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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 10 Dec 2016 14:18:23 +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/10/t1481375994rkdzr9s4yxx3582.htm/, Retrieved Mon, 06 May 2024 01:16:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298680, Retrieved Mon, 06 May 2024 01:16:11 +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] [Autocorrelatie fu...] [2016-12-10 13:18:23] [6fe662842930c5949e61d44eeb8a265b] [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=298680&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=298680&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298680&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	0.944615	10.4336	0
2	0.895065	9.8863	0
3	0.85764	9.4729	0
4	0.829591	9.1631	0
5	0.800543	8.8423	0
6	0.776887	8.581	0
7	0.759616	8.3902	0
8	0.745523	8.2346	0
9	0.724874	8.0065	0
10	0.707234	7.8117	0
11	0.700044	7.7322	0
12	0.675351	7.4595	0
13	0.632565	6.9869	0
14	0.581126	6.4187	0
15	0.548949	6.0633	0
16	0.523517	5.7824	0
17	0.493697	5.4531	0
18	0.467796	5.167	0
19	0.450815	4.9794	1e-06
20	0.43141	4.7651	3e-06
21	0.408522	4.5123	7e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.944615 & 10.4336 & 0 \tabularnewline
2 & 0.895065 & 9.8863 & 0 \tabularnewline
3 & 0.85764 & 9.4729 & 0 \tabularnewline
4 & 0.829591 & 9.1631 & 0 \tabularnewline
5 & 0.800543 & 8.8423 & 0 \tabularnewline
6 & 0.776887 & 8.581 & 0 \tabularnewline
7 & 0.759616 & 8.3902 & 0 \tabularnewline
8 & 0.745523 & 8.2346 & 0 \tabularnewline
9 & 0.724874 & 8.0065 & 0 \tabularnewline
10 & 0.707234 & 7.8117 & 0 \tabularnewline
11 & 0.700044 & 7.7322 & 0 \tabularnewline
12 & 0.675351 & 7.4595 & 0 \tabularnewline
13 & 0.632565 & 6.9869 & 0 \tabularnewline
14 & 0.581126 & 6.4187 & 0 \tabularnewline
15 & 0.548949 & 6.0633 & 0 \tabularnewline
16 & 0.523517 & 5.7824 & 0 \tabularnewline
17 & 0.493697 & 5.4531 & 0 \tabularnewline
18 & 0.467796 & 5.167 & 0 \tabularnewline
19 & 0.450815 & 4.9794 & 1e-06 \tabularnewline
20 & 0.43141 & 4.7651 & 3e-06 \tabularnewline
21 & 0.408522 & 4.5123 & 7e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298680&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]0.944615[/C][C]10.4336[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.895065[/C][C]9.8863[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.85764[/C][C]9.4729[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.829591[/C][C]9.1631[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.800543[/C][C]8.8423[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.776887[/C][C]8.581[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.759616[/C][C]8.3902[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.745523[/C][C]8.2346[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.724874[/C][C]8.0065[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.707234[/C][C]7.8117[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.700044[/C][C]7.7322[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.675351[/C][C]7.4595[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.632565[/C][C]6.9869[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.581126[/C][C]6.4187[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.548949[/C][C]6.0633[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.523517[/C][C]5.7824[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.493697[/C][C]5.4531[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.467796[/C][C]5.167[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.450815[/C][C]4.9794[/C][C]1e-06[/C][/ROW]
[ROW][C]20[/C][C]0.43141[/C][C]4.7651[/C][C]3e-06[/C][/ROW]
[ROW][C]21[/C][C]0.408522[/C][C]4.5123[/C][C]7e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298680&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298680&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	0.944615	10.4336	0
2	0.895065	9.8863	0
3	0.85764	9.4729	0
4	0.829591	9.1631	0
5	0.800543	8.8423	0
6	0.776887	8.581	0
7	0.759616	8.3902	0
8	0.745523	8.2346	0
9	0.724874	8.0065	0
10	0.707234	7.8117	0
11	0.700044	7.7322	0
12	0.675351	7.4595	0
13	0.632565	6.9869	0
14	0.581126	6.4187	0
15	0.548949	6.0633	0
16	0.523517	5.7824	0
17	0.493697	5.4531	0
18	0.467796	5.167	0
19	0.450815	4.9794	1e-06
20	0.43141	4.7651	3e-06
21	0.408522	4.5123	7e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.944615	10.4336	0
2	0.025703	0.2839	0.388483
3	0.089199	0.9852	0.163228
4	0.079186	0.8746	0.191745
5	-0.002219	-0.0245	0.490243
6	0.055311	0.6109	0.271191
7	0.063214	0.6982	0.243185
8	0.042784	0.4726	0.318685
9	-0.038222	-0.4222	0.336818
10	0.034436	0.3804	0.35217
11	0.096477	1.0656	0.14435
12	-0.151053	-1.6684	0.048897
13	-0.171583	-1.8952	0.030216
14	-0.149616	-1.6526	0.050495
15	0.077906	0.8605	0.195601
16	0.021214	0.2343	0.407568
17	-0.053668	-0.5928	0.277211
18	0.01222	0.135	0.446427
19	0.03516	0.3884	0.349214
20	-0.009602	-0.1061	0.457855
21	-0.005035	-0.0556	0.47787

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.944615 & 10.4336 & 0 \tabularnewline
2 & 0.025703 & 0.2839 & 0.388483 \tabularnewline
3 & 0.089199 & 0.9852 & 0.163228 \tabularnewline
4 & 0.079186 & 0.8746 & 0.191745 \tabularnewline
5 & -0.002219 & -0.0245 & 0.490243 \tabularnewline
6 & 0.055311 & 0.6109 & 0.271191 \tabularnewline
7 & 0.063214 & 0.6982 & 0.243185 \tabularnewline
8 & 0.042784 & 0.4726 & 0.318685 \tabularnewline
9 & -0.038222 & -0.4222 & 0.336818 \tabularnewline
10 & 0.034436 & 0.3804 & 0.35217 \tabularnewline
11 & 0.096477 & 1.0656 & 0.14435 \tabularnewline
12 & -0.151053 & -1.6684 & 0.048897 \tabularnewline
13 & -0.171583 & -1.8952 & 0.030216 \tabularnewline
14 & -0.149616 & -1.6526 & 0.050495 \tabularnewline
15 & 0.077906 & 0.8605 & 0.195601 \tabularnewline
16 & 0.021214 & 0.2343 & 0.407568 \tabularnewline
17 & -0.053668 & -0.5928 & 0.277211 \tabularnewline
18 & 0.01222 & 0.135 & 0.446427 \tabularnewline
19 & 0.03516 & 0.3884 & 0.349214 \tabularnewline
20 & -0.009602 & -0.1061 & 0.457855 \tabularnewline
21 & -0.005035 & -0.0556 & 0.47787 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298680&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]0.944615[/C][C]10.4336[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.025703[/C][C]0.2839[/C][C]0.388483[/C][/ROW]
[ROW][C]3[/C][C]0.089199[/C][C]0.9852[/C][C]0.163228[/C][/ROW]
[ROW][C]4[/C][C]0.079186[/C][C]0.8746[/C][C]0.191745[/C][/ROW]
[ROW][C]5[/C][C]-0.002219[/C][C]-0.0245[/C][C]0.490243[/C][/ROW]
[ROW][C]6[/C][C]0.055311[/C][C]0.6109[/C][C]0.271191[/C][/ROW]
[ROW][C]7[/C][C]0.063214[/C][C]0.6982[/C][C]0.243185[/C][/ROW]
[ROW][C]8[/C][C]0.042784[/C][C]0.4726[/C][C]0.318685[/C][/ROW]
[ROW][C]9[/C][C]-0.038222[/C][C]-0.4222[/C][C]0.336818[/C][/ROW]
[ROW][C]10[/C][C]0.034436[/C][C]0.3804[/C][C]0.35217[/C][/ROW]
[ROW][C]11[/C][C]0.096477[/C][C]1.0656[/C][C]0.14435[/C][/ROW]
[ROW][C]12[/C][C]-0.151053[/C][C]-1.6684[/C][C]0.048897[/C][/ROW]
[ROW][C]13[/C][C]-0.171583[/C][C]-1.8952[/C][C]0.030216[/C][/ROW]
[ROW][C]14[/C][C]-0.149616[/C][C]-1.6526[/C][C]0.050495[/C][/ROW]
[ROW][C]15[/C][C]0.077906[/C][C]0.8605[/C][C]0.195601[/C][/ROW]
[ROW][C]16[/C][C]0.021214[/C][C]0.2343[/C][C]0.407568[/C][/ROW]
[ROW][C]17[/C][C]-0.053668[/C][C]-0.5928[/C][C]0.277211[/C][/ROW]
[ROW][C]18[/C][C]0.01222[/C][C]0.135[/C][C]0.446427[/C][/ROW]
[ROW][C]19[/C][C]0.03516[/C][C]0.3884[/C][C]0.349214[/C][/ROW]
[ROW][C]20[/C][C]-0.009602[/C][C]-0.1061[/C][C]0.457855[/C][/ROW]
[ROW][C]21[/C][C]-0.005035[/C][C]-0.0556[/C][C]0.47787[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298680&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298680&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	0.944615	10.4336	0
2	0.025703	0.2839	0.388483
3	0.089199	0.9852	0.163228
4	0.079186	0.8746	0.191745
5	-0.002219	-0.0245	0.490243
6	0.055311	0.6109	0.271191
7	0.063214	0.6982	0.243185
8	0.042784	0.4726	0.318685
9	-0.038222	-0.4222	0.336818
10	0.034436	0.3804	0.35217
11	0.096477	1.0656	0.14435
12	-0.151053	-1.6684	0.048897
13	-0.171583	-1.8952	0.030216
14	-0.149616	-1.6526	0.050495
15	0.077906	0.8605	0.195601
16	0.021214	0.2343	0.407568
17	-0.053668	-0.5928	0.277211
18	0.01222	0.135	0.446427
19	0.03516	0.3884	0.349214
20	-0.009602	-0.1061	0.457855
21	-0.005035	-0.0556	0.47787

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

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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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code