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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 15:09:32 +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/17/t1481984329l46e4zapcwo6cer.htm/, Retrieved Thu, 02 May 2024 08:21:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300803, Retrieved Thu, 02 May 2024 08:21:28 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [Autocorrelatie Te...] [2016-12-17 14:09:32] [549e222e79c75c10edc4b0c7b20158c3] [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=300803&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=300803&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300803&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	0.849652	9.7247	0
2	0.486153	5.5643	0
3	0.001855	0.0212	0.491544
4	-0.471456	-5.3961	0
5	-0.812299	-9.2972	0
6	-0.930648	-10.6518	0
7	-0.802078	-9.1802	0
8	-0.46215	-5.2895	0
9	-0.002732	-0.0313	0.48755
10	0.452781	5.1823	0
11	0.787215	9.0101	0
12	0.904022	10.347	0
13	0.772451	8.8411	0
14	0.442528	5.065	1e-06
15	0.004153	0.0475	0.481082
16	-0.428898	-4.909	1e-06
17	-0.739777	-8.4671	0
18	-0.850426	-9.7336	0
19	-0.735567	-8.419	0
20	-0.427039	-4.8877	1e-06
21	-0.009141	-0.1046	0.458418

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.849652 & 9.7247 & 0 \tabularnewline
2 & 0.486153 & 5.5643 & 0 \tabularnewline
3 & 0.001855 & 0.0212 & 0.491544 \tabularnewline
4 & -0.471456 & -5.3961 & 0 \tabularnewline
5 & -0.812299 & -9.2972 & 0 \tabularnewline
6 & -0.930648 & -10.6518 & 0 \tabularnewline
7 & -0.802078 & -9.1802 & 0 \tabularnewline
8 & -0.46215 & -5.2895 & 0 \tabularnewline
9 & -0.002732 & -0.0313 & 0.48755 \tabularnewline
10 & 0.452781 & 5.1823 & 0 \tabularnewline
11 & 0.787215 & 9.0101 & 0 \tabularnewline
12 & 0.904022 & 10.347 & 0 \tabularnewline
13 & 0.772451 & 8.8411 & 0 \tabularnewline
14 & 0.442528 & 5.065 & 1e-06 \tabularnewline
15 & 0.004153 & 0.0475 & 0.481082 \tabularnewline
16 & -0.428898 & -4.909 & 1e-06 \tabularnewline
17 & -0.739777 & -8.4671 & 0 \tabularnewline
18 & -0.850426 & -9.7336 & 0 \tabularnewline
19 & -0.735567 & -8.419 & 0 \tabularnewline
20 & -0.427039 & -4.8877 & 1e-06 \tabularnewline
21 & -0.009141 & -0.1046 & 0.458418 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300803&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]0.849652[/C][C]9.7247[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.486153[/C][C]5.5643[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.001855[/C][C]0.0212[/C][C]0.491544[/C][/ROW]
[ROW][C]4[/C][C]-0.471456[/C][C]-5.3961[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.812299[/C][C]-9.2972[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.930648[/C][C]-10.6518[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.802078[/C][C]-9.1802[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]-0.46215[/C][C]-5.2895[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]-0.002732[/C][C]-0.0313[/C][C]0.48755[/C][/ROW]
[ROW][C]10[/C][C]0.452781[/C][C]5.1823[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.787215[/C][C]9.0101[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.904022[/C][C]10.347[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.772451[/C][C]8.8411[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.442528[/C][C]5.065[/C][C]1e-06[/C][/ROW]
[ROW][C]15[/C][C]0.004153[/C][C]0.0475[/C][C]0.481082[/C][/ROW]
[ROW][C]16[/C][C]-0.428898[/C][C]-4.909[/C][C]1e-06[/C][/ROW]
[ROW][C]17[/C][C]-0.739777[/C][C]-8.4671[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]-0.850426[/C][C]-9.7336[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]-0.735567[/C][C]-8.419[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]-0.427039[/C][C]-4.8877[/C][C]1e-06[/C][/ROW]
[ROW][C]21[/C][C]-0.009141[/C][C]-0.1046[/C][C]0.458418[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300803&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300803&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	0.849652	9.7247	0
2	0.486153	5.5643	0
3	0.001855	0.0212	0.491544
4	-0.471456	-5.3961	0
5	-0.812299	-9.2972	0
6	-0.930648	-10.6518	0
7	-0.802078	-9.1802	0
8	-0.46215	-5.2895	0
9	-0.002732	-0.0313	0.48755
10	0.452781	5.1823	0
11	0.787215	9.0101	0
12	0.904022	10.347	0
13	0.772451	8.8411	0
14	0.442528	5.065	1e-06
15	0.004153	0.0475	0.481082
16	-0.428898	-4.909	1e-06
17	-0.739777	-8.4671	0
18	-0.850426	-9.7336	0
19	-0.735567	-8.419	0
20	-0.427039	-4.8877	1e-06
21	-0.009141	-0.1046	0.458418

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.849652	9.7247	0
2	-0.847769	-9.7032	0
3	-0.525117	-6.0102	0
4	-0.282806	-3.2369	0.000765
5	-0.211826	-2.4245	0.008348
6	-0.075424	-0.8633	0.194785
7	-0.066852	-0.7652	0.222777
8	0.021401	0.245	0.403439
9	0.082242	0.9413	0.174142
10	0.076868	0.8798	0.19029
11	0.144131	1.6497	0.050704
12	-0.06836	-0.7824	0.21769
13	-0.132509	-1.5166	0.065884
14	0.150579	1.7235	0.043583
15	0.121924	1.3955	0.082616
16	-0.018785	-0.215	0.415047
17	0.01652	0.1891	0.425162
18	-0.016032	-0.1835	0.427347
19	-0.015648	-0.1791	0.429068
20	0.019354	0.2215	0.412519
21	0.014639	0.1675	0.433599

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.849652 & 9.7247 & 0 \tabularnewline
2 & -0.847769 & -9.7032 & 0 \tabularnewline
3 & -0.525117 & -6.0102 & 0 \tabularnewline
4 & -0.282806 & -3.2369 & 0.000765 \tabularnewline
5 & -0.211826 & -2.4245 & 0.008348 \tabularnewline
6 & -0.075424 & -0.8633 & 0.194785 \tabularnewline
7 & -0.066852 & -0.7652 & 0.222777 \tabularnewline
8 & 0.021401 & 0.245 & 0.403439 \tabularnewline
9 & 0.082242 & 0.9413 & 0.174142 \tabularnewline
10 & 0.076868 & 0.8798 & 0.19029 \tabularnewline
11 & 0.144131 & 1.6497 & 0.050704 \tabularnewline
12 & -0.06836 & -0.7824 & 0.21769 \tabularnewline
13 & -0.132509 & -1.5166 & 0.065884 \tabularnewline
14 & 0.150579 & 1.7235 & 0.043583 \tabularnewline
15 & 0.121924 & 1.3955 & 0.082616 \tabularnewline
16 & -0.018785 & -0.215 & 0.415047 \tabularnewline
17 & 0.01652 & 0.1891 & 0.425162 \tabularnewline
18 & -0.016032 & -0.1835 & 0.427347 \tabularnewline
19 & -0.015648 & -0.1791 & 0.429068 \tabularnewline
20 & 0.019354 & 0.2215 & 0.412519 \tabularnewline
21 & 0.014639 & 0.1675 & 0.433599 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300803&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]0.849652[/C][C]9.7247[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.847769[/C][C]-9.7032[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.525117[/C][C]-6.0102[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]-0.282806[/C][C]-3.2369[/C][C]0.000765[/C][/ROW]
[ROW][C]5[/C][C]-0.211826[/C][C]-2.4245[/C][C]0.008348[/C][/ROW]
[ROW][C]6[/C][C]-0.075424[/C][C]-0.8633[/C][C]0.194785[/C][/ROW]
[ROW][C]7[/C][C]-0.066852[/C][C]-0.7652[/C][C]0.222777[/C][/ROW]
[ROW][C]8[/C][C]0.021401[/C][C]0.245[/C][C]0.403439[/C][/ROW]
[ROW][C]9[/C][C]0.082242[/C][C]0.9413[/C][C]0.174142[/C][/ROW]
[ROW][C]10[/C][C]0.076868[/C][C]0.8798[/C][C]0.19029[/C][/ROW]
[ROW][C]11[/C][C]0.144131[/C][C]1.6497[/C][C]0.050704[/C][/ROW]
[ROW][C]12[/C][C]-0.06836[/C][C]-0.7824[/C][C]0.21769[/C][/ROW]
[ROW][C]13[/C][C]-0.132509[/C][C]-1.5166[/C][C]0.065884[/C][/ROW]
[ROW][C]14[/C][C]0.150579[/C][C]1.7235[/C][C]0.043583[/C][/ROW]
[ROW][C]15[/C][C]0.121924[/C][C]1.3955[/C][C]0.082616[/C][/ROW]
[ROW][C]16[/C][C]-0.018785[/C][C]-0.215[/C][C]0.415047[/C][/ROW]
[ROW][C]17[/C][C]0.01652[/C][C]0.1891[/C][C]0.425162[/C][/ROW]
[ROW][C]18[/C][C]-0.016032[/C][C]-0.1835[/C][C]0.427347[/C][/ROW]
[ROW][C]19[/C][C]-0.015648[/C][C]-0.1791[/C][C]0.429068[/C][/ROW]
[ROW][C]20[/C][C]0.019354[/C][C]0.2215[/C][C]0.412519[/C][/ROW]
[ROW][C]21[/C][C]0.014639[/C][C]0.1675[/C][C]0.433599[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300803&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300803&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	0.849652	9.7247	0
2	-0.847769	-9.7032	0
3	-0.525117	-6.0102	0
4	-0.282806	-3.2369	0.000765
5	-0.211826	-2.4245	0.008348
6	-0.075424	-0.8633	0.194785
7	-0.066852	-0.7652	0.222777
8	0.021401	0.245	0.403439
9	0.082242	0.9413	0.174142
10	0.076868	0.8798	0.19029
11	0.144131	1.6497	0.050704
12	-0.06836	-0.7824	0.21769
13	-0.132509	-1.5166	0.065884
14	0.150579	1.7235	0.043583
15	0.121924	1.3955	0.082616
16	-0.018785	-0.215	0.415047
17	0.01652	0.1891	0.425162
18	-0.016032	-0.1835	0.427347
19	-0.015648	-0.1791	0.429068
20	0.019354	0.2215	0.412519
21	0.014639	0.1675	0.433599

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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