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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Dec 2016 16:09:03 +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/18/t1482073764e7jombvxqsibwth.htm/, Retrieved Wed, 08 May 2024 23:20:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301126, Retrieved Wed, 08 May 2024 23:20:14 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-18 15:09:03] [9ac947b5174fcc9cd01e144b03ceb277] [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=301126&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=301126&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301126&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	0.95551	7.5841	0
2	0.910564	7.2274	0
3	0.866759	6.8797	0
4	0.821622	6.5214	0
5	0.773674	6.1408	0
6	0.727692	5.7759	0
7	0.682146	5.4144	1e-06
8	0.634809	5.0386	2e-06
9	0.587395	4.6623	8e-06
10	0.540662	4.2914	3.1e-05
11	0.493877	3.92	0.00011
12	0.449322	3.5664	0.000349
13	0.404857	3.2134	0.001034
14	0.36136	2.8682	0.002805
15	0.317939	2.5236	0.007076
16	0.277829	2.2052	0.015549
17	0.239977	1.9048	0.03069

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.95551 & 7.5841 & 0 \tabularnewline
2 & 0.910564 & 7.2274 & 0 \tabularnewline
3 & 0.866759 & 6.8797 & 0 \tabularnewline
4 & 0.821622 & 6.5214 & 0 \tabularnewline
5 & 0.773674 & 6.1408 & 0 \tabularnewline
6 & 0.727692 & 5.7759 & 0 \tabularnewline
7 & 0.682146 & 5.4144 & 1e-06 \tabularnewline
8 & 0.634809 & 5.0386 & 2e-06 \tabularnewline
9 & 0.587395 & 4.6623 & 8e-06 \tabularnewline
10 & 0.540662 & 4.2914 & 3.1e-05 \tabularnewline
11 & 0.493877 & 3.92 & 0.00011 \tabularnewline
12 & 0.449322 & 3.5664 & 0.000349 \tabularnewline
13 & 0.404857 & 3.2134 & 0.001034 \tabularnewline
14 & 0.36136 & 2.8682 & 0.002805 \tabularnewline
15 & 0.317939 & 2.5236 & 0.007076 \tabularnewline
16 & 0.277829 & 2.2052 & 0.015549 \tabularnewline
17 & 0.239977 & 1.9048 & 0.03069 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301126&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]0.95551[/C][C]7.5841[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.910564[/C][C]7.2274[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.866759[/C][C]6.8797[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.821622[/C][C]6.5214[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.773674[/C][C]6.1408[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.727692[/C][C]5.7759[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.682146[/C][C]5.4144[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.634809[/C][C]5.0386[/C][C]2e-06[/C][/ROW]
[ROW][C]9[/C][C]0.587395[/C][C]4.6623[/C][C]8e-06[/C][/ROW]
[ROW][C]10[/C][C]0.540662[/C][C]4.2914[/C][C]3.1e-05[/C][/ROW]
[ROW][C]11[/C][C]0.493877[/C][C]3.92[/C][C]0.00011[/C][/ROW]
[ROW][C]12[/C][C]0.449322[/C][C]3.5664[/C][C]0.000349[/C][/ROW]
[ROW][C]13[/C][C]0.404857[/C][C]3.2134[/C][C]0.001034[/C][/ROW]
[ROW][C]14[/C][C]0.36136[/C][C]2.8682[/C][C]0.002805[/C][/ROW]
[ROW][C]15[/C][C]0.317939[/C][C]2.5236[/C][C]0.007076[/C][/ROW]
[ROW][C]16[/C][C]0.277829[/C][C]2.2052[/C][C]0.015549[/C][/ROW]
[ROW][C]17[/C][C]0.239977[/C][C]1.9048[/C][C]0.03069[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301126&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301126&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	0.95551	7.5841	0
2	0.910564	7.2274	0
3	0.866759	6.8797	0
4	0.821622	6.5214	0
5	0.773674	6.1408	0
6	0.727692	5.7759	0
7	0.682146	5.4144	1e-06
8	0.634809	5.0386	2e-06
9	0.587395	4.6623	8e-06
10	0.540662	4.2914	3.1e-05
11	0.493877	3.92	0.00011
12	0.449322	3.5664	0.000349
13	0.404857	3.2134	0.001034
14	0.36136	2.8682	0.002805
15	0.317939	2.5236	0.007076
16	0.277829	2.2052	0.015549
17	0.239977	1.9048	0.03069

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.95551	7.5841	0
2	-0.028002	-0.2223	0.412415
3	-0.010363	-0.0823	0.467354
4	-0.038939	-0.3091	0.379144
5	-0.056834	-0.4511	0.326731
6	-0.004446	-0.0353	0.485981
7	-0.022412	-0.1779	0.42969
8	-0.04636	-0.368	0.357063
9	-0.029172	-0.2315	0.40882
10	-0.023995	-0.1905	0.424782
11	-0.030321	-0.2407	0.405299
12	-0.003804	-0.0302	0.488006
13	-0.030921	-0.2454	0.403462
14	-0.020372	-0.1617	0.436032
15	-0.031208	-0.2477	0.402583
16	0.004259	0.0338	0.48657
17	-0.005177	-0.0411	0.483677

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.95551 & 7.5841 & 0 \tabularnewline
2 & -0.028002 & -0.2223 & 0.412415 \tabularnewline
3 & -0.010363 & -0.0823 & 0.467354 \tabularnewline
4 & -0.038939 & -0.3091 & 0.379144 \tabularnewline
5 & -0.056834 & -0.4511 & 0.326731 \tabularnewline
6 & -0.004446 & -0.0353 & 0.485981 \tabularnewline
7 & -0.022412 & -0.1779 & 0.42969 \tabularnewline
8 & -0.04636 & -0.368 & 0.357063 \tabularnewline
9 & -0.029172 & -0.2315 & 0.40882 \tabularnewline
10 & -0.023995 & -0.1905 & 0.424782 \tabularnewline
11 & -0.030321 & -0.2407 & 0.405299 \tabularnewline
12 & -0.003804 & -0.0302 & 0.488006 \tabularnewline
13 & -0.030921 & -0.2454 & 0.403462 \tabularnewline
14 & -0.020372 & -0.1617 & 0.436032 \tabularnewline
15 & -0.031208 & -0.2477 & 0.402583 \tabularnewline
16 & 0.004259 & 0.0338 & 0.48657 \tabularnewline
17 & -0.005177 & -0.0411 & 0.483677 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301126&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]0.95551[/C][C]7.5841[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.028002[/C][C]-0.2223[/C][C]0.412415[/C][/ROW]
[ROW][C]3[/C][C]-0.010363[/C][C]-0.0823[/C][C]0.467354[/C][/ROW]
[ROW][C]4[/C][C]-0.038939[/C][C]-0.3091[/C][C]0.379144[/C][/ROW]
[ROW][C]5[/C][C]-0.056834[/C][C]-0.4511[/C][C]0.326731[/C][/ROW]
[ROW][C]6[/C][C]-0.004446[/C][C]-0.0353[/C][C]0.485981[/C][/ROW]
[ROW][C]7[/C][C]-0.022412[/C][C]-0.1779[/C][C]0.42969[/C][/ROW]
[ROW][C]8[/C][C]-0.04636[/C][C]-0.368[/C][C]0.357063[/C][/ROW]
[ROW][C]9[/C][C]-0.029172[/C][C]-0.2315[/C][C]0.40882[/C][/ROW]
[ROW][C]10[/C][C]-0.023995[/C][C]-0.1905[/C][C]0.424782[/C][/ROW]
[ROW][C]11[/C][C]-0.030321[/C][C]-0.2407[/C][C]0.405299[/C][/ROW]
[ROW][C]12[/C][C]-0.003804[/C][C]-0.0302[/C][C]0.488006[/C][/ROW]
[ROW][C]13[/C][C]-0.030921[/C][C]-0.2454[/C][C]0.403462[/C][/ROW]
[ROW][C]14[/C][C]-0.020372[/C][C]-0.1617[/C][C]0.436032[/C][/ROW]
[ROW][C]15[/C][C]-0.031208[/C][C]-0.2477[/C][C]0.402583[/C][/ROW]
[ROW][C]16[/C][C]0.004259[/C][C]0.0338[/C][C]0.48657[/C][/ROW]
[ROW][C]17[/C][C]-0.005177[/C][C]-0.0411[/C][C]0.483677[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301126&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301126&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	0.95551	7.5841	0
2	-0.028002	-0.2223	0.412415
3	-0.010363	-0.0823	0.467354
4	-0.038939	-0.3091	0.379144
5	-0.056834	-0.4511	0.326731
6	-0.004446	-0.0353	0.485981
7	-0.022412	-0.1779	0.42969
8	-0.04636	-0.368	0.357063
9	-0.029172	-0.2315	0.40882
10	-0.023995	-0.1905	0.424782
11	-0.030321	-0.2407	0.405299
12	-0.003804	-0.0302	0.488006
13	-0.030921	-0.2454	0.403462
14	-0.020372	-0.1617	0.436032
15	-0.031208	-0.2477	0.402583
16	0.004259	0.0338	0.48657
17	-0.005177	-0.0411	0.483677

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 = 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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