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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2016 14:51:34 +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/2016/Dec/23/t148250110632z9oadq74toujs.htm/, Retrieved Tue, 07 May 2024 13:22:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302948, Retrieved Tue, 07 May 2024 13:22:27 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-23 13:51:34] [c6ea875f0603e0876d03f43aca979571] [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=302948&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=302948&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302948&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	0.793732	8.5487	0
2	0.683481	7.3613	0
3	0.543952	5.8585	0
4	0.411895	4.4362	1e-05
5	0.357483	3.8502	9.7e-05
6	0.298001	3.2096	0.00086
7	0.269734	2.9051	0.002199
8	0.316269	3.4063	0.000453
9	0.336881	3.6283	0.000213
10	0.459592	4.95	1e-06
11	0.515749	5.5548	0
12	0.568925	6.1275	0
13	0.490985	5.2881	0
14	0.384388	4.14	3.3e-05
15	0.229026	2.4667	0.007549
16	0.105404	1.1352	0.129309
17	0.06811	0.7336	0.232345
18	-0.027905	-0.3005	0.382148
19	-0.038173	-0.4111	0.340865
20	-0.029803	-0.321	0.3744

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.793732 & 8.5487 & 0 \tabularnewline
2 & 0.683481 & 7.3613 & 0 \tabularnewline
3 & 0.543952 & 5.8585 & 0 \tabularnewline
4 & 0.411895 & 4.4362 & 1e-05 \tabularnewline
5 & 0.357483 & 3.8502 & 9.7e-05 \tabularnewline
6 & 0.298001 & 3.2096 & 0.00086 \tabularnewline
7 & 0.269734 & 2.9051 & 0.002199 \tabularnewline
8 & 0.316269 & 3.4063 & 0.000453 \tabularnewline
9 & 0.336881 & 3.6283 & 0.000213 \tabularnewline
10 & 0.459592 & 4.95 & 1e-06 \tabularnewline
11 & 0.515749 & 5.5548 & 0 \tabularnewline
12 & 0.568925 & 6.1275 & 0 \tabularnewline
13 & 0.490985 & 5.2881 & 0 \tabularnewline
14 & 0.384388 & 4.14 & 3.3e-05 \tabularnewline
15 & 0.229026 & 2.4667 & 0.007549 \tabularnewline
16 & 0.105404 & 1.1352 & 0.129309 \tabularnewline
17 & 0.06811 & 0.7336 & 0.232345 \tabularnewline
18 & -0.027905 & -0.3005 & 0.382148 \tabularnewline
19 & -0.038173 & -0.4111 & 0.340865 \tabularnewline
20 & -0.029803 & -0.321 & 0.3744 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302948&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]0.793732[/C][C]8.5487[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.683481[/C][C]7.3613[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.543952[/C][C]5.8585[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.411895[/C][C]4.4362[/C][C]1e-05[/C][/ROW]
[ROW][C]5[/C][C]0.357483[/C][C]3.8502[/C][C]9.7e-05[/C][/ROW]
[ROW][C]6[/C][C]0.298001[/C][C]3.2096[/C][C]0.00086[/C][/ROW]
[ROW][C]7[/C][C]0.269734[/C][C]2.9051[/C][C]0.002199[/C][/ROW]
[ROW][C]8[/C][C]0.316269[/C][C]3.4063[/C][C]0.000453[/C][/ROW]
[ROW][C]9[/C][C]0.336881[/C][C]3.6283[/C][C]0.000213[/C][/ROW]
[ROW][C]10[/C][C]0.459592[/C][C]4.95[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.515749[/C][C]5.5548[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.568925[/C][C]6.1275[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.490985[/C][C]5.2881[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.384388[/C][C]4.14[/C][C]3.3e-05[/C][/ROW]
[ROW][C]15[/C][C]0.229026[/C][C]2.4667[/C][C]0.007549[/C][/ROW]
[ROW][C]16[/C][C]0.105404[/C][C]1.1352[/C][C]0.129309[/C][/ROW]
[ROW][C]17[/C][C]0.06811[/C][C]0.7336[/C][C]0.232345[/C][/ROW]
[ROW][C]18[/C][C]-0.027905[/C][C]-0.3005[/C][C]0.382148[/C][/ROW]
[ROW][C]19[/C][C]-0.038173[/C][C]-0.4111[/C][C]0.340865[/C][/ROW]
[ROW][C]20[/C][C]-0.029803[/C][C]-0.321[/C][C]0.3744[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302948&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302948&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	0.793732	8.5487	0
2	0.683481	7.3613	0
3	0.543952	5.8585	0
4	0.411895	4.4362	1e-05
5	0.357483	3.8502	9.7e-05
6	0.298001	3.2096	0.00086
7	0.269734	2.9051	0.002199
8	0.316269	3.4063	0.000453
9	0.336881	3.6283	0.000213
10	0.459592	4.95	1e-06
11	0.515749	5.5548	0
12	0.568925	6.1275	0
13	0.490985	5.2881	0
14	0.384388	4.14	3.3e-05
15	0.229026	2.4667	0.007549
16	0.105404	1.1352	0.129309
17	0.06811	0.7336	0.232345
18	-0.027905	-0.3005	0.382148
19	-0.038173	-0.4111	0.340865
20	-0.029803	-0.321	0.3744

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.793732	8.5487	0
2	0.14452	1.5565	0.061154
3	-0.096216	-1.0363	0.151113
4	-0.089395	-0.9628	0.168823
5	0.128183	1.3806	0.085032
6	0.020531	0.2211	0.412693
7	0.025791	0.2778	0.390837
8	0.210758	2.2699	0.012529
9	0.066603	0.7173	0.237303
10	0.303732	3.2713	0.000705
11	0.069199	0.7453	0.228801
12	0.103052	1.1099	0.134669
13	-0.284982	-3.0694	0.001336
14	-0.150825	-1.6244	0.053499
15	-0.262055	-2.8224	0.002805
16	-0.091906	-0.9899	0.162151
17	0.185859	2.0018	0.023822
18	-0.208754	-2.2483	0.013222
19	0.098793	1.064	0.144763
20	-0.105195	-1.133	0.129779

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.793732 & 8.5487 & 0 \tabularnewline
2 & 0.14452 & 1.5565 & 0.061154 \tabularnewline
3 & -0.096216 & -1.0363 & 0.151113 \tabularnewline
4 & -0.089395 & -0.9628 & 0.168823 \tabularnewline
5 & 0.128183 & 1.3806 & 0.085032 \tabularnewline
6 & 0.020531 & 0.2211 & 0.412693 \tabularnewline
7 & 0.025791 & 0.2778 & 0.390837 \tabularnewline
8 & 0.210758 & 2.2699 & 0.012529 \tabularnewline
9 & 0.066603 & 0.7173 & 0.237303 \tabularnewline
10 & 0.303732 & 3.2713 & 0.000705 \tabularnewline
11 & 0.069199 & 0.7453 & 0.228801 \tabularnewline
12 & 0.103052 & 1.1099 & 0.134669 \tabularnewline
13 & -0.284982 & -3.0694 & 0.001336 \tabularnewline
14 & -0.150825 & -1.6244 & 0.053499 \tabularnewline
15 & -0.262055 & -2.8224 & 0.002805 \tabularnewline
16 & -0.091906 & -0.9899 & 0.162151 \tabularnewline
17 & 0.185859 & 2.0018 & 0.023822 \tabularnewline
18 & -0.208754 & -2.2483 & 0.013222 \tabularnewline
19 & 0.098793 & 1.064 & 0.144763 \tabularnewline
20 & -0.105195 & -1.133 & 0.129779 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302948&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]0.793732[/C][C]8.5487[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.14452[/C][C]1.5565[/C][C]0.061154[/C][/ROW]
[ROW][C]3[/C][C]-0.096216[/C][C]-1.0363[/C][C]0.151113[/C][/ROW]
[ROW][C]4[/C][C]-0.089395[/C][C]-0.9628[/C][C]0.168823[/C][/ROW]
[ROW][C]5[/C][C]0.128183[/C][C]1.3806[/C][C]0.085032[/C][/ROW]
[ROW][C]6[/C][C]0.020531[/C][C]0.2211[/C][C]0.412693[/C][/ROW]
[ROW][C]7[/C][C]0.025791[/C][C]0.2778[/C][C]0.390837[/C][/ROW]
[ROW][C]8[/C][C]0.210758[/C][C]2.2699[/C][C]0.012529[/C][/ROW]
[ROW][C]9[/C][C]0.066603[/C][C]0.7173[/C][C]0.237303[/C][/ROW]
[ROW][C]10[/C][C]0.303732[/C][C]3.2713[/C][C]0.000705[/C][/ROW]
[ROW][C]11[/C][C]0.069199[/C][C]0.7453[/C][C]0.228801[/C][/ROW]
[ROW][C]12[/C][C]0.103052[/C][C]1.1099[/C][C]0.134669[/C][/ROW]
[ROW][C]13[/C][C]-0.284982[/C][C]-3.0694[/C][C]0.001336[/C][/ROW]
[ROW][C]14[/C][C]-0.150825[/C][C]-1.6244[/C][C]0.053499[/C][/ROW]
[ROW][C]15[/C][C]-0.262055[/C][C]-2.8224[/C][C]0.002805[/C][/ROW]
[ROW][C]16[/C][C]-0.091906[/C][C]-0.9899[/C][C]0.162151[/C][/ROW]
[ROW][C]17[/C][C]0.185859[/C][C]2.0018[/C][C]0.023822[/C][/ROW]
[ROW][C]18[/C][C]-0.208754[/C][C]-2.2483[/C][C]0.013222[/C][/ROW]
[ROW][C]19[/C][C]0.098793[/C][C]1.064[/C][C]0.144763[/C][/ROW]
[ROW][C]20[/C][C]-0.105195[/C][C]-1.133[/C][C]0.129779[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302948&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302948&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	0.793732	8.5487	0
2	0.14452	1.5565	0.061154
3	-0.096216	-1.0363	0.151113
4	-0.089395	-0.9628	0.168823
5	0.128183	1.3806	0.085032
6	0.020531	0.2211	0.412693
7	0.025791	0.2778	0.390837
8	0.210758	2.2699	0.012529
9	0.066603	0.7173	0.237303
10	0.303732	3.2713	0.000705
11	0.069199	0.7453	0.228801
12	0.103052	1.1099	0.134669
13	-0.284982	-3.0694	0.001336
14	-0.150825	-1.6244	0.053499
15	-0.262055	-2.8224	0.002805
16	-0.091906	-0.9899	0.162151
17	0.185859	2.0018	0.023822
18	-0.208754	-2.2483	0.013222
19	0.098793	1.064	0.144763
20	-0.105195	-1.133	0.129779

Figure 1

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Figure 2

PNG link

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Figure 3

PNG link

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Parameters (Session):

par2 = grey ; par3 = FALSE ; par4 = 5-point Likert ;

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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code