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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 11:51:39 +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/Dec/17/t1481971908qti8su4bos7iwsq.htm/, Retrieved Thu, 02 May 2024 00:35:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300681, Retrieved Thu, 02 May 2024 00:35:55 +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] [ACF voorbeeld] [2016-12-17 10:51:39] [d41d8cd98f00b204e9800998ecf8427e] [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=300681&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=300681&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300681&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	0.904765	5.7222	1e-06
2	0.803341	5.0808	5e-06
3	0.710195	4.4917	2.9e-05
4	0.626429	3.9619	0.000149
5	0.542943	3.4339	0.000699
6	0.468229	2.9613	0.002566
7	0.404304	2.557	0.007227
8	0.347724	2.1992	0.016853
9	0.288825	1.8267	0.037608
10	0.236445	1.4954	0.071328
11	0.189217	1.1967	0.119231
12	0.145838	0.9224	0.180936
13	0.104686	0.6621	0.255854
14	0.066552	0.4209	0.338035
15	0.018077	0.1143	0.454773
16	-0.030052	-0.1901	0.42511

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.904765 & 5.7222 & 1e-06 \tabularnewline
2 & 0.803341 & 5.0808 & 5e-06 \tabularnewline
3 & 0.710195 & 4.4917 & 2.9e-05 \tabularnewline
4 & 0.626429 & 3.9619 & 0.000149 \tabularnewline
5 & 0.542943 & 3.4339 & 0.000699 \tabularnewline
6 & 0.468229 & 2.9613 & 0.002566 \tabularnewline
7 & 0.404304 & 2.557 & 0.007227 \tabularnewline
8 & 0.347724 & 2.1992 & 0.016853 \tabularnewline
9 & 0.288825 & 1.8267 & 0.037608 \tabularnewline
10 & 0.236445 & 1.4954 & 0.071328 \tabularnewline
11 & 0.189217 & 1.1967 & 0.119231 \tabularnewline
12 & 0.145838 & 0.9224 & 0.180936 \tabularnewline
13 & 0.104686 & 0.6621 & 0.255854 \tabularnewline
14 & 0.066552 & 0.4209 & 0.338035 \tabularnewline
15 & 0.018077 & 0.1143 & 0.454773 \tabularnewline
16 & -0.030052 & -0.1901 & 0.42511 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300681&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]0.904765[/C][C]5.7222[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]0.803341[/C][C]5.0808[/C][C]5e-06[/C][/ROW]
[ROW][C]3[/C][C]0.710195[/C][C]4.4917[/C][C]2.9e-05[/C][/ROW]
[ROW][C]4[/C][C]0.626429[/C][C]3.9619[/C][C]0.000149[/C][/ROW]
[ROW][C]5[/C][C]0.542943[/C][C]3.4339[/C][C]0.000699[/C][/ROW]
[ROW][C]6[/C][C]0.468229[/C][C]2.9613[/C][C]0.002566[/C][/ROW]
[ROW][C]7[/C][C]0.404304[/C][C]2.557[/C][C]0.007227[/C][/ROW]
[ROW][C]8[/C][C]0.347724[/C][C]2.1992[/C][C]0.016853[/C][/ROW]
[ROW][C]9[/C][C]0.288825[/C][C]1.8267[/C][C]0.037608[/C][/ROW]
[ROW][C]10[/C][C]0.236445[/C][C]1.4954[/C][C]0.071328[/C][/ROW]
[ROW][C]11[/C][C]0.189217[/C][C]1.1967[/C][C]0.119231[/C][/ROW]
[ROW][C]12[/C][C]0.145838[/C][C]0.9224[/C][C]0.180936[/C][/ROW]
[ROW][C]13[/C][C]0.104686[/C][C]0.6621[/C][C]0.255854[/C][/ROW]
[ROW][C]14[/C][C]0.066552[/C][C]0.4209[/C][C]0.338035[/C][/ROW]
[ROW][C]15[/C][C]0.018077[/C][C]0.1143[/C][C]0.454773[/C][/ROW]
[ROW][C]16[/C][C]-0.030052[/C][C]-0.1901[/C][C]0.42511[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300681&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300681&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	0.904765	5.7222	1e-06
2	0.803341	5.0808	5e-06
3	0.710195	4.4917	2.9e-05
4	0.626429	3.9619	0.000149
5	0.542943	3.4339	0.000699
6	0.468229	2.9613	0.002566
7	0.404304	2.557	0.007227
8	0.347724	2.1992	0.016853
9	0.288825	1.8267	0.037608
10	0.236445	1.4954	0.071328
11	0.189217	1.1967	0.119231
12	0.145838	0.9224	0.180936
13	0.104686	0.6621	0.255854
14	0.066552	0.4209	0.338035
15	0.018077	0.1143	0.454773
16	-0.030052	-0.1901	0.42511

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.904765	5.7222	1e-06
2	-0.084115	-0.532	0.298838
3	-0.00929	-0.0588	0.476721
4	-0.005368	-0.0339	0.486544
5	-0.051832	-0.3278	0.37238
6	-0.001781	-0.0113	0.495534
7	0.007052	0.0446	0.482324
8	-0.007171	-0.0454	0.482026
9	-0.052213	-0.3302	0.371478
10	-0.003329	-0.0211	0.491653
11	-0.0155	-0.098	0.461198
12	-0.018527	-0.1172	0.453654
13	-0.020981	-0.1327	0.44755
14	-0.020686	-0.1308	0.448283
15	-0.095517	-0.6041	0.274594
16	-0.037373	-0.2364	0.407176

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.904765 & 5.7222 & 1e-06 \tabularnewline
2 & -0.084115 & -0.532 & 0.298838 \tabularnewline
3 & -0.00929 & -0.0588 & 0.476721 \tabularnewline
4 & -0.005368 & -0.0339 & 0.486544 \tabularnewline
5 & -0.051832 & -0.3278 & 0.37238 \tabularnewline
6 & -0.001781 & -0.0113 & 0.495534 \tabularnewline
7 & 0.007052 & 0.0446 & 0.482324 \tabularnewline
8 & -0.007171 & -0.0454 & 0.482026 \tabularnewline
9 & -0.052213 & -0.3302 & 0.371478 \tabularnewline
10 & -0.003329 & -0.0211 & 0.491653 \tabularnewline
11 & -0.0155 & -0.098 & 0.461198 \tabularnewline
12 & -0.018527 & -0.1172 & 0.453654 \tabularnewline
13 & -0.020981 & -0.1327 & 0.44755 \tabularnewline
14 & -0.020686 & -0.1308 & 0.448283 \tabularnewline
15 & -0.095517 & -0.6041 & 0.274594 \tabularnewline
16 & -0.037373 & -0.2364 & 0.407176 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300681&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]0.904765[/C][C]5.7222[/C][C]1e-06[/C][/ROW]
[ROW][C]2[/C][C]-0.084115[/C][C]-0.532[/C][C]0.298838[/C][/ROW]
[ROW][C]3[/C][C]-0.00929[/C][C]-0.0588[/C][C]0.476721[/C][/ROW]
[ROW][C]4[/C][C]-0.005368[/C][C]-0.0339[/C][C]0.486544[/C][/ROW]
[ROW][C]5[/C][C]-0.051832[/C][C]-0.3278[/C][C]0.37238[/C][/ROW]
[ROW][C]6[/C][C]-0.001781[/C][C]-0.0113[/C][C]0.495534[/C][/ROW]
[ROW][C]7[/C][C]0.007052[/C][C]0.0446[/C][C]0.482324[/C][/ROW]
[ROW][C]8[/C][C]-0.007171[/C][C]-0.0454[/C][C]0.482026[/C][/ROW]
[ROW][C]9[/C][C]-0.052213[/C][C]-0.3302[/C][C]0.371478[/C][/ROW]
[ROW][C]10[/C][C]-0.003329[/C][C]-0.0211[/C][C]0.491653[/C][/ROW]
[ROW][C]11[/C][C]-0.0155[/C][C]-0.098[/C][C]0.461198[/C][/ROW]
[ROW][C]12[/C][C]-0.018527[/C][C]-0.1172[/C][C]0.453654[/C][/ROW]
[ROW][C]13[/C][C]-0.020981[/C][C]-0.1327[/C][C]0.44755[/C][/ROW]
[ROW][C]14[/C][C]-0.020686[/C][C]-0.1308[/C][C]0.448283[/C][/ROW]
[ROW][C]15[/C][C]-0.095517[/C][C]-0.6041[/C][C]0.274594[/C][/ROW]
[ROW][C]16[/C][C]-0.037373[/C][C]-0.2364[/C][C]0.407176[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300681&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300681&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	0.904765	5.7222	1e-06
2	-0.084115	-0.532	0.298838
3	-0.00929	-0.0588	0.476721
4	-0.005368	-0.0339	0.486544
5	-0.051832	-0.3278	0.37238
6	-0.001781	-0.0113	0.495534
7	0.007052	0.0446	0.482324
8	-0.007171	-0.0454	0.482026
9	-0.052213	-0.3302	0.371478
10	-0.003329	-0.0211	0.491653
11	-0.0155	-0.098	0.461198
12	-0.018527	-0.1172	0.453654
13	-0.020981	-0.1327	0.44755
14	-0.020686	-0.1308	0.448283
15	-0.095517	-0.6041	0.274594
16	-0.037373	-0.2364	0.407176

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