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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 21:59:13 +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/t1482008379z3y6u8fj81pinrc.htm/, Retrieved Thu, 02 May 2024 02:12:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300950, Retrieved Thu, 02 May 2024 02:12:32 +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 ] [2016-12-17 20:59:13] [f20c721eaecf28dbff8d9b9768e8b0c7] [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=300950&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=300950&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300950&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	-0.035357	-0.3588	0.360226
2	-0.0246	-0.2497	0.401675
3	0.070966	0.7202	0.236509
4	-0.165857	-1.6833	0.047676
5	0.033489	0.3399	0.36732
6	-0.12682	-1.2871	0.100474
7	-0.027001	-0.274	0.392307
8	0.08036	0.8156	0.208316
9	0.018401	0.1867	0.426112
10	-0.029251	-0.2969	0.383582
11	-0.005678	-0.0576	0.47708
12	-0.291893	-2.9624	0.001895
13	0.016788	0.1704	0.432523
14	0.026343	0.2674	0.394865
15	-0.134322	-1.3632	0.087893
16	0.002883	0.0293	0.488357
17	-0.005865	-0.0595	0.476325
18	0.14826	1.5047	0.067734
19	0.07846	0.7963	0.21385
20	0.057066	0.5792	0.281876

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.035357 & -0.3588 & 0.360226 \tabularnewline
2 & -0.0246 & -0.2497 & 0.401675 \tabularnewline
3 & 0.070966 & 0.7202 & 0.236509 \tabularnewline
4 & -0.165857 & -1.6833 & 0.047676 \tabularnewline
5 & 0.033489 & 0.3399 & 0.36732 \tabularnewline
6 & -0.12682 & -1.2871 & 0.100474 \tabularnewline
7 & -0.027001 & -0.274 & 0.392307 \tabularnewline
8 & 0.08036 & 0.8156 & 0.208316 \tabularnewline
9 & 0.018401 & 0.1867 & 0.426112 \tabularnewline
10 & -0.029251 & -0.2969 & 0.383582 \tabularnewline
11 & -0.005678 & -0.0576 & 0.47708 \tabularnewline
12 & -0.291893 & -2.9624 & 0.001895 \tabularnewline
13 & 0.016788 & 0.1704 & 0.432523 \tabularnewline
14 & 0.026343 & 0.2674 & 0.394865 \tabularnewline
15 & -0.134322 & -1.3632 & 0.087893 \tabularnewline
16 & 0.002883 & 0.0293 & 0.488357 \tabularnewline
17 & -0.005865 & -0.0595 & 0.476325 \tabularnewline
18 & 0.14826 & 1.5047 & 0.067734 \tabularnewline
19 & 0.07846 & 0.7963 & 0.21385 \tabularnewline
20 & 0.057066 & 0.5792 & 0.281876 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300950&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]-0.035357[/C][C]-0.3588[/C][C]0.360226[/C][/ROW]
[ROW][C]2[/C][C]-0.0246[/C][C]-0.2497[/C][C]0.401675[/C][/ROW]
[ROW][C]3[/C][C]0.070966[/C][C]0.7202[/C][C]0.236509[/C][/ROW]
[ROW][C]4[/C][C]-0.165857[/C][C]-1.6833[/C][C]0.047676[/C][/ROW]
[ROW][C]5[/C][C]0.033489[/C][C]0.3399[/C][C]0.36732[/C][/ROW]
[ROW][C]6[/C][C]-0.12682[/C][C]-1.2871[/C][C]0.100474[/C][/ROW]
[ROW][C]7[/C][C]-0.027001[/C][C]-0.274[/C][C]0.392307[/C][/ROW]
[ROW][C]8[/C][C]0.08036[/C][C]0.8156[/C][C]0.208316[/C][/ROW]
[ROW][C]9[/C][C]0.018401[/C][C]0.1867[/C][C]0.426112[/C][/ROW]
[ROW][C]10[/C][C]-0.029251[/C][C]-0.2969[/C][C]0.383582[/C][/ROW]
[ROW][C]11[/C][C]-0.005678[/C][C]-0.0576[/C][C]0.47708[/C][/ROW]
[ROW][C]12[/C][C]-0.291893[/C][C]-2.9624[/C][C]0.001895[/C][/ROW]
[ROW][C]13[/C][C]0.016788[/C][C]0.1704[/C][C]0.432523[/C][/ROW]
[ROW][C]14[/C][C]0.026343[/C][C]0.2674[/C][C]0.394865[/C][/ROW]
[ROW][C]15[/C][C]-0.134322[/C][C]-1.3632[/C][C]0.087893[/C][/ROW]
[ROW][C]16[/C][C]0.002883[/C][C]0.0293[/C][C]0.488357[/C][/ROW]
[ROW][C]17[/C][C]-0.005865[/C][C]-0.0595[/C][C]0.476325[/C][/ROW]
[ROW][C]18[/C][C]0.14826[/C][C]1.5047[/C][C]0.067734[/C][/ROW]
[ROW][C]19[/C][C]0.07846[/C][C]0.7963[/C][C]0.21385[/C][/ROW]
[ROW][C]20[/C][C]0.057066[/C][C]0.5792[/C][C]0.281876[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300950&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300950&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	-0.035357	-0.3588	0.360226
2	-0.0246	-0.2497	0.401675
3	0.070966	0.7202	0.236509
4	-0.165857	-1.6833	0.047676
5	0.033489	0.3399	0.36732
6	-0.12682	-1.2871	0.100474
7	-0.027001	-0.274	0.392307
8	0.08036	0.8156	0.208316
9	0.018401	0.1867	0.426112
10	-0.029251	-0.2969	0.383582
11	-0.005678	-0.0576	0.47708
12	-0.291893	-2.9624	0.001895
13	0.016788	0.1704	0.432523
14	0.026343	0.2674	0.394865
15	-0.134322	-1.3632	0.087893
16	0.002883	0.0293	0.488357
17	-0.005865	-0.0595	0.476325
18	0.14826	1.5047	0.067734
19	0.07846	0.7963	0.21385
20	0.057066	0.5792	0.281876

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.035357	-0.3588	0.360226
2	-0.025882	-0.2627	0.396663
3	0.069291	0.7032	0.24175
4	-0.162626	-1.6505	0.050946
5	0.028318	0.2874	0.387192
6	-0.1434	-1.4554	0.074306
7	-0.007951	-0.0807	0.467923
8	0.040009	0.406	0.342777
9	0.050525	0.5128	0.304603
10	-0.069346	-0.7038	0.241577
11	-0.011355	-0.1152	0.454238
12	-0.318924	-3.2367	0.000813
13	0.019974	0.2027	0.419878
14	-0.005799	-0.0589	0.476593
15	-0.082439	-0.8367	0.202358
16	-0.135725	-1.3775	0.085679
17	-0.011101	-0.1127	0.45526
18	0.079048	0.8022	0.212129
19	0.073132	0.7422	0.229825
20	0.100466	1.0196	0.155148

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.035357 & -0.3588 & 0.360226 \tabularnewline
2 & -0.025882 & -0.2627 & 0.396663 \tabularnewline
3 & 0.069291 & 0.7032 & 0.24175 \tabularnewline
4 & -0.162626 & -1.6505 & 0.050946 \tabularnewline
5 & 0.028318 & 0.2874 & 0.387192 \tabularnewline
6 & -0.1434 & -1.4554 & 0.074306 \tabularnewline
7 & -0.007951 & -0.0807 & 0.467923 \tabularnewline
8 & 0.040009 & 0.406 & 0.342777 \tabularnewline
9 & 0.050525 & 0.5128 & 0.304603 \tabularnewline
10 & -0.069346 & -0.7038 & 0.241577 \tabularnewline
11 & -0.011355 & -0.1152 & 0.454238 \tabularnewline
12 & -0.318924 & -3.2367 & 0.000813 \tabularnewline
13 & 0.019974 & 0.2027 & 0.419878 \tabularnewline
14 & -0.005799 & -0.0589 & 0.476593 \tabularnewline
15 & -0.082439 & -0.8367 & 0.202358 \tabularnewline
16 & -0.135725 & -1.3775 & 0.085679 \tabularnewline
17 & -0.011101 & -0.1127 & 0.45526 \tabularnewline
18 & 0.079048 & 0.8022 & 0.212129 \tabularnewline
19 & 0.073132 & 0.7422 & 0.229825 \tabularnewline
20 & 0.100466 & 1.0196 & 0.155148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300950&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]-0.035357[/C][C]-0.3588[/C][C]0.360226[/C][/ROW]
[ROW][C]2[/C][C]-0.025882[/C][C]-0.2627[/C][C]0.396663[/C][/ROW]
[ROW][C]3[/C][C]0.069291[/C][C]0.7032[/C][C]0.24175[/C][/ROW]
[ROW][C]4[/C][C]-0.162626[/C][C]-1.6505[/C][C]0.050946[/C][/ROW]
[ROW][C]5[/C][C]0.028318[/C][C]0.2874[/C][C]0.387192[/C][/ROW]
[ROW][C]6[/C][C]-0.1434[/C][C]-1.4554[/C][C]0.074306[/C][/ROW]
[ROW][C]7[/C][C]-0.007951[/C][C]-0.0807[/C][C]0.467923[/C][/ROW]
[ROW][C]8[/C][C]0.040009[/C][C]0.406[/C][C]0.342777[/C][/ROW]
[ROW][C]9[/C][C]0.050525[/C][C]0.5128[/C][C]0.304603[/C][/ROW]
[ROW][C]10[/C][C]-0.069346[/C][C]-0.7038[/C][C]0.241577[/C][/ROW]
[ROW][C]11[/C][C]-0.011355[/C][C]-0.1152[/C][C]0.454238[/C][/ROW]
[ROW][C]12[/C][C]-0.318924[/C][C]-3.2367[/C][C]0.000813[/C][/ROW]
[ROW][C]13[/C][C]0.019974[/C][C]0.2027[/C][C]0.419878[/C][/ROW]
[ROW][C]14[/C][C]-0.005799[/C][C]-0.0589[/C][C]0.476593[/C][/ROW]
[ROW][C]15[/C][C]-0.082439[/C][C]-0.8367[/C][C]0.202358[/C][/ROW]
[ROW][C]16[/C][C]-0.135725[/C][C]-1.3775[/C][C]0.085679[/C][/ROW]
[ROW][C]17[/C][C]-0.011101[/C][C]-0.1127[/C][C]0.45526[/C][/ROW]
[ROW][C]18[/C][C]0.079048[/C][C]0.8022[/C][C]0.212129[/C][/ROW]
[ROW][C]19[/C][C]0.073132[/C][C]0.7422[/C][C]0.229825[/C][/ROW]
[ROW][C]20[/C][C]0.100466[/C][C]1.0196[/C][C]0.155148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300950&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300950&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	-0.035357	-0.3588	0.360226
2	-0.025882	-0.2627	0.396663
3	0.069291	0.7032	0.24175
4	-0.162626	-1.6505	0.050946
5	0.028318	0.2874	0.387192
6	-0.1434	-1.4554	0.074306
7	-0.007951	-0.0807	0.467923
8	0.040009	0.406	0.342777
9	0.050525	0.5128	0.304603
10	-0.069346	-0.7038	0.241577
11	-0.011355	-0.1152	0.454238
12	-0.318924	-3.2367	0.000813
13	0.019974	0.2027	0.419878
14	-0.005799	-0.0589	0.476593
15	-0.082439	-0.8367	0.202358
16	-0.135725	-1.3775	0.085679
17	-0.011101	-0.1127	0.45526
18	0.079048	0.8022	0.212129
19	0.073132	0.7422	0.229825
20	0.100466	1.0196	0.155148

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

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Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code