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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 17 Nov 2016 10:21:19 +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/Nov/17/t1479374505ibh8ruk89u98e3x.htm/, Retrieved Sun, 05 May 2024 18:19:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296793, Retrieved Sun, 05 May 2024 18:19:35 +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] [] [2016-11-17 09:21:19] [219800a2f11ddd28e3280d87dbde8c8d] [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=296793&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=296793&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296793&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	-0.138438	-0.9078	0.184521
2	0.040885	0.2681	0.394953
3	0.120525	0.7903	0.216835
4	-0.009876	-0.0648	0.474333
5	0.240067	1.5742	0.061383
6	-0.037931	-0.2487	0.402376
7	-0.127506	-0.8361	0.203857
8	0.220429	1.4454	0.07779
9	-0.111731	-0.7327	0.233869
10	0.111643	0.7321	0.234041
11	0.045813	0.3004	0.382654
12	0.001734	0.0114	0.495489
13	0.091859	0.6024	0.275049
14	-0.136033	-0.892	0.188671
15	0.114582	0.7514	0.228262
16	-0.061552	-0.4036	0.344244

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.138438 & -0.9078 & 0.184521 \tabularnewline
2 & 0.040885 & 0.2681 & 0.394953 \tabularnewline
3 & 0.120525 & 0.7903 & 0.216835 \tabularnewline
4 & -0.009876 & -0.0648 & 0.474333 \tabularnewline
5 & 0.240067 & 1.5742 & 0.061383 \tabularnewline
6 & -0.037931 & -0.2487 & 0.402376 \tabularnewline
7 & -0.127506 & -0.8361 & 0.203857 \tabularnewline
8 & 0.220429 & 1.4454 & 0.07779 \tabularnewline
9 & -0.111731 & -0.7327 & 0.233869 \tabularnewline
10 & 0.111643 & 0.7321 & 0.234041 \tabularnewline
11 & 0.045813 & 0.3004 & 0.382654 \tabularnewline
12 & 0.001734 & 0.0114 & 0.495489 \tabularnewline
13 & 0.091859 & 0.6024 & 0.275049 \tabularnewline
14 & -0.136033 & -0.892 & 0.188671 \tabularnewline
15 & 0.114582 & 0.7514 & 0.228262 \tabularnewline
16 & -0.061552 & -0.4036 & 0.344244 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296793&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]-0.138438[/C][C]-0.9078[/C][C]0.184521[/C][/ROW]
[ROW][C]2[/C][C]0.040885[/C][C]0.2681[/C][C]0.394953[/C][/ROW]
[ROW][C]3[/C][C]0.120525[/C][C]0.7903[/C][C]0.216835[/C][/ROW]
[ROW][C]4[/C][C]-0.009876[/C][C]-0.0648[/C][C]0.474333[/C][/ROW]
[ROW][C]5[/C][C]0.240067[/C][C]1.5742[/C][C]0.061383[/C][/ROW]
[ROW][C]6[/C][C]-0.037931[/C][C]-0.2487[/C][C]0.402376[/C][/ROW]
[ROW][C]7[/C][C]-0.127506[/C][C]-0.8361[/C][C]0.203857[/C][/ROW]
[ROW][C]8[/C][C]0.220429[/C][C]1.4454[/C][C]0.07779[/C][/ROW]
[ROW][C]9[/C][C]-0.111731[/C][C]-0.7327[/C][C]0.233869[/C][/ROW]
[ROW][C]10[/C][C]0.111643[/C][C]0.7321[/C][C]0.234041[/C][/ROW]
[ROW][C]11[/C][C]0.045813[/C][C]0.3004[/C][C]0.382654[/C][/ROW]
[ROW][C]12[/C][C]0.001734[/C][C]0.0114[/C][C]0.495489[/C][/ROW]
[ROW][C]13[/C][C]0.091859[/C][C]0.6024[/C][C]0.275049[/C][/ROW]
[ROW][C]14[/C][C]-0.136033[/C][C]-0.892[/C][C]0.188671[/C][/ROW]
[ROW][C]15[/C][C]0.114582[/C][C]0.7514[/C][C]0.228262[/C][/ROW]
[ROW][C]16[/C][C]-0.061552[/C][C]-0.4036[/C][C]0.344244[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296793&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296793&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	-0.138438	-0.9078	0.184521
2	0.040885	0.2681	0.394953
3	0.120525	0.7903	0.216835
4	-0.009876	-0.0648	0.474333
5	0.240067	1.5742	0.061383
6	-0.037931	-0.2487	0.402376
7	-0.127506	-0.8361	0.203857
8	0.220429	1.4454	0.07779
9	-0.111731	-0.7327	0.233869
10	0.111643	0.7321	0.234041
11	0.045813	0.3004	0.382654
12	0.001734	0.0114	0.495489
13	0.091859	0.6024	0.275049
14	-0.136033	-0.892	0.188671
15	0.114582	0.7514	0.228262
16	-0.061552	-0.4036	0.344244

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.138438	-0.9078	0.184521
2	0.022144	0.1452	0.442613
3	0.131713	0.8637	0.196273
4	0.024281	0.1592	0.437119
5	0.24077	1.5788	0.060852
6	0.014666	0.0962	0.461915
7	-0.163524	-1.0723	0.144783
8	0.136381	0.8943	0.188068
9	-0.071035	-0.4658	0.321852
10	0.061245	0.4016	0.344981
11	0.063808	0.4184	0.338863
12	0.084174	0.552	0.291914
13	0.00181	0.0119	0.495293
14	-0.140013	-0.9181	0.181837
15	0.086524	0.5674	0.286705
16	-0.138577	-0.9087	0.184284

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.138438 & -0.9078 & 0.184521 \tabularnewline
2 & 0.022144 & 0.1452 & 0.442613 \tabularnewline
3 & 0.131713 & 0.8637 & 0.196273 \tabularnewline
4 & 0.024281 & 0.1592 & 0.437119 \tabularnewline
5 & 0.24077 & 1.5788 & 0.060852 \tabularnewline
6 & 0.014666 & 0.0962 & 0.461915 \tabularnewline
7 & -0.163524 & -1.0723 & 0.144783 \tabularnewline
8 & 0.136381 & 0.8943 & 0.188068 \tabularnewline
9 & -0.071035 & -0.4658 & 0.321852 \tabularnewline
10 & 0.061245 & 0.4016 & 0.344981 \tabularnewline
11 & 0.063808 & 0.4184 & 0.338863 \tabularnewline
12 & 0.084174 & 0.552 & 0.291914 \tabularnewline
13 & 0.00181 & 0.0119 & 0.495293 \tabularnewline
14 & -0.140013 & -0.9181 & 0.181837 \tabularnewline
15 & 0.086524 & 0.5674 & 0.286705 \tabularnewline
16 & -0.138577 & -0.9087 & 0.184284 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296793&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]-0.138438[/C][C]-0.9078[/C][C]0.184521[/C][/ROW]
[ROW][C]2[/C][C]0.022144[/C][C]0.1452[/C][C]0.442613[/C][/ROW]
[ROW][C]3[/C][C]0.131713[/C][C]0.8637[/C][C]0.196273[/C][/ROW]
[ROW][C]4[/C][C]0.024281[/C][C]0.1592[/C][C]0.437119[/C][/ROW]
[ROW][C]5[/C][C]0.24077[/C][C]1.5788[/C][C]0.060852[/C][/ROW]
[ROW][C]6[/C][C]0.014666[/C][C]0.0962[/C][C]0.461915[/C][/ROW]
[ROW][C]7[/C][C]-0.163524[/C][C]-1.0723[/C][C]0.144783[/C][/ROW]
[ROW][C]8[/C][C]0.136381[/C][C]0.8943[/C][C]0.188068[/C][/ROW]
[ROW][C]9[/C][C]-0.071035[/C][C]-0.4658[/C][C]0.321852[/C][/ROW]
[ROW][C]10[/C][C]0.061245[/C][C]0.4016[/C][C]0.344981[/C][/ROW]
[ROW][C]11[/C][C]0.063808[/C][C]0.4184[/C][C]0.338863[/C][/ROW]
[ROW][C]12[/C][C]0.084174[/C][C]0.552[/C][C]0.291914[/C][/ROW]
[ROW][C]13[/C][C]0.00181[/C][C]0.0119[/C][C]0.495293[/C][/ROW]
[ROW][C]14[/C][C]-0.140013[/C][C]-0.9181[/C][C]0.181837[/C][/ROW]
[ROW][C]15[/C][C]0.086524[/C][C]0.5674[/C][C]0.286705[/C][/ROW]
[ROW][C]16[/C][C]-0.138577[/C][C]-0.9087[/C][C]0.184284[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296793&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296793&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	-0.138438	-0.9078	0.184521
2	0.022144	0.1452	0.442613
3	0.131713	0.8637	0.196273
4	0.024281	0.1592	0.437119
5	0.24077	1.5788	0.060852
6	0.014666	0.0962	0.461915
7	-0.163524	-1.0723	0.144783
8	0.136381	0.8943	0.188068
9	-0.071035	-0.4658	0.321852
10	0.061245	0.4016	0.344981
11	0.063808	0.4184	0.338863
12	0.084174	0.552	0.291914
13	0.00181	0.0119	0.495293
14	-0.140013	-0.9181	0.181837
15	0.086524	0.5674	0.286705
16	-0.138577	-0.9087	0.184284

Figure 1

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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 = 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')

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