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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 25 Jan 2017 10:48:34 +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/2017/Jan/25/t1485337769rk1bwsmd0fx9l9y.htm/, Retrieved Tue, 14 May 2024 23:34:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=306387, Retrieved Tue, 14 May 2024 23:34:58 +0000

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-       [(Partial) Autocorrelation Function] [Vraag6] [2017-01-25 09:48:34] [b4126e05c087c2e17325bcff741d4cf7] [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=306387&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=306387&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306387&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	0.340974	2.8731	0.002679
2	0.074645	0.629	0.265695
3	0.02613	0.2202	0.413183
4	-0.247708	-2.0872	0.020229
5	-0.434435	-3.6606	0.00024
6	-0.406575	-3.4259	0.000511
7	-0.382653	-3.2243	0.000955
8	-0.321345	-2.7077	0.004241
9	-0.064734	-0.5455	0.293573
10	0.290281	2.446	0.008464
11	0.417349	3.5166	0.000383
12	0.39356	3.3162	0.00072
13	0.415377	3.5	0.000404
14	0.233065	1.9638	0.026733
15	-0.064493	-0.5434	0.294269
16	-0.19988	-1.6842	0.048266
17	-0.285758	-2.4078	0.009324
18	-0.372595	-3.1395	0.001233

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.340974 & 2.8731 & 0.002679 \tabularnewline
2 & 0.074645 & 0.629 & 0.265695 \tabularnewline
3 & 0.02613 & 0.2202 & 0.413183 \tabularnewline
4 & -0.247708 & -2.0872 & 0.020229 \tabularnewline
5 & -0.434435 & -3.6606 & 0.00024 \tabularnewline
6 & -0.406575 & -3.4259 & 0.000511 \tabularnewline
7 & -0.382653 & -3.2243 & 0.000955 \tabularnewline
8 & -0.321345 & -2.7077 & 0.004241 \tabularnewline
9 & -0.064734 & -0.5455 & 0.293573 \tabularnewline
10 & 0.290281 & 2.446 & 0.008464 \tabularnewline
11 & 0.417349 & 3.5166 & 0.000383 \tabularnewline
12 & 0.39356 & 3.3162 & 0.00072 \tabularnewline
13 & 0.415377 & 3.5 & 0.000404 \tabularnewline
14 & 0.233065 & 1.9638 & 0.026733 \tabularnewline
15 & -0.064493 & -0.5434 & 0.294269 \tabularnewline
16 & -0.19988 & -1.6842 & 0.048266 \tabularnewline
17 & -0.285758 & -2.4078 & 0.009324 \tabularnewline
18 & -0.372595 & -3.1395 & 0.001233 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306387&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]0.340974[/C][C]2.8731[/C][C]0.002679[/C][/ROW]
[ROW][C]2[/C][C]0.074645[/C][C]0.629[/C][C]0.265695[/C][/ROW]
[ROW][C]3[/C][C]0.02613[/C][C]0.2202[/C][C]0.413183[/C][/ROW]
[ROW][C]4[/C][C]-0.247708[/C][C]-2.0872[/C][C]0.020229[/C][/ROW]
[ROW][C]5[/C][C]-0.434435[/C][C]-3.6606[/C][C]0.00024[/C][/ROW]
[ROW][C]6[/C][C]-0.406575[/C][C]-3.4259[/C][C]0.000511[/C][/ROW]
[ROW][C]7[/C][C]-0.382653[/C][C]-3.2243[/C][C]0.000955[/C][/ROW]
[ROW][C]8[/C][C]-0.321345[/C][C]-2.7077[/C][C]0.004241[/C][/ROW]
[ROW][C]9[/C][C]-0.064734[/C][C]-0.5455[/C][C]0.293573[/C][/ROW]
[ROW][C]10[/C][C]0.290281[/C][C]2.446[/C][C]0.008464[/C][/ROW]
[ROW][C]11[/C][C]0.417349[/C][C]3.5166[/C][C]0.000383[/C][/ROW]
[ROW][C]12[/C][C]0.39356[/C][C]3.3162[/C][C]0.00072[/C][/ROW]
[ROW][C]13[/C][C]0.415377[/C][C]3.5[/C][C]0.000404[/C][/ROW]
[ROW][C]14[/C][C]0.233065[/C][C]1.9638[/C][C]0.026733[/C][/ROW]
[ROW][C]15[/C][C]-0.064493[/C][C]-0.5434[/C][C]0.294269[/C][/ROW]
[ROW][C]16[/C][C]-0.19988[/C][C]-1.6842[/C][C]0.048266[/C][/ROW]
[ROW][C]17[/C][C]-0.285758[/C][C]-2.4078[/C][C]0.009324[/C][/ROW]
[ROW][C]18[/C][C]-0.372595[/C][C]-3.1395[/C][C]0.001233[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306387&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306387&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	0.340974	2.8731	0.002679
2	0.074645	0.629	0.265695
3	0.02613	0.2202	0.413183
4	-0.247708	-2.0872	0.020229
5	-0.434435	-3.6606	0.00024
6	-0.406575	-3.4259	0.000511
7	-0.382653	-3.2243	0.000955
8	-0.321345	-2.7077	0.004241
9	-0.064734	-0.5455	0.293573
10	0.290281	2.446	0.008464
11	0.417349	3.5166	0.000383
12	0.39356	3.3162	0.00072
13	0.415377	3.5	0.000404
14	0.233065	1.9638	0.026733
15	-0.064493	-0.5434	0.294269
16	-0.19988	-1.6842	0.048266
17	-0.285758	-2.4078	0.009324
18	-0.372595	-3.1395	0.001233

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.340974	2.8731	0.002679
2	-0.047094	-0.3968	0.346345
3	0.017621	0.1485	0.441195
4	-0.29391	-2.4765	0.007826
5	-0.312474	-2.633	0.00519
6	-0.246297	-2.0753	0.02079
7	-0.289831	-2.4422	0.008546
8	-0.352215	-2.9678	0.002043
9	-0.279361	-2.3539	0.010674
10	-0.025793	-0.2173	0.414287
11	0.023699	0.1997	0.421145
12	-0.029732	-0.2505	0.401452
13	0.076144	0.6416	0.2616
14	0.023835	0.2008	0.420699
15	-0.08644	-0.7284	0.234396
16	-0.070378	-0.593	0.277527
17	0.002076	0.0175	0.493048
18	0.071138	0.5994	0.2754

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.340974 & 2.8731 & 0.002679 \tabularnewline
2 & -0.047094 & -0.3968 & 0.346345 \tabularnewline
3 & 0.017621 & 0.1485 & 0.441195 \tabularnewline
4 & -0.29391 & -2.4765 & 0.007826 \tabularnewline
5 & -0.312474 & -2.633 & 0.00519 \tabularnewline
6 & -0.246297 & -2.0753 & 0.02079 \tabularnewline
7 & -0.289831 & -2.4422 & 0.008546 \tabularnewline
8 & -0.352215 & -2.9678 & 0.002043 \tabularnewline
9 & -0.279361 & -2.3539 & 0.010674 \tabularnewline
10 & -0.025793 & -0.2173 & 0.414287 \tabularnewline
11 & 0.023699 & 0.1997 & 0.421145 \tabularnewline
12 & -0.029732 & -0.2505 & 0.401452 \tabularnewline
13 & 0.076144 & 0.6416 & 0.2616 \tabularnewline
14 & 0.023835 & 0.2008 & 0.420699 \tabularnewline
15 & -0.08644 & -0.7284 & 0.234396 \tabularnewline
16 & -0.070378 & -0.593 & 0.277527 \tabularnewline
17 & 0.002076 & 0.0175 & 0.493048 \tabularnewline
18 & 0.071138 & 0.5994 & 0.2754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306387&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]0.340974[/C][C]2.8731[/C][C]0.002679[/C][/ROW]
[ROW][C]2[/C][C]-0.047094[/C][C]-0.3968[/C][C]0.346345[/C][/ROW]
[ROW][C]3[/C][C]0.017621[/C][C]0.1485[/C][C]0.441195[/C][/ROW]
[ROW][C]4[/C][C]-0.29391[/C][C]-2.4765[/C][C]0.007826[/C][/ROW]
[ROW][C]5[/C][C]-0.312474[/C][C]-2.633[/C][C]0.00519[/C][/ROW]
[ROW][C]6[/C][C]-0.246297[/C][C]-2.0753[/C][C]0.02079[/C][/ROW]
[ROW][C]7[/C][C]-0.289831[/C][C]-2.4422[/C][C]0.008546[/C][/ROW]
[ROW][C]8[/C][C]-0.352215[/C][C]-2.9678[/C][C]0.002043[/C][/ROW]
[ROW][C]9[/C][C]-0.279361[/C][C]-2.3539[/C][C]0.010674[/C][/ROW]
[ROW][C]10[/C][C]-0.025793[/C][C]-0.2173[/C][C]0.414287[/C][/ROW]
[ROW][C]11[/C][C]0.023699[/C][C]0.1997[/C][C]0.421145[/C][/ROW]
[ROW][C]12[/C][C]-0.029732[/C][C]-0.2505[/C][C]0.401452[/C][/ROW]
[ROW][C]13[/C][C]0.076144[/C][C]0.6416[/C][C]0.2616[/C][/ROW]
[ROW][C]14[/C][C]0.023835[/C][C]0.2008[/C][C]0.420699[/C][/ROW]
[ROW][C]15[/C][C]-0.08644[/C][C]-0.7284[/C][C]0.234396[/C][/ROW]
[ROW][C]16[/C][C]-0.070378[/C][C]-0.593[/C][C]0.277527[/C][/ROW]
[ROW][C]17[/C][C]0.002076[/C][C]0.0175[/C][C]0.493048[/C][/ROW]
[ROW][C]18[/C][C]0.071138[/C][C]0.5994[/C][C]0.2754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306387&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306387&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	0.340974	2.8731	0.002679
2	-0.047094	-0.3968	0.346345
3	0.017621	0.1485	0.441195
4	-0.29391	-2.4765	0.007826
5	-0.312474	-2.633	0.00519
6	-0.246297	-2.0753	0.02079
7	-0.289831	-2.4422	0.008546
8	-0.352215	-2.9678	0.002043
9	-0.279361	-2.3539	0.010674
10	-0.025793	-0.2173	0.414287
11	0.023699	0.1997	0.421145
12	-0.029732	-0.2505	0.401452
13	0.076144	0.6416	0.2616
14	0.023835	0.2008	0.420699
15	-0.08644	-0.7284	0.234396
16	-0.070378	-0.593	0.277527
17	0.002076	0.0175	0.493048
18	0.071138	0.5994	0.2754

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

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Figure 3

PNG link

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Parameters (Session):

par1 = 0.85 ; par2 = 0 ;

Parameters (R input):

par1 = Default ; par2 = 0.4 ; 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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