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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 20 Nov 2016 15:55:22 +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/20/t1479653756m1dh11ec1sr6vbd.htm/, Retrieved Mon, 06 May 2024 09:29:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296868, Retrieved Mon, 06 May 2024 09:29:29 +0000

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-     [Skewness and Kurtosis Test] [F1 competitie n 1...] [2016-11-18 16:59:44] [95b24d8e95676a05c34b365fb6729343]
- RM      [(Partial) Autocorrelation Function] [F1 competitie par...] [2016-11-20 14:55:22] [673dd365cbcfe0c4e35658a2fe545652] [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=296868&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=296868&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296868&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	0.931064	6.176	0
2	0.850552	5.6419	1e-06
3	0.775676	5.1453	3e-06
4	0.705737	4.6813	1.4e-05
5	0.636239	4.2203	6e-05
6	0.565881	3.7536	0.000254
7	0.489724	3.2485	0.001113
8	0.412401	2.7356	0.004472
9	0.339392	2.2513	0.014707
10	0.269907	1.7904	0.040139
11	0.195127	1.2943	0.101152
12	0.095189	0.6314	0.265518
13	-0.000544	-0.0036	0.498568
14	-0.080964	-0.5371	0.296968
15	-0.14025	-0.9303	0.178643
16	-0.184092	-1.2211	0.114271

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.931064 & 6.176 & 0 \tabularnewline
2 & 0.850552 & 5.6419 & 1e-06 \tabularnewline
3 & 0.775676 & 5.1453 & 3e-06 \tabularnewline
4 & 0.705737 & 4.6813 & 1.4e-05 \tabularnewline
5 & 0.636239 & 4.2203 & 6e-05 \tabularnewline
6 & 0.565881 & 3.7536 & 0.000254 \tabularnewline
7 & 0.489724 & 3.2485 & 0.001113 \tabularnewline
8 & 0.412401 & 2.7356 & 0.004472 \tabularnewline
9 & 0.339392 & 2.2513 & 0.014707 \tabularnewline
10 & 0.269907 & 1.7904 & 0.040139 \tabularnewline
11 & 0.195127 & 1.2943 & 0.101152 \tabularnewline
12 & 0.095189 & 0.6314 & 0.265518 \tabularnewline
13 & -0.000544 & -0.0036 & 0.498568 \tabularnewline
14 & -0.080964 & -0.5371 & 0.296968 \tabularnewline
15 & -0.14025 & -0.9303 & 0.178643 \tabularnewline
16 & -0.184092 & -1.2211 & 0.114271 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296868&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]0.931064[/C][C]6.176[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.850552[/C][C]5.6419[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.775676[/C][C]5.1453[/C][C]3e-06[/C][/ROW]
[ROW][C]4[/C][C]0.705737[/C][C]4.6813[/C][C]1.4e-05[/C][/ROW]
[ROW][C]5[/C][C]0.636239[/C][C]4.2203[/C][C]6e-05[/C][/ROW]
[ROW][C]6[/C][C]0.565881[/C][C]3.7536[/C][C]0.000254[/C][/ROW]
[ROW][C]7[/C][C]0.489724[/C][C]3.2485[/C][C]0.001113[/C][/ROW]
[ROW][C]8[/C][C]0.412401[/C][C]2.7356[/C][C]0.004472[/C][/ROW]
[ROW][C]9[/C][C]0.339392[/C][C]2.2513[/C][C]0.014707[/C][/ROW]
[ROW][C]10[/C][C]0.269907[/C][C]1.7904[/C][C]0.040139[/C][/ROW]
[ROW][C]11[/C][C]0.195127[/C][C]1.2943[/C][C]0.101152[/C][/ROW]
[ROW][C]12[/C][C]0.095189[/C][C]0.6314[/C][C]0.265518[/C][/ROW]
[ROW][C]13[/C][C]-0.000544[/C][C]-0.0036[/C][C]0.498568[/C][/ROW]
[ROW][C]14[/C][C]-0.080964[/C][C]-0.5371[/C][C]0.296968[/C][/ROW]
[ROW][C]15[/C][C]-0.14025[/C][C]-0.9303[/C][C]0.178643[/C][/ROW]
[ROW][C]16[/C][C]-0.184092[/C][C]-1.2211[/C][C]0.114271[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296868&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296868&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	0.931064	6.176	0
2	0.850552	5.6419	1e-06
3	0.775676	5.1453	3e-06
4	0.705737	4.6813	1.4e-05
5	0.636239	4.2203	6e-05
6	0.565881	3.7536	0.000254
7	0.489724	3.2485	0.001113
8	0.412401	2.7356	0.004472
9	0.339392	2.2513	0.014707
10	0.269907	1.7904	0.040139
11	0.195127	1.2943	0.101152
12	0.095189	0.6314	0.265518
13	-0.000544	-0.0036	0.498568
14	-0.080964	-0.5371	0.296968
15	-0.14025	-0.9303	0.178643
16	-0.184092	-1.2211	0.114271

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.931064	6.176	0
2	-0.122651	-0.8136	0.210134
3	0.006286	0.0417	0.483465
4	-0.012107	-0.0803	0.468179
5	-0.041461	-0.275	0.392295
6	-0.046692	-0.3097	0.379118
7	-0.087376	-0.5796	0.282575
8	-0.0532	-0.3529	0.362928
9	-0.024071	-0.1597	0.436936
10	-0.035565	-0.2359	0.407298
11	-0.09785	-0.6491	0.259835
12	-0.249022	-1.6518	0.052845
13	-0.030599	-0.203	0.420045
14	0.004943	0.0328	0.486995
15	0.059094	0.392	0.348481
16	0.038993	0.2587	0.398555

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.931064 & 6.176 & 0 \tabularnewline
2 & -0.122651 & -0.8136 & 0.210134 \tabularnewline
3 & 0.006286 & 0.0417 & 0.483465 \tabularnewline
4 & -0.012107 & -0.0803 & 0.468179 \tabularnewline
5 & -0.041461 & -0.275 & 0.392295 \tabularnewline
6 & -0.046692 & -0.3097 & 0.379118 \tabularnewline
7 & -0.087376 & -0.5796 & 0.282575 \tabularnewline
8 & -0.0532 & -0.3529 & 0.362928 \tabularnewline
9 & -0.024071 & -0.1597 & 0.436936 \tabularnewline
10 & -0.035565 & -0.2359 & 0.407298 \tabularnewline
11 & -0.09785 & -0.6491 & 0.259835 \tabularnewline
12 & -0.249022 & -1.6518 & 0.052845 \tabularnewline
13 & -0.030599 & -0.203 & 0.420045 \tabularnewline
14 & 0.004943 & 0.0328 & 0.486995 \tabularnewline
15 & 0.059094 & 0.392 & 0.348481 \tabularnewline
16 & 0.038993 & 0.2587 & 0.398555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296868&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]0.931064[/C][C]6.176[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.122651[/C][C]-0.8136[/C][C]0.210134[/C][/ROW]
[ROW][C]3[/C][C]0.006286[/C][C]0.0417[/C][C]0.483465[/C][/ROW]
[ROW][C]4[/C][C]-0.012107[/C][C]-0.0803[/C][C]0.468179[/C][/ROW]
[ROW][C]5[/C][C]-0.041461[/C][C]-0.275[/C][C]0.392295[/C][/ROW]
[ROW][C]6[/C][C]-0.046692[/C][C]-0.3097[/C][C]0.379118[/C][/ROW]
[ROW][C]7[/C][C]-0.087376[/C][C]-0.5796[/C][C]0.282575[/C][/ROW]
[ROW][C]8[/C][C]-0.0532[/C][C]-0.3529[/C][C]0.362928[/C][/ROW]
[ROW][C]9[/C][C]-0.024071[/C][C]-0.1597[/C][C]0.436936[/C][/ROW]
[ROW][C]10[/C][C]-0.035565[/C][C]-0.2359[/C][C]0.407298[/C][/ROW]
[ROW][C]11[/C][C]-0.09785[/C][C]-0.6491[/C][C]0.259835[/C][/ROW]
[ROW][C]12[/C][C]-0.249022[/C][C]-1.6518[/C][C]0.052845[/C][/ROW]
[ROW][C]13[/C][C]-0.030599[/C][C]-0.203[/C][C]0.420045[/C][/ROW]
[ROW][C]14[/C][C]0.004943[/C][C]0.0328[/C][C]0.486995[/C][/ROW]
[ROW][C]15[/C][C]0.059094[/C][C]0.392[/C][C]0.348481[/C][/ROW]
[ROW][C]16[/C][C]0.038993[/C][C]0.2587[/C][C]0.398555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296868&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296868&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	0.931064	6.176	0
2	-0.122651	-0.8136	0.210134
3	0.006286	0.0417	0.483465
4	-0.012107	-0.0803	0.468179
5	-0.041461	-0.275	0.392295
6	-0.046692	-0.3097	0.379118
7	-0.087376	-0.5796	0.282575
8	-0.0532	-0.3529	0.362928
9	-0.024071	-0.1597	0.436936
10	-0.035565	-0.2359	0.407298
11	-0.09785	-0.6491	0.259835
12	-0.249022	-1.6518	0.052845
13	-0.030599	-0.203	0.420045
14	0.004943	0.0328	0.486995
15	0.059094	0.392	0.348481
16	0.038993	0.2587	0.398555

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 = 8 ; par2 = 0 ;

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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