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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Dec 2016 13:23:55 +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/22/t1482409476gtymd3sf5n7m40b.htm/, Retrieved Sun, 28 Apr 2024 22:58:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302535, Retrieved Sun, 28 Apr 2024 22:58:46 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Multiple Regression] [] [2016-12-19 12:24:41] [937b9e6718912fc8986df66e31b6c342]
- RMPD    [(Partial) Autocorrelation Function] [] [2016-12-22 12:23:55] [863feeaf19a0ddfce7bd9c25059c4d8a] [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=302535&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=302535&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302535&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	-0.159012	-1.1017	0.13805
2	0.02437	0.1688	0.433317
3	0.019565	0.1356	0.446372
4	0.269126	1.8646	0.034182
5	0.028432	0.197	0.422336
6	-0.142749	-0.989	0.163813
7	-0.147586	-1.0225	0.155834
8	0.154447	1.07	0.144976
9	-0.065486	-0.4537	0.326044
10	-0.050413	-0.3493	0.364207
11	-0.113967	-0.7896	0.216826
12	-0.218622	-1.5147	0.068208
13	0.13583	0.9411	0.175695
14	-0.055915	-0.3874	0.35009
15	-0.12001	-0.8315	0.204917
16	0.075364	0.5221	0.301987
17	-0.088648	-0.6142	0.271001

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.159012 & -1.1017 & 0.13805 \tabularnewline
2 & 0.02437 & 0.1688 & 0.433317 \tabularnewline
3 & 0.019565 & 0.1356 & 0.446372 \tabularnewline
4 & 0.269126 & 1.8646 & 0.034182 \tabularnewline
5 & 0.028432 & 0.197 & 0.422336 \tabularnewline
6 & -0.142749 & -0.989 & 0.163813 \tabularnewline
7 & -0.147586 & -1.0225 & 0.155834 \tabularnewline
8 & 0.154447 & 1.07 & 0.144976 \tabularnewline
9 & -0.065486 & -0.4537 & 0.326044 \tabularnewline
10 & -0.050413 & -0.3493 & 0.364207 \tabularnewline
11 & -0.113967 & -0.7896 & 0.216826 \tabularnewline
12 & -0.218622 & -1.5147 & 0.068208 \tabularnewline
13 & 0.13583 & 0.9411 & 0.175695 \tabularnewline
14 & -0.055915 & -0.3874 & 0.35009 \tabularnewline
15 & -0.12001 & -0.8315 & 0.204917 \tabularnewline
16 & 0.075364 & 0.5221 & 0.301987 \tabularnewline
17 & -0.088648 & -0.6142 & 0.271001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302535&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]-0.159012[/C][C]-1.1017[/C][C]0.13805[/C][/ROW]
[ROW][C]2[/C][C]0.02437[/C][C]0.1688[/C][C]0.433317[/C][/ROW]
[ROW][C]3[/C][C]0.019565[/C][C]0.1356[/C][C]0.446372[/C][/ROW]
[ROW][C]4[/C][C]0.269126[/C][C]1.8646[/C][C]0.034182[/C][/ROW]
[ROW][C]5[/C][C]0.028432[/C][C]0.197[/C][C]0.422336[/C][/ROW]
[ROW][C]6[/C][C]-0.142749[/C][C]-0.989[/C][C]0.163813[/C][/ROW]
[ROW][C]7[/C][C]-0.147586[/C][C]-1.0225[/C][C]0.155834[/C][/ROW]
[ROW][C]8[/C][C]0.154447[/C][C]1.07[/C][C]0.144976[/C][/ROW]
[ROW][C]9[/C][C]-0.065486[/C][C]-0.4537[/C][C]0.326044[/C][/ROW]
[ROW][C]10[/C][C]-0.050413[/C][C]-0.3493[/C][C]0.364207[/C][/ROW]
[ROW][C]11[/C][C]-0.113967[/C][C]-0.7896[/C][C]0.216826[/C][/ROW]
[ROW][C]12[/C][C]-0.218622[/C][C]-1.5147[/C][C]0.068208[/C][/ROW]
[ROW][C]13[/C][C]0.13583[/C][C]0.9411[/C][C]0.175695[/C][/ROW]
[ROW][C]14[/C][C]-0.055915[/C][C]-0.3874[/C][C]0.35009[/C][/ROW]
[ROW][C]15[/C][C]-0.12001[/C][C]-0.8315[/C][C]0.204917[/C][/ROW]
[ROW][C]16[/C][C]0.075364[/C][C]0.5221[/C][C]0.301987[/C][/ROW]
[ROW][C]17[/C][C]-0.088648[/C][C]-0.6142[/C][C]0.271001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302535&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302535&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	-0.159012	-1.1017	0.13805
2	0.02437	0.1688	0.433317
3	0.019565	0.1356	0.446372
4	0.269126	1.8646	0.034182
5	0.028432	0.197	0.422336
6	-0.142749	-0.989	0.163813
7	-0.147586	-1.0225	0.155834
8	0.154447	1.07	0.144976
9	-0.065486	-0.4537	0.326044
10	-0.050413	-0.3493	0.364207
11	-0.113967	-0.7896	0.216826
12	-0.218622	-1.5147	0.068208
13	0.13583	0.9411	0.175695
14	-0.055915	-0.3874	0.35009
15	-0.12001	-0.8315	0.204917
16	0.075364	0.5221	0.301987
17	-0.088648	-0.6142	0.271001

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.159012	-1.1017	0.13805
2	-0.000939	-0.0065	0.497418
3	0.023899	0.1656	0.434593
4	0.283291	1.9627	0.027746
5	0.129923	0.9001	0.186271
6	-0.139909	-0.9693	0.168622
7	-0.262494	-1.8186	0.037606
8	-0.000536	-0.0037	0.498526
9	-0.035606	-0.2467	0.403101
10	0.051653	0.3579	0.361009
11	0.007931	0.0549	0.478205
12	-0.352688	-2.4435	0.009137
13	-0.025179	-0.1744	0.431126
14	0.049335	0.3418	0.366995
15	0.005304	0.0367	0.485421
16	0.247374	1.7139	0.046503
17	-0.128488	-0.8902	0.188901

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.159012 & -1.1017 & 0.13805 \tabularnewline
2 & -0.000939 & -0.0065 & 0.497418 \tabularnewline
3 & 0.023899 & 0.1656 & 0.434593 \tabularnewline
4 & 0.283291 & 1.9627 & 0.027746 \tabularnewline
5 & 0.129923 & 0.9001 & 0.186271 \tabularnewline
6 & -0.139909 & -0.9693 & 0.168622 \tabularnewline
7 & -0.262494 & -1.8186 & 0.037606 \tabularnewline
8 & -0.000536 & -0.0037 & 0.498526 \tabularnewline
9 & -0.035606 & -0.2467 & 0.403101 \tabularnewline
10 & 0.051653 & 0.3579 & 0.361009 \tabularnewline
11 & 0.007931 & 0.0549 & 0.478205 \tabularnewline
12 & -0.352688 & -2.4435 & 0.009137 \tabularnewline
13 & -0.025179 & -0.1744 & 0.431126 \tabularnewline
14 & 0.049335 & 0.3418 & 0.366995 \tabularnewline
15 & 0.005304 & 0.0367 & 0.485421 \tabularnewline
16 & 0.247374 & 1.7139 & 0.046503 \tabularnewline
17 & -0.128488 & -0.8902 & 0.188901 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302535&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]-0.159012[/C][C]-1.1017[/C][C]0.13805[/C][/ROW]
[ROW][C]2[/C][C]-0.000939[/C][C]-0.0065[/C][C]0.497418[/C][/ROW]
[ROW][C]3[/C][C]0.023899[/C][C]0.1656[/C][C]0.434593[/C][/ROW]
[ROW][C]4[/C][C]0.283291[/C][C]1.9627[/C][C]0.027746[/C][/ROW]
[ROW][C]5[/C][C]0.129923[/C][C]0.9001[/C][C]0.186271[/C][/ROW]
[ROW][C]6[/C][C]-0.139909[/C][C]-0.9693[/C][C]0.168622[/C][/ROW]
[ROW][C]7[/C][C]-0.262494[/C][C]-1.8186[/C][C]0.037606[/C][/ROW]
[ROW][C]8[/C][C]-0.000536[/C][C]-0.0037[/C][C]0.498526[/C][/ROW]
[ROW][C]9[/C][C]-0.035606[/C][C]-0.2467[/C][C]0.403101[/C][/ROW]
[ROW][C]10[/C][C]0.051653[/C][C]0.3579[/C][C]0.361009[/C][/ROW]
[ROW][C]11[/C][C]0.007931[/C][C]0.0549[/C][C]0.478205[/C][/ROW]
[ROW][C]12[/C][C]-0.352688[/C][C]-2.4435[/C][C]0.009137[/C][/ROW]
[ROW][C]13[/C][C]-0.025179[/C][C]-0.1744[/C][C]0.431126[/C][/ROW]
[ROW][C]14[/C][C]0.049335[/C][C]0.3418[/C][C]0.366995[/C][/ROW]
[ROW][C]15[/C][C]0.005304[/C][C]0.0367[/C][C]0.485421[/C][/ROW]
[ROW][C]16[/C][C]0.247374[/C][C]1.7139[/C][C]0.046503[/C][/ROW]
[ROW][C]17[/C][C]-0.128488[/C][C]-0.8902[/C][C]0.188901[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302535&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302535&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	-0.159012	-1.1017	0.13805
2	-0.000939	-0.0065	0.497418
3	0.023899	0.1656	0.434593
4	0.283291	1.9627	0.027746
5	0.129923	0.9001	0.186271
6	-0.139909	-0.9693	0.168622
7	-0.262494	-1.8186	0.037606
8	-0.000536	-0.0037	0.498526
9	-0.035606	-0.2467	0.403101
10	0.051653	0.3579	0.361009
11	0.007931	0.0549	0.478205
12	-0.352688	-2.4435	0.009137
13	-0.025179	-0.1744	0.431126
14	0.049335	0.3418	0.366995
15	0.005304	0.0367	0.485421
16	0.247374	1.7139	0.046503
17	-0.128488	-0.8902	0.188901

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 = 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')

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Input Parameters & R Code