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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Dec 2016 17:08:47 +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/21/t1482336607i3px2igty34597f.htm/, Retrieved Mon, 06 May 2024 12:41:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302409, Retrieved Mon, 06 May 2024 12:41:47 +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] [] [2016-12-21 16:08:47] [2802fcbee976b89d2ab84425d3d65dcf] [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=302409&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=302409&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302409&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	-0.410852	-4.5751	6e-06
2	-0.169911	-1.8921	0.030408
3	0.145942	1.6251	0.053336
4	0.029614	0.3298	0.371064
5	-0.093891	-1.0455	0.148906
6	-0.033914	-0.3777	0.353166
7	0.089104	0.9922	0.161511
8	-0.044051	-0.4905	0.312312
9	-0.036929	-0.4112	0.340811
10	-0.044054	-0.4906	0.312301
11	-0.002796	-0.0311	0.487606
12	0.12454	1.3868	0.083992
13	0.019247	0.2143	0.415322
14	-0.120079	-1.3371	0.091812
15	0.114696	1.2772	0.101959
16	-0.015085	-0.168	0.433435
17	-0.126567	-1.4094	0.080612
18	0.12451	1.3865	0.084043
19	0.009112	0.1015	0.459672
20	-0.044453	-0.495	0.310736

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.410852 & -4.5751 & 6e-06 \tabularnewline
2 & -0.169911 & -1.8921 & 0.030408 \tabularnewline
3 & 0.145942 & 1.6251 & 0.053336 \tabularnewline
4 & 0.029614 & 0.3298 & 0.371064 \tabularnewline
5 & -0.093891 & -1.0455 & 0.148906 \tabularnewline
6 & -0.033914 & -0.3777 & 0.353166 \tabularnewline
7 & 0.089104 & 0.9922 & 0.161511 \tabularnewline
8 & -0.044051 & -0.4905 & 0.312312 \tabularnewline
9 & -0.036929 & -0.4112 & 0.340811 \tabularnewline
10 & -0.044054 & -0.4906 & 0.312301 \tabularnewline
11 & -0.002796 & -0.0311 & 0.487606 \tabularnewline
12 & 0.12454 & 1.3868 & 0.083992 \tabularnewline
13 & 0.019247 & 0.2143 & 0.415322 \tabularnewline
14 & -0.120079 & -1.3371 & 0.091812 \tabularnewline
15 & 0.114696 & 1.2772 & 0.101959 \tabularnewline
16 & -0.015085 & -0.168 & 0.433435 \tabularnewline
17 & -0.126567 & -1.4094 & 0.080612 \tabularnewline
18 & 0.12451 & 1.3865 & 0.084043 \tabularnewline
19 & 0.009112 & 0.1015 & 0.459672 \tabularnewline
20 & -0.044453 & -0.495 & 0.310736 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302409&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]-0.410852[/C][C]-4.5751[/C][C]6e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.169911[/C][C]-1.8921[/C][C]0.030408[/C][/ROW]
[ROW][C]3[/C][C]0.145942[/C][C]1.6251[/C][C]0.053336[/C][/ROW]
[ROW][C]4[/C][C]0.029614[/C][C]0.3298[/C][C]0.371064[/C][/ROW]
[ROW][C]5[/C][C]-0.093891[/C][C]-1.0455[/C][C]0.148906[/C][/ROW]
[ROW][C]6[/C][C]-0.033914[/C][C]-0.3777[/C][C]0.353166[/C][/ROW]
[ROW][C]7[/C][C]0.089104[/C][C]0.9922[/C][C]0.161511[/C][/ROW]
[ROW][C]8[/C][C]-0.044051[/C][C]-0.4905[/C][C]0.312312[/C][/ROW]
[ROW][C]9[/C][C]-0.036929[/C][C]-0.4112[/C][C]0.340811[/C][/ROW]
[ROW][C]10[/C][C]-0.044054[/C][C]-0.4906[/C][C]0.312301[/C][/ROW]
[ROW][C]11[/C][C]-0.002796[/C][C]-0.0311[/C][C]0.487606[/C][/ROW]
[ROW][C]12[/C][C]0.12454[/C][C]1.3868[/C][C]0.083992[/C][/ROW]
[ROW][C]13[/C][C]0.019247[/C][C]0.2143[/C][C]0.415322[/C][/ROW]
[ROW][C]14[/C][C]-0.120079[/C][C]-1.3371[/C][C]0.091812[/C][/ROW]
[ROW][C]15[/C][C]0.114696[/C][C]1.2772[/C][C]0.101959[/C][/ROW]
[ROW][C]16[/C][C]-0.015085[/C][C]-0.168[/C][C]0.433435[/C][/ROW]
[ROW][C]17[/C][C]-0.126567[/C][C]-1.4094[/C][C]0.080612[/C][/ROW]
[ROW][C]18[/C][C]0.12451[/C][C]1.3865[/C][C]0.084043[/C][/ROW]
[ROW][C]19[/C][C]0.009112[/C][C]0.1015[/C][C]0.459672[/C][/ROW]
[ROW][C]20[/C][C]-0.044453[/C][C]-0.495[/C][C]0.310736[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302409&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302409&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	-0.410852	-4.5751	6e-06
2	-0.169911	-1.8921	0.030408
3	0.145942	1.6251	0.053336
4	0.029614	0.3298	0.371064
5	-0.093891	-1.0455	0.148906
6	-0.033914	-0.3777	0.353166
7	0.089104	0.9922	0.161511
8	-0.044051	-0.4905	0.312312
9	-0.036929	-0.4112	0.340811
10	-0.044054	-0.4906	0.312301
11	-0.002796	-0.0311	0.487606
12	0.12454	1.3868	0.083992
13	0.019247	0.2143	0.415322
14	-0.120079	-1.3371	0.091812
15	0.114696	1.2772	0.101959
16	-0.015085	-0.168	0.433435
17	-0.126567	-1.4094	0.080612
18	0.12451	1.3865	0.084043
19	0.009112	0.1015	0.459672
20	-0.044453	-0.495	0.310736

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.410852	-4.5751	6e-06
2	-0.407496	-4.5377	7e-06
3	-0.172731	-1.9235	0.028358
4	-0.048916	-0.5447	0.293468
5	-0.076911	-0.8564	0.196703
6	-0.138581	-1.5432	0.062669
7	-0.058254	-0.6487	0.258868
8	-0.075406	-0.8397	0.201351
9	-0.085448	-0.9515	0.171599
10	-0.193314	-2.1527	0.016641
11	-0.256517	-2.8565	0.002512
12	-0.084181	-0.9374	0.175189
13	0.069727	0.7764	0.219483
14	-0.021024	-0.2341	0.407639
15	0.067341	0.7499	0.227374
16	0.020671	0.2302	0.409166
17	-0.115848	-1.29	0.09972
18	0.005408	0.0602	0.47604
19	0.009954	0.1108	0.45596
20	0.035896	0.3997	0.345024

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.410852 & -4.5751 & 6e-06 \tabularnewline
2 & -0.407496 & -4.5377 & 7e-06 \tabularnewline
3 & -0.172731 & -1.9235 & 0.028358 \tabularnewline
4 & -0.048916 & -0.5447 & 0.293468 \tabularnewline
5 & -0.076911 & -0.8564 & 0.196703 \tabularnewline
6 & -0.138581 & -1.5432 & 0.062669 \tabularnewline
7 & -0.058254 & -0.6487 & 0.258868 \tabularnewline
8 & -0.075406 & -0.8397 & 0.201351 \tabularnewline
9 & -0.085448 & -0.9515 & 0.171599 \tabularnewline
10 & -0.193314 & -2.1527 & 0.016641 \tabularnewline
11 & -0.256517 & -2.8565 & 0.002512 \tabularnewline
12 & -0.084181 & -0.9374 & 0.175189 \tabularnewline
13 & 0.069727 & 0.7764 & 0.219483 \tabularnewline
14 & -0.021024 & -0.2341 & 0.407639 \tabularnewline
15 & 0.067341 & 0.7499 & 0.227374 \tabularnewline
16 & 0.020671 & 0.2302 & 0.409166 \tabularnewline
17 & -0.115848 & -1.29 & 0.09972 \tabularnewline
18 & 0.005408 & 0.0602 & 0.47604 \tabularnewline
19 & 0.009954 & 0.1108 & 0.45596 \tabularnewline
20 & 0.035896 & 0.3997 & 0.345024 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302409&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]-0.410852[/C][C]-4.5751[/C][C]6e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.407496[/C][C]-4.5377[/C][C]7e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.172731[/C][C]-1.9235[/C][C]0.028358[/C][/ROW]
[ROW][C]4[/C][C]-0.048916[/C][C]-0.5447[/C][C]0.293468[/C][/ROW]
[ROW][C]5[/C][C]-0.076911[/C][C]-0.8564[/C][C]0.196703[/C][/ROW]
[ROW][C]6[/C][C]-0.138581[/C][C]-1.5432[/C][C]0.062669[/C][/ROW]
[ROW][C]7[/C][C]-0.058254[/C][C]-0.6487[/C][C]0.258868[/C][/ROW]
[ROW][C]8[/C][C]-0.075406[/C][C]-0.8397[/C][C]0.201351[/C][/ROW]
[ROW][C]9[/C][C]-0.085448[/C][C]-0.9515[/C][C]0.171599[/C][/ROW]
[ROW][C]10[/C][C]-0.193314[/C][C]-2.1527[/C][C]0.016641[/C][/ROW]
[ROW][C]11[/C][C]-0.256517[/C][C]-2.8565[/C][C]0.002512[/C][/ROW]
[ROW][C]12[/C][C]-0.084181[/C][C]-0.9374[/C][C]0.175189[/C][/ROW]
[ROW][C]13[/C][C]0.069727[/C][C]0.7764[/C][C]0.219483[/C][/ROW]
[ROW][C]14[/C][C]-0.021024[/C][C]-0.2341[/C][C]0.407639[/C][/ROW]
[ROW][C]15[/C][C]0.067341[/C][C]0.7499[/C][C]0.227374[/C][/ROW]
[ROW][C]16[/C][C]0.020671[/C][C]0.2302[/C][C]0.409166[/C][/ROW]
[ROW][C]17[/C][C]-0.115848[/C][C]-1.29[/C][C]0.09972[/C][/ROW]
[ROW][C]18[/C][C]0.005408[/C][C]0.0602[/C][C]0.47604[/C][/ROW]
[ROW][C]19[/C][C]0.009954[/C][C]0.1108[/C][C]0.45596[/C][/ROW]
[ROW][C]20[/C][C]0.035896[/C][C]0.3997[/C][C]0.345024[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302409&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302409&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	-0.410852	-4.5751	6e-06
2	-0.407496	-4.5377	7e-06
3	-0.172731	-1.9235	0.028358
4	-0.048916	-0.5447	0.293468
5	-0.076911	-0.8564	0.196703
6	-0.138581	-1.5432	0.062669
7	-0.058254	-0.6487	0.258868
8	-0.075406	-0.8397	0.201351
9	-0.085448	-0.9515	0.171599
10	-0.193314	-2.1527	0.016641
11	-0.256517	-2.8565	0.002512
12	-0.084181	-0.9374	0.175189
13	0.069727	0.7764	0.219483
14	-0.021024	-0.2341	0.407639
15	0.067341	0.7499	0.227374
16	0.020671	0.2302	0.409166
17	-0.115848	-1.29	0.09972
18	0.005408	0.0602	0.47604
19	0.009954	0.1108	0.45596
20	0.035896	0.3997	0.345024

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

Parameters (R input):

par1 = Default ; par2 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code