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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 25 Jan 2017 10:51:27 +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/t1485337898gswof2i8cfjv5lk.htm/, Retrieved Tue, 14 May 2024 13:16:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=306406, Retrieved Tue, 14 May 2024 13:16:47 +0000

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-       [(Partial) Autocorrelation Function] [] [2017-01-25 09:51:27] [a7a7548920aea9a2d444ee0f03dc394a] [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=306406&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=306406&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306406&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	0.073021	0.5656	0.286881
2	-0.258163	-1.9997	0.025032
3	-0.018534	-0.1436	0.443164
4	-0.016363	-0.1267	0.449783
5	-0.045964	-0.356	0.361531
6	-7e-05	-5e-04	0.499786
7	0.000784	0.0061	0.497587
8	-0.023463	-0.1817	0.428198
9	0.073171	0.5668	0.286488
10	0.35062	2.7159	0.004311
11	0.023211	0.1798	0.42896
12	-0.591345	-4.5805	1.2e-05
13	-0.065005	-0.5035	0.308219
14	0.09447	0.7318	0.233582
15	-0.062522	-0.4843	0.31497
16	0.028668	0.2221	0.412509
17	0.037975	0.2942	0.384829
18	-0.008068	-0.0625	0.475188

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.073021 & 0.5656 & 0.286881 \tabularnewline
2 & -0.258163 & -1.9997 & 0.025032 \tabularnewline
3 & -0.018534 & -0.1436 & 0.443164 \tabularnewline
4 & -0.016363 & -0.1267 & 0.449783 \tabularnewline
5 & -0.045964 & -0.356 & 0.361531 \tabularnewline
6 & -7e-05 & -5e-04 & 0.499786 \tabularnewline
7 & 0.000784 & 0.0061 & 0.497587 \tabularnewline
8 & -0.023463 & -0.1817 & 0.428198 \tabularnewline
9 & 0.073171 & 0.5668 & 0.286488 \tabularnewline
10 & 0.35062 & 2.7159 & 0.004311 \tabularnewline
11 & 0.023211 & 0.1798 & 0.42896 \tabularnewline
12 & -0.591345 & -4.5805 & 1.2e-05 \tabularnewline
13 & -0.065005 & -0.5035 & 0.308219 \tabularnewline
14 & 0.09447 & 0.7318 & 0.233582 \tabularnewline
15 & -0.062522 & -0.4843 & 0.31497 \tabularnewline
16 & 0.028668 & 0.2221 & 0.412509 \tabularnewline
17 & 0.037975 & 0.2942 & 0.384829 \tabularnewline
18 & -0.008068 & -0.0625 & 0.475188 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306406&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]0.073021[/C][C]0.5656[/C][C]0.286881[/C][/ROW]
[ROW][C]2[/C][C]-0.258163[/C][C]-1.9997[/C][C]0.025032[/C][/ROW]
[ROW][C]3[/C][C]-0.018534[/C][C]-0.1436[/C][C]0.443164[/C][/ROW]
[ROW][C]4[/C][C]-0.016363[/C][C]-0.1267[/C][C]0.449783[/C][/ROW]
[ROW][C]5[/C][C]-0.045964[/C][C]-0.356[/C][C]0.361531[/C][/ROW]
[ROW][C]6[/C][C]-7e-05[/C][C]-5e-04[/C][C]0.499786[/C][/ROW]
[ROW][C]7[/C][C]0.000784[/C][C]0.0061[/C][C]0.497587[/C][/ROW]
[ROW][C]8[/C][C]-0.023463[/C][C]-0.1817[/C][C]0.428198[/C][/ROW]
[ROW][C]9[/C][C]0.073171[/C][C]0.5668[/C][C]0.286488[/C][/ROW]
[ROW][C]10[/C][C]0.35062[/C][C]2.7159[/C][C]0.004311[/C][/ROW]
[ROW][C]11[/C][C]0.023211[/C][C]0.1798[/C][C]0.42896[/C][/ROW]
[ROW][C]12[/C][C]-0.591345[/C][C]-4.5805[/C][C]1.2e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.065005[/C][C]-0.5035[/C][C]0.308219[/C][/ROW]
[ROW][C]14[/C][C]0.09447[/C][C]0.7318[/C][C]0.233582[/C][/ROW]
[ROW][C]15[/C][C]-0.062522[/C][C]-0.4843[/C][C]0.31497[/C][/ROW]
[ROW][C]16[/C][C]0.028668[/C][C]0.2221[/C][C]0.412509[/C][/ROW]
[ROW][C]17[/C][C]0.037975[/C][C]0.2942[/C][C]0.384829[/C][/ROW]
[ROW][C]18[/C][C]-0.008068[/C][C]-0.0625[/C][C]0.475188[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306406&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306406&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	0.073021	0.5656	0.286881
2	-0.258163	-1.9997	0.025032
3	-0.018534	-0.1436	0.443164
4	-0.016363	-0.1267	0.449783
5	-0.045964	-0.356	0.361531
6	-7e-05	-5e-04	0.499786
7	0.000784	0.0061	0.497587
8	-0.023463	-0.1817	0.428198
9	0.073171	0.5668	0.286488
10	0.35062	2.7159	0.004311
11	0.023211	0.1798	0.42896
12	-0.591345	-4.5805	1.2e-05
13	-0.065005	-0.5035	0.308219
14	0.09447	0.7318	0.233582
15	-0.062522	-0.4843	0.31497
16	0.028668	0.2221	0.412509
17	0.037975	0.2942	0.384829
18	-0.008068	-0.0625	0.475188

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.073021	0.5656	0.286881
2	-0.264907	-2.052	0.022272
3	0.026658	0.2065	0.418552
4	-0.092502	-0.7165	0.238225
5	-0.036778	-0.2849	0.388358
6	-0.021925	-0.1698	0.432857
7	-0.023336	-0.1808	0.428582
8	-0.030811	-0.2387	0.406092
9	0.073351	0.5682	0.28602
10	0.351576	2.7233	0.004226
11	0.00531	0.0411	0.483664
12	-0.511133	-3.9592	0.000101
13	0.038119	0.2953	0.384403
14	-0.116932	-0.9058	0.184344
15	-0.051427	-0.3984	0.345891
16	0.00478	0.037	0.485294
17	-0.028442	-0.2203	0.413188
18	-0.006314	-0.0489	0.480577

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.073021 & 0.5656 & 0.286881 \tabularnewline
2 & -0.264907 & -2.052 & 0.022272 \tabularnewline
3 & 0.026658 & 0.2065 & 0.418552 \tabularnewline
4 & -0.092502 & -0.7165 & 0.238225 \tabularnewline
5 & -0.036778 & -0.2849 & 0.388358 \tabularnewline
6 & -0.021925 & -0.1698 & 0.432857 \tabularnewline
7 & -0.023336 & -0.1808 & 0.428582 \tabularnewline
8 & -0.030811 & -0.2387 & 0.406092 \tabularnewline
9 & 0.073351 & 0.5682 & 0.28602 \tabularnewline
10 & 0.351576 & 2.7233 & 0.004226 \tabularnewline
11 & 0.00531 & 0.0411 & 0.483664 \tabularnewline
12 & -0.511133 & -3.9592 & 0.000101 \tabularnewline
13 & 0.038119 & 0.2953 & 0.384403 \tabularnewline
14 & -0.116932 & -0.9058 & 0.184344 \tabularnewline
15 & -0.051427 & -0.3984 & 0.345891 \tabularnewline
16 & 0.00478 & 0.037 & 0.485294 \tabularnewline
17 & -0.028442 & -0.2203 & 0.413188 \tabularnewline
18 & -0.006314 & -0.0489 & 0.480577 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=306406&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]0.073021[/C][C]0.5656[/C][C]0.286881[/C][/ROW]
[ROW][C]2[/C][C]-0.264907[/C][C]-2.052[/C][C]0.022272[/C][/ROW]
[ROW][C]3[/C][C]0.026658[/C][C]0.2065[/C][C]0.418552[/C][/ROW]
[ROW][C]4[/C][C]-0.092502[/C][C]-0.7165[/C][C]0.238225[/C][/ROW]
[ROW][C]5[/C][C]-0.036778[/C][C]-0.2849[/C][C]0.388358[/C][/ROW]
[ROW][C]6[/C][C]-0.021925[/C][C]-0.1698[/C][C]0.432857[/C][/ROW]
[ROW][C]7[/C][C]-0.023336[/C][C]-0.1808[/C][C]0.428582[/C][/ROW]
[ROW][C]8[/C][C]-0.030811[/C][C]-0.2387[/C][C]0.406092[/C][/ROW]
[ROW][C]9[/C][C]0.073351[/C][C]0.5682[/C][C]0.28602[/C][/ROW]
[ROW][C]10[/C][C]0.351576[/C][C]2.7233[/C][C]0.004226[/C][/ROW]
[ROW][C]11[/C][C]0.00531[/C][C]0.0411[/C][C]0.483664[/C][/ROW]
[ROW][C]12[/C][C]-0.511133[/C][C]-3.9592[/C][C]0.000101[/C][/ROW]
[ROW][C]13[/C][C]0.038119[/C][C]0.2953[/C][C]0.384403[/C][/ROW]
[ROW][C]14[/C][C]-0.116932[/C][C]-0.9058[/C][C]0.184344[/C][/ROW]
[ROW][C]15[/C][C]-0.051427[/C][C]-0.3984[/C][C]0.345891[/C][/ROW]
[ROW][C]16[/C][C]0.00478[/C][C]0.037[/C][C]0.485294[/C][/ROW]
[ROW][C]17[/C][C]-0.028442[/C][C]-0.2203[/C][C]0.413188[/C][/ROW]
[ROW][C]18[/C][C]-0.006314[/C][C]-0.0489[/C][C]0.480577[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=306406&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=306406&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	0.073021	0.5656	0.286881
2	-0.264907	-2.052	0.022272
3	0.026658	0.2065	0.418552
4	-0.092502	-0.7165	0.238225
5	-0.036778	-0.2849	0.388358
6	-0.021925	-0.1698	0.432857
7	-0.023336	-0.1808	0.428582
8	-0.030811	-0.2387	0.406092
9	0.073351	0.5682	0.28602
10	0.351576	2.7233	0.004226
11	0.00531	0.0411	0.483664
12	-0.511133	-3.9592	0.000101
13	0.038119	0.2953	0.384403
14	-0.116932	-0.9058	0.184344
15	-0.051427	-0.3984	0.345891
16	0.00478	0.037	0.485294
17	-0.028442	-0.2203	0.413188
18	-0.006314	-0.0489	0.480577

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 = 1 ; par2 = 2 ; par3 = Exact Pearson Chi-Squared by Simulation ;

Parameters (R input):

par1 = Default ; par2 = 2.0 ; par3 = 0 ; par4 = 1 ; 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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