303 & -1.0774 & 0.143653 \tabularnewline
10 & -0.088003 & -0.5771 & 0.283449 \tabularnewline
11 & -0.122009 & -0.8001 & 0.214034 \tabularnewline
12 & 0.247357 & 1.622 & 0.056054 \tabularnewline
13 & -0.093746 & -0.6147 & 0.270985 \tabularnewline
14 & -0.047521 & -0.3116 & 0.378418 \tabularnewline
15 & -0.072433 & -0.475 & 0.318603 \tabularnewline
16 & 0.096742 & 0.6344 & 0.264597 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301153&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]-0.325191[/C][C]-2.1324[/C][C]0.019362[/C][/ROW]
[ROW][C]2[/C][C]0.007389[/C][C]0.0485[/C][C]0.48079[/C][/ROW]
[ROW][C]3[/C][C]-0.355473[/C][C]-2.331[/C][C]0.012256[/C][/ROW]
[ROW][C]4[/C][C]0.558722[/C][C]3.6638[/C][C]0.000339[/C][/ROW]
[ROW][C]5[/C][C]-0.20665[/C][C]-1.3551[/C][C]0.091231[/C][/ROW]
[ROW][C]6[/C][C]-0.007518[/C][C]-0.0493[/C][C]0.480456[/C][/ROW]
[ROW][C]7[/C][C]-0.167903[/C][C]-1.101[/C][C]0.138508[/C][/ROW]
[ROW][C]8[/C][C]0.301334[/C][C]1.976[/C][C]0.027298[/C][/ROW]
[ROW][C]9[/C][C]-0.164303[/C][C]-1.0774[/C][C]0.143653[/C][/ROW]
[ROW][C]10[/C][C]-0.088003[/C][C]-0.5771[/C][C]0.283449[/C][/ROW]
[ROW][C]11[/C][C]-0.122009[/C][C]-0.8001[/C][C]0.214034[/C][/ROW]
[ROW][C]12[/C][C]0.247357[/C][C]1.622[/C][C]0.056054[/C][/ROW]
[ROW][C]13[/C][C]-0.093746[/C][C]-0.6147[/C][C]0.270985[/C][/ROW]
[ROW][C]14[/C][C]-0.047521[/C][C]-0.3116[/C][C]0.378418[/C][/ROW]
[ROW][C]15[/C][C]-0.072433[/C][C]-0.475[/C][C]0.318603[/C][/ROW]
[ROW][C]16[/C][C]0.096742[/C][C]0.6344[/C][C]0.264597[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301153&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301153&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	-0.325191	-2.1324	0.019362
2	0.007389	0.0485	0.48079
3	-0.355473	-2.331	0.012256
4	0.558722	3.6638	0.000339
5	-0.20665	-1.3551	0.091231
6	-0.007518	-0.0493	0.480456
7	-0.167903	-1.101	0.138508
8	0.301334	1.976	0.027298
9	-0.164303	-1.0774	0.143653
10	-0.088003	-0.5771	0.283449
11	-0.122009	-0.8001	0.214034
12	0.247357	1.622	0.056054
13	-0.093746	-0.6147	0.270985
14	-0.047521	-0.3116	0.378418
15	-0.072433	-0.475	0.318603
16	0.096742	0.6344	0.264597

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.325191	-2.1324	0.019362
2	-0.109992	-0.7213	0.237325
3	-0.439846	-2.8843	0.003054
4	0.381976	2.5048	0.008061
5	-0.007475	-0.049	0.480566
6	-0.113824	-0.7464	0.229746
7	0.121948	0.7997	0.214151
8	-0.003363	-0.0221	0.491254
9	-0.096945	-0.6357	0.264167
10	-0.124052	-0.8135	0.210216
11	-0.160768	-1.0542	0.148834
12	0.008221	0.0539	0.47863
13	-0.038585	-0.253	0.400731
14	-0.013393	-0.0878	0.465212
15	0.052891	0.3468	0.365207
16	-0.135633	-0.8894	0.189367

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.325191 & -2.1324 & 0.019362 \tabularnewline
2 & -0.109992 & -0.7213 & 0.237325 \tabularnewline
3 & -0.439846 & -2.8843 & 0.003054 \tabularnewline
4 & 0.381976 & 2.5048 & 0.008061 \tabularnewline
5 & -0.007475 & -0.049 & 0.480566 \tabularnewline
6 & -0.113824 & -0.7464 & 0.229746 \tabularnewline
7 & 0.121948 & 0.7997 & 0.214151 \tabularnewline
8 & -0.003363 & -0.0221 & 0.491254 \tabularnewline
9 & -0.096945 & -0.6357 & 0.264167 \tabularnewline
10 & -0.124052 & -0.8135 & 0.210216 \tabularnewline
11 & -0.160768 & -1.0542 & 0.148834 \tabularnewline
12 & 0.008221 & 0.0539 & 0.47863 \tabularnewline
13 & -0.038585 & -0.253 & 0.400731 \tabularnewline
14 & -0.013393 & -0.0878 & 0.465212 \tabularnewline
15 & 0.052891 & 0.3468 & 0.365207 \tabularnewline
16 & -0.135633 & -0.8894 & 0.189367 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301153&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]-0.325191[/C][C]-2.1324[/C][C]0.019362[/C][/ROW]
[ROW][C]2[/C][C]-0.109992[/C][C]-0.7213[/C][C]0.237325[/C][/ROW]
[ROW][C]3[/C][C]-0.439846[/C][C]-2.8843[/C][C]0.003054[/C][/ROW]
[ROW][C]4[/C][C]0.381976[/C][C]2.5048[/C][C]0.008061[/C][/ROW]
[ROW][C]5[/C][C]-0.007475[/C][C]-0.049[/C][C]0.480566[/C][/ROW]
[ROW][C]6[/C][C]-0.113824[/C][C]-0.7464[/C][C]0.229746[/C][/ROW]
[ROW][C]7[/C][C]0.121948[/C][C]0.7997[/C][C]0.214151[/C][/ROW]
[ROW][C]8[/C][C]-0.003363[/C][C]-0.0221[/C][C]0.491254[/C][/ROW]
[ROW][C]9[/C][C]-0.096945[/C][C]-0.6357[/C][C]0.264167[/C][/ROW]
[ROW][C]10[/C][C]-0.124052[/C][C]-0.8135[/C][C]0.210216[/C][/ROW]
[ROW][C]11[/C][C]-0.160768[/C][C]-1.0542[/C][C]0.148834[/C][/ROW]
[ROW][C]12[/C][C]0.008221[/C][C]0.0539[/C][C]0.47863[/C][/ROW]
[ROW][C]13[/C][C]-0.038585[/C][C]-0.253[/C][C]0.400731[/C][/ROW]
[ROW][C]14[/C][C]-0.013393[/C][C]-0.0878[/C][C]0.465212[/C][/ROW]
[ROW][C]15[/C][C]0.052891[/C][C]0.3468[/C][C]0.365207[/C][/ROW]
[ROW][C]16[/C][C]-0.135633[/C][C]-0.8894[/C][C]0.189367[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301153&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301153&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	-0.325191	-2.1324	0.019362
2	-0.109992	-0.7213	0.237325
3	-0.439846	-2.8843	0.003054
4	0.381976	2.5048	0.008061
5	-0.007475	-0.049	0.480566
6	-0.113824	-0.7464	0.229746
7	0.121948	0.7997	0.214151
8	-0.003363	-0.0221	0.491254
9	-0.096945	-0.6357	0.264167
10	-0.124052	-0.8135	0.210216
11	-0.160768	-1.0542	0.148834
12	0.008221	0.0539	0.47863
13	-0.038585	-0.253	0.400731
14	-0.013393	-0.0878	0.465212
15	0.052891	0.3468	0.365207
16	-0.135633	-0.8894	0.189367

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 = 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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '1'
par4 <- '0'
par3 <- '2'
par2 <- '1'
par1 <- 'Default'
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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