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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 20 Jan 2019 16:50:07 +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/2019/Jan/20/t1547999418kq9hy5jx0mtxkkk.htm/, Retrieved Fri, 03 May 2024 04:49:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=316507, Retrieved Fri, 03 May 2024 04:49:26 +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] [] [2019-01-20 15:50:07] [f89b53e457d92bd7c0c6f0d06c3b79f6] [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	2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316507&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]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=316507&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316507&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	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.95	-4.2485	0.000197
2	0.9	4.0249	0.000332
3	-0.85	-3.8013	0.00056
4	0.8	3.5777	0.000942
5	-0.75	-3.3541	0.001579
6	0.7	3.1305	0.002634
7	-0.65	-2.9069	0.004359
8	0.6	2.6833	0.007145
9	-0.55	-2.4597	0.011569
10	0.5	2.2361	0.018452
11	-0.45	-2.0125	0.028917
12	0.4	1.7889	0.044398
13	-0.35	-1.5652	0.066605

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.95 & -4.2485 & 0.000197 \tabularnewline
2 & 0.9 & 4.0249 & 0.000332 \tabularnewline
3 & -0.85 & -3.8013 & 0.00056 \tabularnewline
4 & 0.8 & 3.5777 & 0.000942 \tabularnewline
5 & -0.75 & -3.3541 & 0.001579 \tabularnewline
6 & 0.7 & 3.1305 & 0.002634 \tabularnewline
7 & -0.65 & -2.9069 & 0.004359 \tabularnewline
8 & 0.6 & 2.6833 & 0.007145 \tabularnewline
9 & -0.55 & -2.4597 & 0.011569 \tabularnewline
10 & 0.5 & 2.2361 & 0.018452 \tabularnewline
11 & -0.45 & -2.0125 & 0.028917 \tabularnewline
12 & 0.4 & 1.7889 & 0.044398 \tabularnewline
13 & -0.35 & -1.5652 & 0.066605 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316507&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]-0.95[/C][C]-4.2485[/C][C]0.000197[/C][/ROW]
[ROW][C]2[/C][C]0.9[/C][C]4.0249[/C][C]0.000332[/C][/ROW]
[ROW][C]3[/C][C]-0.85[/C][C]-3.8013[/C][C]0.00056[/C][/ROW]
[ROW][C]4[/C][C]0.8[/C][C]3.5777[/C][C]0.000942[/C][/ROW]
[ROW][C]5[/C][C]-0.75[/C][C]-3.3541[/C][C]0.001579[/C][/ROW]
[ROW][C]6[/C][C]0.7[/C][C]3.1305[/C][C]0.002634[/C][/ROW]
[ROW][C]7[/C][C]-0.65[/C][C]-2.9069[/C][C]0.004359[/C][/ROW]
[ROW][C]8[/C][C]0.6[/C][C]2.6833[/C][C]0.007145[/C][/ROW]
[ROW][C]9[/C][C]-0.55[/C][C]-2.4597[/C][C]0.011569[/C][/ROW]
[ROW][C]10[/C][C]0.5[/C][C]2.2361[/C][C]0.018452[/C][/ROW]
[ROW][C]11[/C][C]-0.45[/C][C]-2.0125[/C][C]0.028917[/C][/ROW]
[ROW][C]12[/C][C]0.4[/C][C]1.7889[/C][C]0.044398[/C][/ROW]
[ROW][C]13[/C][C]-0.35[/C][C]-1.5652[/C][C]0.066605[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316507&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316507&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	-0.95	-4.2485	0.000197
2	0.9	4.0249	0.000332
3	-0.85	-3.8013	0.00056
4	0.8	3.5777	0.000942
5	-0.75	-3.3541	0.001579
6	0.7	3.1305	0.002634
7	-0.65	-2.9069	0.004359
8	0.6	2.6833	0.007145
9	-0.55	-2.4597	0.011569
10	0.5	2.2361	0.018452
11	-0.45	-2.0125	0.028917
12	0.4	1.7889	0.044398
13	-0.35	-1.5652	0.066605

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.95	-4.2485	0.000197
2	-0.025641	-0.1147	0.454925
3	0.026316	0.1177	0.453744
4	-0.027027	-0.1209	0.452501
5	0.027778	0.1242	0.451188
6	-0.028571	-0.1278	0.449801
7	0.029412	0.1315	0.448334
8	-0.030303	-0.1355	0.446778
9	0.03125	0.1398	0.445126
10	-0.032258	-0.1443	0.443369
11	0.033333	0.1491	0.441495
12	-0.034483	-0.1542	0.439494
13	0.035714	0.1597	0.437352

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.95 & -4.2485 & 0.000197 \tabularnewline
2 & -0.025641 & -0.1147 & 0.454925 \tabularnewline
3 & 0.026316 & 0.1177 & 0.453744 \tabularnewline
4 & -0.027027 & -0.1209 & 0.452501 \tabularnewline
5 & 0.027778 & 0.1242 & 0.451188 \tabularnewline
6 & -0.028571 & -0.1278 & 0.449801 \tabularnewline
7 & 0.029412 & 0.1315 & 0.448334 \tabularnewline
8 & -0.030303 & -0.1355 & 0.446778 \tabularnewline
9 & 0.03125 & 0.1398 & 0.445126 \tabularnewline
10 & -0.032258 & -0.1443 & 0.443369 \tabularnewline
11 & 0.033333 & 0.1491 & 0.441495 \tabularnewline
12 & -0.034483 & -0.1542 & 0.439494 \tabularnewline
13 & 0.035714 & 0.1597 & 0.437352 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316507&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]-0.95[/C][C]-4.2485[/C][C]0.000197[/C][/ROW]
[ROW][C]2[/C][C]-0.025641[/C][C]-0.1147[/C][C]0.454925[/C][/ROW]
[ROW][C]3[/C][C]0.026316[/C][C]0.1177[/C][C]0.453744[/C][/ROW]
[ROW][C]4[/C][C]-0.027027[/C][C]-0.1209[/C][C]0.452501[/C][/ROW]
[ROW][C]5[/C][C]0.027778[/C][C]0.1242[/C][C]0.451188[/C][/ROW]
[ROW][C]6[/C][C]-0.028571[/C][C]-0.1278[/C][C]0.449801[/C][/ROW]
[ROW][C]7[/C][C]0.029412[/C][C]0.1315[/C][C]0.448334[/C][/ROW]
[ROW][C]8[/C][C]-0.030303[/C][C]-0.1355[/C][C]0.446778[/C][/ROW]
[ROW][C]9[/C][C]0.03125[/C][C]0.1398[/C][C]0.445126[/C][/ROW]
[ROW][C]10[/C][C]-0.032258[/C][C]-0.1443[/C][C]0.443369[/C][/ROW]
[ROW][C]11[/C][C]0.033333[/C][C]0.1491[/C][C]0.441495[/C][/ROW]
[ROW][C]12[/C][C]-0.034483[/C][C]-0.1542[/C][C]0.439494[/C][/ROW]
[ROW][C]13[/C][C]0.035714[/C][C]0.1597[/C][C]0.437352[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316507&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316507&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	-0.95	-4.2485	0.000197
2	-0.025641	-0.1147	0.454925
3	0.026316	0.1177	0.453744
4	-0.027027	-0.1209	0.452501
5	0.027778	0.1242	0.451188
6	-0.028571	-0.1278	0.449801
7	0.029412	0.1315	0.448334
8	-0.030303	-0.1355	0.446778
9	0.03125	0.1398	0.445126
10	-0.032258	-0.1443	0.443369
11	0.033333	0.1491	0.441495
12	-0.034483	-0.1542	0.439494
13	0.035714	0.1597	0.437352

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 = 0.95 ; par2 = 50 ;

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