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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 16:46:42 +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/t148198965455he9ozbatekqdd.htm/, Retrieved Thu, 02 May 2024 01:37:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300861, Retrieved Thu, 02 May 2024 01:37:07 +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] [Autocorrelation F...] [2016-12-17 15:46:42] [153c3207812fd13fe5ceee3276565119] [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=300861&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=300861&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300861&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	-0.541587	-3.8296	0.000179
2	-0.001451	-0.0103	0.495927
3	0.033723	0.2385	0.40625
4	0.142828	1.0099	0.158692
5	-0.13736	-0.9713	0.168041
6	0.082196	0.5812	0.281854
7	-0.057312	-0.4053	0.343507
8	0.110476	0.7812	0.219188
9	-0.147906	-1.0459	0.150329
10	0.097375	0.6885	0.247145
11	-0.058865	-0.4162	0.339508
12	0.196192	1.3873	0.085753
13	-0.226643	-1.6026	0.05766
14	0.027005	0.191	0.424667
15	0.104534	0.7392	0.231631
16	-0.043675	-0.3088	0.379368
17	0.00256	0.0181	0.492814

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.541587 & -3.8296 & 0.000179 \tabularnewline
2 & -0.001451 & -0.0103 & 0.495927 \tabularnewline
3 & 0.033723 & 0.2385 & 0.40625 \tabularnewline
4 & 0.142828 & 1.0099 & 0.158692 \tabularnewline
5 & -0.13736 & -0.9713 & 0.168041 \tabularnewline
6 & 0.082196 & 0.5812 & 0.281854 \tabularnewline
7 & -0.057312 & -0.4053 & 0.343507 \tabularnewline
8 & 0.110476 & 0.7812 & 0.219188 \tabularnewline
9 & -0.147906 & -1.0459 & 0.150329 \tabularnewline
10 & 0.097375 & 0.6885 & 0.247145 \tabularnewline
11 & -0.058865 & -0.4162 & 0.339508 \tabularnewline
12 & 0.196192 & 1.3873 & 0.085753 \tabularnewline
13 & -0.226643 & -1.6026 & 0.05766 \tabularnewline
14 & 0.027005 & 0.191 & 0.424667 \tabularnewline
15 & 0.104534 & 0.7392 & 0.231631 \tabularnewline
16 & -0.043675 & -0.3088 & 0.379368 \tabularnewline
17 & 0.00256 & 0.0181 & 0.492814 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300861&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]-0.541587[/C][C]-3.8296[/C][C]0.000179[/C][/ROW]
[ROW][C]2[/C][C]-0.001451[/C][C]-0.0103[/C][C]0.495927[/C][/ROW]
[ROW][C]3[/C][C]0.033723[/C][C]0.2385[/C][C]0.40625[/C][/ROW]
[ROW][C]4[/C][C]0.142828[/C][C]1.0099[/C][C]0.158692[/C][/ROW]
[ROW][C]5[/C][C]-0.13736[/C][C]-0.9713[/C][C]0.168041[/C][/ROW]
[ROW][C]6[/C][C]0.082196[/C][C]0.5812[/C][C]0.281854[/C][/ROW]
[ROW][C]7[/C][C]-0.057312[/C][C]-0.4053[/C][C]0.343507[/C][/ROW]
[ROW][C]8[/C][C]0.110476[/C][C]0.7812[/C][C]0.219188[/C][/ROW]
[ROW][C]9[/C][C]-0.147906[/C][C]-1.0459[/C][C]0.150329[/C][/ROW]
[ROW][C]10[/C][C]0.097375[/C][C]0.6885[/C][C]0.247145[/C][/ROW]
[ROW][C]11[/C][C]-0.058865[/C][C]-0.4162[/C][C]0.339508[/C][/ROW]
[ROW][C]12[/C][C]0.196192[/C][C]1.3873[/C][C]0.085753[/C][/ROW]
[ROW][C]13[/C][C]-0.226643[/C][C]-1.6026[/C][C]0.05766[/C][/ROW]
[ROW][C]14[/C][C]0.027005[/C][C]0.191[/C][C]0.424667[/C][/ROW]
[ROW][C]15[/C][C]0.104534[/C][C]0.7392[/C][C]0.231631[/C][/ROW]
[ROW][C]16[/C][C]-0.043675[/C][C]-0.3088[/C][C]0.379368[/C][/ROW]
[ROW][C]17[/C][C]0.00256[/C][C]0.0181[/C][C]0.492814[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300861&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300861&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	-0.541587	-3.8296	0.000179
2	-0.001451	-0.0103	0.495927
3	0.033723	0.2385	0.40625
4	0.142828	1.0099	0.158692
5	-0.13736	-0.9713	0.168041
6	0.082196	0.5812	0.281854
7	-0.057312	-0.4053	0.343507
8	0.110476	0.7812	0.219188
9	-0.147906	-1.0459	0.150329
10	0.097375	0.6885	0.247145
11	-0.058865	-0.4162	0.339508
12	0.196192	1.3873	0.085753
13	-0.226643	-1.6026	0.05766
14	0.027005	0.191	0.424667
15	0.104534	0.7392	0.231631
16	-0.043675	-0.3088	0.379368
17	0.00256	0.0181	0.492814

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.541587	-3.8296	0.000179
2	-0.417114	-2.9494	0.002416
3	-0.331136	-2.3415	0.011617
4	-0.013362	-0.0945	0.46255
5	0.015054	0.1065	0.457825
6	0.140557	0.9939	0.162531
7	0.076406	0.5403	0.295704
8	0.181866	1.286	0.102185
9	0.013055	0.0923	0.463408
10	-0.007408	-0.0524	0.479216
11	-0.107759	-0.762	0.224829
12	0.198839	1.406	0.082954
13	0.117391	0.8301	0.20522
14	-0.051903	-0.367	0.35758
15	-0.012213	-0.0864	0.465764
16	-0.099276	-0.702	0.24297
17	0.04081	0.2886	0.38705

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.541587 & -3.8296 & 0.000179 \tabularnewline
2 & -0.417114 & -2.9494 & 0.002416 \tabularnewline
3 & -0.331136 & -2.3415 & 0.011617 \tabularnewline
4 & -0.013362 & -0.0945 & 0.46255 \tabularnewline
5 & 0.015054 & 0.1065 & 0.457825 \tabularnewline
6 & 0.140557 & 0.9939 & 0.162531 \tabularnewline
7 & 0.076406 & 0.5403 & 0.295704 \tabularnewline
8 & 0.181866 & 1.286 & 0.102185 \tabularnewline
9 & 0.013055 & 0.0923 & 0.463408 \tabularnewline
10 & -0.007408 & -0.0524 & 0.479216 \tabularnewline
11 & -0.107759 & -0.762 & 0.224829 \tabularnewline
12 & 0.198839 & 1.406 & 0.082954 \tabularnewline
13 & 0.117391 & 0.8301 & 0.20522 \tabularnewline
14 & -0.051903 & -0.367 & 0.35758 \tabularnewline
15 & -0.012213 & -0.0864 & 0.465764 \tabularnewline
16 & -0.099276 & -0.702 & 0.24297 \tabularnewline
17 & 0.04081 & 0.2886 & 0.38705 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300861&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]-0.541587[/C][C]-3.8296[/C][C]0.000179[/C][/ROW]
[ROW][C]2[/C][C]-0.417114[/C][C]-2.9494[/C][C]0.002416[/C][/ROW]
[ROW][C]3[/C][C]-0.331136[/C][C]-2.3415[/C][C]0.011617[/C][/ROW]
[ROW][C]4[/C][C]-0.013362[/C][C]-0.0945[/C][C]0.46255[/C][/ROW]
[ROW][C]5[/C][C]0.015054[/C][C]0.1065[/C][C]0.457825[/C][/ROW]
[ROW][C]6[/C][C]0.140557[/C][C]0.9939[/C][C]0.162531[/C][/ROW]
[ROW][C]7[/C][C]0.076406[/C][C]0.5403[/C][C]0.295704[/C][/ROW]
[ROW][C]8[/C][C]0.181866[/C][C]1.286[/C][C]0.102185[/C][/ROW]
[ROW][C]9[/C][C]0.013055[/C][C]0.0923[/C][C]0.463408[/C][/ROW]
[ROW][C]10[/C][C]-0.007408[/C][C]-0.0524[/C][C]0.479216[/C][/ROW]
[ROW][C]11[/C][C]-0.107759[/C][C]-0.762[/C][C]0.224829[/C][/ROW]
[ROW][C]12[/C][C]0.198839[/C][C]1.406[/C][C]0.082954[/C][/ROW]
[ROW][C]13[/C][C]0.117391[/C][C]0.8301[/C][C]0.20522[/C][/ROW]
[ROW][C]14[/C][C]-0.051903[/C][C]-0.367[/C][C]0.35758[/C][/ROW]
[ROW][C]15[/C][C]-0.012213[/C][C]-0.0864[/C][C]0.465764[/C][/ROW]
[ROW][C]16[/C][C]-0.099276[/C][C]-0.702[/C][C]0.24297[/C][/ROW]
[ROW][C]17[/C][C]0.04081[/C][C]0.2886[/C][C]0.38705[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300861&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300861&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	-0.541587	-3.8296	0.000179
2	-0.417114	-2.9494	0.002416
3	-0.331136	-2.3415	0.011617
4	-0.013362	-0.0945	0.46255
5	0.015054	0.1065	0.457825
6	0.140557	0.9939	0.162531
7	0.076406	0.5403	0.295704
8	0.181866	1.286	0.102185
9	0.013055	0.0923	0.463408
10	-0.007408	-0.0524	0.479216
11	-0.107759	-0.762	0.224829
12	0.198839	1.406	0.082954
13	0.117391	0.8301	0.20522
14	-0.051903	-0.367	0.35758
15	-0.012213	-0.0864	0.465764
16	-0.099276	-0.702	0.24297
17	0.04081	0.2886	0.38705

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 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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