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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 21 Dec 2016 11:42:39 +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/21/t1482316983h6ofvlsjkimhl04.htm/, Retrieved Tue, 07 May 2024 01:31:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302129, Retrieved Tue, 07 May 2024 01:31:48 +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] [] [2016-12-21 10:42:39] [bde5266f17215258f6d7c4cd7e531432] [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=302129&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=302129&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302129&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	-0.121784	-1.3341	0.092352
2	0.028296	0.31	0.378563
3	0.320942	3.5157	0.00031
4	-0.100839	-1.1046	0.135764
5	0.049876	0.5464	0.292915
6	0.297371	3.2575	0.000731
7	-0.188708	-2.0672	0.020433
8	0.171561	1.8794	0.03131
9	0.25241	2.765	0.003296
10	-0.052159	-0.5714	0.284408
11	0.200437	2.1957	0.015019
12	-0.069954	-0.7663	0.222498
13	-0.071202	-0.78	0.21847
14	0.134016	1.4681	0.07235
15	-0.01332	-0.1459	0.442117
16	-0.162863	-1.7841	0.03847
17	0.168088	1.8413	0.034023
18	-0.091661	-1.0041	0.158676
19	-0.069041	-0.7563	0.225475
20	0.177893	1.9487	0.026832
21	-0.187808	-2.0573	0.020911

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.121784 & -1.3341 & 0.092352 \tabularnewline
2 & 0.028296 & 0.31 & 0.378563 \tabularnewline
3 & 0.320942 & 3.5157 & 0.00031 \tabularnewline
4 & -0.100839 & -1.1046 & 0.135764 \tabularnewline
5 & 0.049876 & 0.5464 & 0.292915 \tabularnewline
6 & 0.297371 & 3.2575 & 0.000731 \tabularnewline
7 & -0.188708 & -2.0672 & 0.020433 \tabularnewline
8 & 0.171561 & 1.8794 & 0.03131 \tabularnewline
9 & 0.25241 & 2.765 & 0.003296 \tabularnewline
10 & -0.052159 & -0.5714 & 0.284408 \tabularnewline
11 & 0.200437 & 2.1957 & 0.015019 \tabularnewline
12 & -0.069954 & -0.7663 & 0.222498 \tabularnewline
13 & -0.071202 & -0.78 & 0.21847 \tabularnewline
14 & 0.134016 & 1.4681 & 0.07235 \tabularnewline
15 & -0.01332 & -0.1459 & 0.442117 \tabularnewline
16 & -0.162863 & -1.7841 & 0.03847 \tabularnewline
17 & 0.168088 & 1.8413 & 0.034023 \tabularnewline
18 & -0.091661 & -1.0041 & 0.158676 \tabularnewline
19 & -0.069041 & -0.7563 & 0.225475 \tabularnewline
20 & 0.177893 & 1.9487 & 0.026832 \tabularnewline
21 & -0.187808 & -2.0573 & 0.020911 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302129&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]-0.121784[/C][C]-1.3341[/C][C]0.092352[/C][/ROW]
[ROW][C]2[/C][C]0.028296[/C][C]0.31[/C][C]0.378563[/C][/ROW]
[ROW][C]3[/C][C]0.320942[/C][C]3.5157[/C][C]0.00031[/C][/ROW]
[ROW][C]4[/C][C]-0.100839[/C][C]-1.1046[/C][C]0.135764[/C][/ROW]
[ROW][C]5[/C][C]0.049876[/C][C]0.5464[/C][C]0.292915[/C][/ROW]
[ROW][C]6[/C][C]0.297371[/C][C]3.2575[/C][C]0.000731[/C][/ROW]
[ROW][C]7[/C][C]-0.188708[/C][C]-2.0672[/C][C]0.020433[/C][/ROW]
[ROW][C]8[/C][C]0.171561[/C][C]1.8794[/C][C]0.03131[/C][/ROW]
[ROW][C]9[/C][C]0.25241[/C][C]2.765[/C][C]0.003296[/C][/ROW]
[ROW][C]10[/C][C]-0.052159[/C][C]-0.5714[/C][C]0.284408[/C][/ROW]
[ROW][C]11[/C][C]0.200437[/C][C]2.1957[/C][C]0.015019[/C][/ROW]
[ROW][C]12[/C][C]-0.069954[/C][C]-0.7663[/C][C]0.222498[/C][/ROW]
[ROW][C]13[/C][C]-0.071202[/C][C]-0.78[/C][C]0.21847[/C][/ROW]
[ROW][C]14[/C][C]0.134016[/C][C]1.4681[/C][C]0.07235[/C][/ROW]
[ROW][C]15[/C][C]-0.01332[/C][C]-0.1459[/C][C]0.442117[/C][/ROW]
[ROW][C]16[/C][C]-0.162863[/C][C]-1.7841[/C][C]0.03847[/C][/ROW]
[ROW][C]17[/C][C]0.168088[/C][C]1.8413[/C][C]0.034023[/C][/ROW]
[ROW][C]18[/C][C]-0.091661[/C][C]-1.0041[/C][C]0.158676[/C][/ROW]
[ROW][C]19[/C][C]-0.069041[/C][C]-0.7563[/C][C]0.225475[/C][/ROW]
[ROW][C]20[/C][C]0.177893[/C][C]1.9487[/C][C]0.026832[/C][/ROW]
[ROW][C]21[/C][C]-0.187808[/C][C]-2.0573[/C][C]0.020911[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302129&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302129&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	-0.121784	-1.3341	0.092352
2	0.028296	0.31	0.378563
3	0.320942	3.5157	0.00031
4	-0.100839	-1.1046	0.135764
5	0.049876	0.5464	0.292915
6	0.297371	3.2575	0.000731
7	-0.188708	-2.0672	0.020433
8	0.171561	1.8794	0.03131
9	0.25241	2.765	0.003296
10	-0.052159	-0.5714	0.284408
11	0.200437	2.1957	0.015019
12	-0.069954	-0.7663	0.222498
13	-0.071202	-0.78	0.21847
14	0.134016	1.4681	0.07235
15	-0.01332	-0.1459	0.442117
16	-0.162863	-1.7841	0.03847
17	0.168088	1.8413	0.034023
18	-0.091661	-1.0041	0.158676
19	-0.069041	-0.7563	0.225475
20	0.177893	1.9487	0.026832
21	-0.187808	-2.0573	0.020911

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.121784	-1.3341	0.092352
2	0.013667	0.1497	0.440621
3	0.330975	3.6257	0.000212
4	-0.025128	-0.2753	0.391792
5	0.009392	0.1029	0.459114
6	0.23406	2.564	0.005791
7	-0.111104	-1.2171	0.112981
8	0.109014	1.1942	0.117381
9	0.186272	2.0405	0.021747
10	0.095873	1.0502	0.14786
11	0.108245	1.1858	0.119029
12	-0.231779	-2.539	0.006198
13	-0.060442	-0.6621	0.254586
14	-0.029519	-0.3234	0.37349
15	0.014185	0.1554	0.438387
16	-0.170987	-1.8731	0.031746
17	0.003113	0.0341	0.486427
18	-0.019213	-0.2105	0.416831
19	-0.126555	-1.3863	0.084106
20	0.090599	0.9925	0.161485
21	-0.070321	-0.7703	0.221309

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.121784 & -1.3341 & 0.092352 \tabularnewline
2 & 0.013667 & 0.1497 & 0.440621 \tabularnewline
3 & 0.330975 & 3.6257 & 0.000212 \tabularnewline
4 & -0.025128 & -0.2753 & 0.391792 \tabularnewline
5 & 0.009392 & 0.1029 & 0.459114 \tabularnewline
6 & 0.23406 & 2.564 & 0.005791 \tabularnewline
7 & -0.111104 & -1.2171 & 0.112981 \tabularnewline
8 & 0.109014 & 1.1942 & 0.117381 \tabularnewline
9 & 0.186272 & 2.0405 & 0.021747 \tabularnewline
10 & 0.095873 & 1.0502 & 0.14786 \tabularnewline
11 & 0.108245 & 1.1858 & 0.119029 \tabularnewline
12 & -0.231779 & -2.539 & 0.006198 \tabularnewline
13 & -0.060442 & -0.6621 & 0.254586 \tabularnewline
14 & -0.029519 & -0.3234 & 0.37349 \tabularnewline
15 & 0.014185 & 0.1554 & 0.438387 \tabularnewline
16 & -0.170987 & -1.8731 & 0.031746 \tabularnewline
17 & 0.003113 & 0.0341 & 0.486427 \tabularnewline
18 & -0.019213 & -0.2105 & 0.416831 \tabularnewline
19 & -0.126555 & -1.3863 & 0.084106 \tabularnewline
20 & 0.090599 & 0.9925 & 0.161485 \tabularnewline
21 & -0.070321 & -0.7703 & 0.221309 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302129&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]-0.121784[/C][C]-1.3341[/C][C]0.092352[/C][/ROW]
[ROW][C]2[/C][C]0.013667[/C][C]0.1497[/C][C]0.440621[/C][/ROW]
[ROW][C]3[/C][C]0.330975[/C][C]3.6257[/C][C]0.000212[/C][/ROW]
[ROW][C]4[/C][C]-0.025128[/C][C]-0.2753[/C][C]0.391792[/C][/ROW]
[ROW][C]5[/C][C]0.009392[/C][C]0.1029[/C][C]0.459114[/C][/ROW]
[ROW][C]6[/C][C]0.23406[/C][C]2.564[/C][C]0.005791[/C][/ROW]
[ROW][C]7[/C][C]-0.111104[/C][C]-1.2171[/C][C]0.112981[/C][/ROW]
[ROW][C]8[/C][C]0.109014[/C][C]1.1942[/C][C]0.117381[/C][/ROW]
[ROW][C]9[/C][C]0.186272[/C][C]2.0405[/C][C]0.021747[/C][/ROW]
[ROW][C]10[/C][C]0.095873[/C][C]1.0502[/C][C]0.14786[/C][/ROW]
[ROW][C]11[/C][C]0.108245[/C][C]1.1858[/C][C]0.119029[/C][/ROW]
[ROW][C]12[/C][C]-0.231779[/C][C]-2.539[/C][C]0.006198[/C][/ROW]
[ROW][C]13[/C][C]-0.060442[/C][C]-0.6621[/C][C]0.254586[/C][/ROW]
[ROW][C]14[/C][C]-0.029519[/C][C]-0.3234[/C][C]0.37349[/C][/ROW]
[ROW][C]15[/C][C]0.014185[/C][C]0.1554[/C][C]0.438387[/C][/ROW]
[ROW][C]16[/C][C]-0.170987[/C][C]-1.8731[/C][C]0.031746[/C][/ROW]
[ROW][C]17[/C][C]0.003113[/C][C]0.0341[/C][C]0.486427[/C][/ROW]
[ROW][C]18[/C][C]-0.019213[/C][C]-0.2105[/C][C]0.416831[/C][/ROW]
[ROW][C]19[/C][C]-0.126555[/C][C]-1.3863[/C][C]0.084106[/C][/ROW]
[ROW][C]20[/C][C]0.090599[/C][C]0.9925[/C][C]0.161485[/C][/ROW]
[ROW][C]21[/C][C]-0.070321[/C][C]-0.7703[/C][C]0.221309[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302129&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302129&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	-0.121784	-1.3341	0.092352
2	0.013667	0.1497	0.440621
3	0.330975	3.6257	0.000212
4	-0.025128	-0.2753	0.391792
5	0.009392	0.1029	0.459114
6	0.23406	2.564	0.005791
7	-0.111104	-1.2171	0.112981
8	0.109014	1.1942	0.117381
9	0.186272	2.0405	0.021747
10	0.095873	1.0502	0.14786
11	0.108245	1.1858	0.119029
12	-0.231779	-2.539	0.006198
13	-0.060442	-0.6621	0.254586
14	-0.029519	-0.3234	0.37349
15	0.014185	0.1554	0.438387
16	-0.170987	-1.8731	0.031746
17	0.003113	0.0341	0.486427
18	-0.019213	-0.2105	0.416831
19	-0.126555	-1.3863	0.084106
20	0.090599	0.9925	0.161485
21	-0.070321	-0.7703	0.221309

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 = 2 ; par2 = 3 ; par3 = Exact Pearson Chi-Squared by Simulation ;

Parameters (R input):

par1 = Default ; par2 = -0.3 ; par3 = 0 ; 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