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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 12 Dec 2016 16:05:40 +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/12/t1481555157bw1cf0yzjva1kc4.htm/, Retrieved Sat, 04 May 2024 01:40:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298919, Retrieved Sat, 04 May 2024 01:40:33 +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] [(Partial) Autocor...] [2016-12-12 15:05:40] [2a4be59ea15844c348dc523b08af79fc] [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=298919&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=298919&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298919&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	0.5331	5.8883	0
2	0.171341	1.8925	0.030396
3	-0.063208	-0.6982	0.243203
4	-0.123871	-1.3682	0.086882
5	-0.16111	-1.7795	0.038823
6	-0.218567	-2.4142	0.008629
7	-0.222605	-2.4588	0.007672
8	-0.136814	-1.5112	0.066667
9	0.008565	0.0946	0.462391
10	-0.050067	-0.553	0.290636
11	-0.068651	-0.7583	0.224873
12	-0.076916	-0.8496	0.198614
13	-0.039349	-0.4346	0.3323
14	0.042172	0.4658	0.321092
15	0.046734	0.5162	0.303325
16	-0.031386	-0.3467	0.36472
17	-0.079668	-0.88	0.190304
18	-0.112024	-1.2373	0.109167
19	-0.075061	-0.8291	0.20434
20	-0.018208	-0.2011	0.420471

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.5331 & 5.8883 & 0 \tabularnewline
2 & 0.171341 & 1.8925 & 0.030396 \tabularnewline
3 & -0.063208 & -0.6982 & 0.243203 \tabularnewline
4 & -0.123871 & -1.3682 & 0.086882 \tabularnewline
5 & -0.16111 & -1.7795 & 0.038823 \tabularnewline
6 & -0.218567 & -2.4142 & 0.008629 \tabularnewline
7 & -0.222605 & -2.4588 & 0.007672 \tabularnewline
8 & -0.136814 & -1.5112 & 0.066667 \tabularnewline
9 & 0.008565 & 0.0946 & 0.462391 \tabularnewline
10 & -0.050067 & -0.553 & 0.290636 \tabularnewline
11 & -0.068651 & -0.7583 & 0.224873 \tabularnewline
12 & -0.076916 & -0.8496 & 0.198614 \tabularnewline
13 & -0.039349 & -0.4346 & 0.3323 \tabularnewline
14 & 0.042172 & 0.4658 & 0.321092 \tabularnewline
15 & 0.046734 & 0.5162 & 0.303325 \tabularnewline
16 & -0.031386 & -0.3467 & 0.36472 \tabularnewline
17 & -0.079668 & -0.88 & 0.190304 \tabularnewline
18 & -0.112024 & -1.2373 & 0.109167 \tabularnewline
19 & -0.075061 & -0.8291 & 0.20434 \tabularnewline
20 & -0.018208 & -0.2011 & 0.420471 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298919&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]0.5331[/C][C]5.8883[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.171341[/C][C]1.8925[/C][C]0.030396[/C][/ROW]
[ROW][C]3[/C][C]-0.063208[/C][C]-0.6982[/C][C]0.243203[/C][/ROW]
[ROW][C]4[/C][C]-0.123871[/C][C]-1.3682[/C][C]0.086882[/C][/ROW]
[ROW][C]5[/C][C]-0.16111[/C][C]-1.7795[/C][C]0.038823[/C][/ROW]
[ROW][C]6[/C][C]-0.218567[/C][C]-2.4142[/C][C]0.008629[/C][/ROW]
[ROW][C]7[/C][C]-0.222605[/C][C]-2.4588[/C][C]0.007672[/C][/ROW]
[ROW][C]8[/C][C]-0.136814[/C][C]-1.5112[/C][C]0.066667[/C][/ROW]
[ROW][C]9[/C][C]0.008565[/C][C]0.0946[/C][C]0.462391[/C][/ROW]
[ROW][C]10[/C][C]-0.050067[/C][C]-0.553[/C][C]0.290636[/C][/ROW]
[ROW][C]11[/C][C]-0.068651[/C][C]-0.7583[/C][C]0.224873[/C][/ROW]
[ROW][C]12[/C][C]-0.076916[/C][C]-0.8496[/C][C]0.198614[/C][/ROW]
[ROW][C]13[/C][C]-0.039349[/C][C]-0.4346[/C][C]0.3323[/C][/ROW]
[ROW][C]14[/C][C]0.042172[/C][C]0.4658[/C][C]0.321092[/C][/ROW]
[ROW][C]15[/C][C]0.046734[/C][C]0.5162[/C][C]0.303325[/C][/ROW]
[ROW][C]16[/C][C]-0.031386[/C][C]-0.3467[/C][C]0.36472[/C][/ROW]
[ROW][C]17[/C][C]-0.079668[/C][C]-0.88[/C][C]0.190304[/C][/ROW]
[ROW][C]18[/C][C]-0.112024[/C][C]-1.2373[/C][C]0.109167[/C][/ROW]
[ROW][C]19[/C][C]-0.075061[/C][C]-0.8291[/C][C]0.20434[/C][/ROW]
[ROW][C]20[/C][C]-0.018208[/C][C]-0.2011[/C][C]0.420471[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298919&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298919&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	0.5331	5.8883	0
2	0.171341	1.8925	0.030396
3	-0.063208	-0.6982	0.243203
4	-0.123871	-1.3682	0.086882
5	-0.16111	-1.7795	0.038823
6	-0.218567	-2.4142	0.008629
7	-0.222605	-2.4588	0.007672
8	-0.136814	-1.5112	0.066667
9	0.008565	0.0946	0.462391
10	-0.050067	-0.553	0.290636
11	-0.068651	-0.7583	0.224873
12	-0.076916	-0.8496	0.198614
13	-0.039349	-0.4346	0.3323
14	0.042172	0.4658	0.321092
15	0.046734	0.5162	0.303325
16	-0.031386	-0.3467	0.36472
17	-0.079668	-0.88	0.190304
18	-0.112024	-1.2373	0.109167
19	-0.075061	-0.8291	0.20434
20	-0.018208	-0.2011	0.420471

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.5331	5.8883	0
2	-0.157662	-1.7414	0.042064
3	-0.121634	-1.3435	0.090804
4	-0.010294	-0.1137	0.45483
5	-0.097721	-1.0794	0.141278
6	-0.144298	-1.5938	0.056782
7	-0.069043	-0.7626	0.223585
8	0.007879	0.087	0.465396
9	0.061259	0.6766	0.249962
10	-0.207716	-2.2943	0.011742
11	-0.018138	-0.2003	0.420773
12	-0.049022	-0.5415	0.294588
13	-0.04603	-0.5084	0.30604
14	0.05112	0.5646	0.286677
15	-0.039547	-0.4368	0.33151
16	-0.12369	-1.3662	0.087194
17	-0.067868	-0.7496	0.227462
18	-0.123568	-1.3649	0.087406
19	0.012606	0.1392	0.444744
20	-0.015456	-0.1707	0.432363

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.5331 & 5.8883 & 0 \tabularnewline
2 & -0.157662 & -1.7414 & 0.042064 \tabularnewline
3 & -0.121634 & -1.3435 & 0.090804 \tabularnewline
4 & -0.010294 & -0.1137 & 0.45483 \tabularnewline
5 & -0.097721 & -1.0794 & 0.141278 \tabularnewline
6 & -0.144298 & -1.5938 & 0.056782 \tabularnewline
7 & -0.069043 & -0.7626 & 0.223585 \tabularnewline
8 & 0.007879 & 0.087 & 0.465396 \tabularnewline
9 & 0.061259 & 0.6766 & 0.249962 \tabularnewline
10 & -0.207716 & -2.2943 & 0.011742 \tabularnewline
11 & -0.018138 & -0.2003 & 0.420773 \tabularnewline
12 & -0.049022 & -0.5415 & 0.294588 \tabularnewline
13 & -0.04603 & -0.5084 & 0.30604 \tabularnewline
14 & 0.05112 & 0.5646 & 0.286677 \tabularnewline
15 & -0.039547 & -0.4368 & 0.33151 \tabularnewline
16 & -0.12369 & -1.3662 & 0.087194 \tabularnewline
17 & -0.067868 & -0.7496 & 0.227462 \tabularnewline
18 & -0.123568 & -1.3649 & 0.087406 \tabularnewline
19 & 0.012606 & 0.1392 & 0.444744 \tabularnewline
20 & -0.015456 & -0.1707 & 0.432363 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298919&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]0.5331[/C][C]5.8883[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.157662[/C][C]-1.7414[/C][C]0.042064[/C][/ROW]
[ROW][C]3[/C][C]-0.121634[/C][C]-1.3435[/C][C]0.090804[/C][/ROW]
[ROW][C]4[/C][C]-0.010294[/C][C]-0.1137[/C][C]0.45483[/C][/ROW]
[ROW][C]5[/C][C]-0.097721[/C][C]-1.0794[/C][C]0.141278[/C][/ROW]
[ROW][C]6[/C][C]-0.144298[/C][C]-1.5938[/C][C]0.056782[/C][/ROW]
[ROW][C]7[/C][C]-0.069043[/C][C]-0.7626[/C][C]0.223585[/C][/ROW]
[ROW][C]8[/C][C]0.007879[/C][C]0.087[/C][C]0.465396[/C][/ROW]
[ROW][C]9[/C][C]0.061259[/C][C]0.6766[/C][C]0.249962[/C][/ROW]
[ROW][C]10[/C][C]-0.207716[/C][C]-2.2943[/C][C]0.011742[/C][/ROW]
[ROW][C]11[/C][C]-0.018138[/C][C]-0.2003[/C][C]0.420773[/C][/ROW]
[ROW][C]12[/C][C]-0.049022[/C][C]-0.5415[/C][C]0.294588[/C][/ROW]
[ROW][C]13[/C][C]-0.04603[/C][C]-0.5084[/C][C]0.30604[/C][/ROW]
[ROW][C]14[/C][C]0.05112[/C][C]0.5646[/C][C]0.286677[/C][/ROW]
[ROW][C]15[/C][C]-0.039547[/C][C]-0.4368[/C][C]0.33151[/C][/ROW]
[ROW][C]16[/C][C]-0.12369[/C][C]-1.3662[/C][C]0.087194[/C][/ROW]
[ROW][C]17[/C][C]-0.067868[/C][C]-0.7496[/C][C]0.227462[/C][/ROW]
[ROW][C]18[/C][C]-0.123568[/C][C]-1.3649[/C][C]0.087406[/C][/ROW]
[ROW][C]19[/C][C]0.012606[/C][C]0.1392[/C][C]0.444744[/C][/ROW]
[ROW][C]20[/C][C]-0.015456[/C][C]-0.1707[/C][C]0.432363[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298919&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298919&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	0.5331	5.8883	0
2	-0.157662	-1.7414	0.042064
3	-0.121634	-1.3435	0.090804
4	-0.010294	-0.1137	0.45483
5	-0.097721	-1.0794	0.141278
6	-0.144298	-1.5938	0.056782
7	-0.069043	-0.7626	0.223585
8	0.007879	0.087	0.465396
9	0.061259	0.6766	0.249962
10	-0.207716	-2.2943	0.011742
11	-0.018138	-0.2003	0.420773
12	-0.049022	-0.5415	0.294588
13	-0.04603	-0.5084	0.30604
14	0.05112	0.5646	0.286677
15	-0.039547	-0.4368	0.33151
16	-0.12369	-1.3662	0.087194
17	-0.067868	-0.7496	0.227462
18	-0.123568	-1.3649	0.087406
19	0.012606	0.1392	0.444744
20	-0.015456	-0.1707	0.432363

Figure 1

PNG link

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 = 1 ; 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