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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 17 Nov 2016 10:19:45 +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/t1479374438k37f4w4owhho4ov.htm/, Retrieved Sun, 05 May 2024 16:41:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296792, Retrieved Sun, 05 May 2024 16:41:42 +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 09:19:45] [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=296792&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=296792&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296792&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	0.931822	6.181	0
2	0.85896	5.6977	0
3	0.786044	5.214	2e-06
4	0.712803	4.7282	1.2e-05
5	0.65059	4.3155	4.4e-05
6	0.58224	3.8621	0.000183
7	0.512345	3.3985	0.000724
8	0.444554	2.9488	0.002546
9	0.373013	2.4743	0.008639
10	0.308096	2.0437	0.0235
11	0.2493	1.6537	0.052656
12	0.193656	1.2846	0.102832
13	0.117463	0.7792	0.220028
14	0.053855	0.3572	0.361313
15	-0.000259	-0.0017	0.49932
16	-0.050873	-0.3375	0.368689

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.931822 & 6.181 & 0 \tabularnewline
2 & 0.85896 & 5.6977 & 0 \tabularnewline
3 & 0.786044 & 5.214 & 2e-06 \tabularnewline
4 & 0.712803 & 4.7282 & 1.2e-05 \tabularnewline
5 & 0.65059 & 4.3155 & 4.4e-05 \tabularnewline
6 & 0.58224 & 3.8621 & 0.000183 \tabularnewline
7 & 0.512345 & 3.3985 & 0.000724 \tabularnewline
8 & 0.444554 & 2.9488 & 0.002546 \tabularnewline
9 & 0.373013 & 2.4743 & 0.008639 \tabularnewline
10 & 0.308096 & 2.0437 & 0.0235 \tabularnewline
11 & 0.2493 & 1.6537 & 0.052656 \tabularnewline
12 & 0.193656 & 1.2846 & 0.102832 \tabularnewline
13 & 0.117463 & 0.7792 & 0.220028 \tabularnewline
14 & 0.053855 & 0.3572 & 0.361313 \tabularnewline
15 & -0.000259 & -0.0017 & 0.49932 \tabularnewline
16 & -0.050873 & -0.3375 & 0.368689 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296792&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]0.931822[/C][C]6.181[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.85896[/C][C]5.6977[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.786044[/C][C]5.214[/C][C]2e-06[/C][/ROW]
[ROW][C]4[/C][C]0.712803[/C][C]4.7282[/C][C]1.2e-05[/C][/ROW]
[ROW][C]5[/C][C]0.65059[/C][C]4.3155[/C][C]4.4e-05[/C][/ROW]
[ROW][C]6[/C][C]0.58224[/C][C]3.8621[/C][C]0.000183[/C][/ROW]
[ROW][C]7[/C][C]0.512345[/C][C]3.3985[/C][C]0.000724[/C][/ROW]
[ROW][C]8[/C][C]0.444554[/C][C]2.9488[/C][C]0.002546[/C][/ROW]
[ROW][C]9[/C][C]0.373013[/C][C]2.4743[/C][C]0.008639[/C][/ROW]
[ROW][C]10[/C][C]0.308096[/C][C]2.0437[/C][C]0.0235[/C][/ROW]
[ROW][C]11[/C][C]0.2493[/C][C]1.6537[/C][C]0.052656[/C][/ROW]
[ROW][C]12[/C][C]0.193656[/C][C]1.2846[/C][C]0.102832[/C][/ROW]
[ROW][C]13[/C][C]0.117463[/C][C]0.7792[/C][C]0.220028[/C][/ROW]
[ROW][C]14[/C][C]0.053855[/C][C]0.3572[/C][C]0.361313[/C][/ROW]
[ROW][C]15[/C][C]-0.000259[/C][C]-0.0017[/C][C]0.49932[/C][/ROW]
[ROW][C]16[/C][C]-0.050873[/C][C]-0.3375[/C][C]0.368689[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296792&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296792&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	0.931822	6.181	0
2	0.85896	5.6977	0
3	0.786044	5.214	2e-06
4	0.712803	4.7282	1.2e-05
5	0.65059	4.3155	4.4e-05
6	0.58224	3.8621	0.000183
7	0.512345	3.3985	0.000724
8	0.444554	2.9488	0.002546
9	0.373013	2.4743	0.008639
10	0.308096	2.0437	0.0235
11	0.2493	1.6537	0.052656
12	0.193656	1.2846	0.102832
13	0.117463	0.7792	0.220028
14	0.053855	0.3572	0.361313
15	-0.000259	-0.0017	0.49932
16	-0.050873	-0.3375	0.368689

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.931822	6.181	0
2	-0.070857	-0.47	0.320333
3	-0.038475	-0.2552	0.399872
4	-0.043319	-0.2873	0.387598
5	0.041822	0.2774	0.39138
6	-0.090637	-0.6012	0.275391
7	-0.051791	-0.3435	0.366413
8	-0.029946	-0.1986	0.421731
9	-0.069924	-0.4638	0.322531
10	-0.006264	-0.0416	0.483523
11	-0.005171	-0.0343	0.486395
12	-0.023032	-0.1528	0.439638
13	-0.216181	-1.434	0.079323
14	0.055677	0.3693	0.356832
15	0.011802	0.0783	0.468979
16	-0.035526	-0.2357	0.407397

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.931822 & 6.181 & 0 \tabularnewline
2 & -0.070857 & -0.47 & 0.320333 \tabularnewline
3 & -0.038475 & -0.2552 & 0.399872 \tabularnewline
4 & -0.043319 & -0.2873 & 0.387598 \tabularnewline
5 & 0.041822 & 0.2774 & 0.39138 \tabularnewline
6 & -0.090637 & -0.6012 & 0.275391 \tabularnewline
7 & -0.051791 & -0.3435 & 0.366413 \tabularnewline
8 & -0.029946 & -0.1986 & 0.421731 \tabularnewline
9 & -0.069924 & -0.4638 & 0.322531 \tabularnewline
10 & -0.006264 & -0.0416 & 0.483523 \tabularnewline
11 & -0.005171 & -0.0343 & 0.486395 \tabularnewline
12 & -0.023032 & -0.1528 & 0.439638 \tabularnewline
13 & -0.216181 & -1.434 & 0.079323 \tabularnewline
14 & 0.055677 & 0.3693 & 0.356832 \tabularnewline
15 & 0.011802 & 0.0783 & 0.468979 \tabularnewline
16 & -0.035526 & -0.2357 & 0.407397 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296792&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]0.931822[/C][C]6.181[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.070857[/C][C]-0.47[/C][C]0.320333[/C][/ROW]
[ROW][C]3[/C][C]-0.038475[/C][C]-0.2552[/C][C]0.399872[/C][/ROW]
[ROW][C]4[/C][C]-0.043319[/C][C]-0.2873[/C][C]0.387598[/C][/ROW]
[ROW][C]5[/C][C]0.041822[/C][C]0.2774[/C][C]0.39138[/C][/ROW]
[ROW][C]6[/C][C]-0.090637[/C][C]-0.6012[/C][C]0.275391[/C][/ROW]
[ROW][C]7[/C][C]-0.051791[/C][C]-0.3435[/C][C]0.366413[/C][/ROW]
[ROW][C]8[/C][C]-0.029946[/C][C]-0.1986[/C][C]0.421731[/C][/ROW]
[ROW][C]9[/C][C]-0.069924[/C][C]-0.4638[/C][C]0.322531[/C][/ROW]
[ROW][C]10[/C][C]-0.006264[/C][C]-0.0416[/C][C]0.483523[/C][/ROW]
[ROW][C]11[/C][C]-0.005171[/C][C]-0.0343[/C][C]0.486395[/C][/ROW]
[ROW][C]12[/C][C]-0.023032[/C][C]-0.1528[/C][C]0.439638[/C][/ROW]
[ROW][C]13[/C][C]-0.216181[/C][C]-1.434[/C][C]0.079323[/C][/ROW]
[ROW][C]14[/C][C]0.055677[/C][C]0.3693[/C][C]0.356832[/C][/ROW]
[ROW][C]15[/C][C]0.011802[/C][C]0.0783[/C][C]0.468979[/C][/ROW]
[ROW][C]16[/C][C]-0.035526[/C][C]-0.2357[/C][C]0.407397[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296792&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296792&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	0.931822	6.181	0
2	-0.070857	-0.47	0.320333
3	-0.038475	-0.2552	0.399872
4	-0.043319	-0.2873	0.387598
5	0.041822	0.2774	0.39138
6	-0.090637	-0.6012	0.275391
7	-0.051791	-0.3435	0.366413
8	-0.029946	-0.1986	0.421731
9	-0.069924	-0.4638	0.322531
10	-0.006264	-0.0416	0.483523
11	-0.005171	-0.0343	0.486395
12	-0.023032	-0.1528	0.439638
13	-0.216181	-1.434	0.079323
14	0.055677	0.3693	0.356832
15	0.011802	0.0783	0.468979
16	-0.035526	-0.2357	0.407397

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 = 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')

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Input Parameters & R Code