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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 09:44:11 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/16/t1481877865x17wkppqjpccaxm.htm/, Retrieved Thu, 02 May 2024 18:02:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300126, Retrieved Thu, 02 May 2024 18:02:44 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-16 08:44:11] [94ac3c9a028ddd47e8862e80eac9f626] [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=300126&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=300126&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300126&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	0.861226	9.1954	0
2	0.737316	7.8724	0
3	0.666394	7.1151	0
4	0.664405	7.0939	0
5	0.744326	7.9472	0
6	0.767111	8.1905	0
7	0.688794	7.3543	0
8	0.560333	5.9827	0
9	0.494565	5.2805	0
10	0.499254	5.3306	0
11	0.585564	6.2521	0
12	0.643339	6.869	0
13	0.557346	5.9508	0
14	0.455036	4.8585	2e-06
15	0.396951	4.2383	2.3e-05
16	0.414601	4.4267	1.1e-05
17	0.49232	5.2565	0
18	0.520877	5.5614	0
19	0.469091	5.0085	1e-06
20	0.358158	3.8241	0.000107

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.861226 & 9.1954 & 0 \tabularnewline
2 & 0.737316 & 7.8724 & 0 \tabularnewline
3 & 0.666394 & 7.1151 & 0 \tabularnewline
4 & 0.664405 & 7.0939 & 0 \tabularnewline
5 & 0.744326 & 7.9472 & 0 \tabularnewline
6 & 0.767111 & 8.1905 & 0 \tabularnewline
7 & 0.688794 & 7.3543 & 0 \tabularnewline
8 & 0.560333 & 5.9827 & 0 \tabularnewline
9 & 0.494565 & 5.2805 & 0 \tabularnewline
10 & 0.499254 & 5.3306 & 0 \tabularnewline
11 & 0.585564 & 6.2521 & 0 \tabularnewline
12 & 0.643339 & 6.869 & 0 \tabularnewline
13 & 0.557346 & 5.9508 & 0 \tabularnewline
14 & 0.455036 & 4.8585 & 2e-06 \tabularnewline
15 & 0.396951 & 4.2383 & 2.3e-05 \tabularnewline
16 & 0.414601 & 4.4267 & 1.1e-05 \tabularnewline
17 & 0.49232 & 5.2565 & 0 \tabularnewline
18 & 0.520877 & 5.5614 & 0 \tabularnewline
19 & 0.469091 & 5.0085 & 1e-06 \tabularnewline
20 & 0.358158 & 3.8241 & 0.000107 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300126&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]0.861226[/C][C]9.1954[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.737316[/C][C]7.8724[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.666394[/C][C]7.1151[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.664405[/C][C]7.0939[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.744326[/C][C]7.9472[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.767111[/C][C]8.1905[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.688794[/C][C]7.3543[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.560333[/C][C]5.9827[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.494565[/C][C]5.2805[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.499254[/C][C]5.3306[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.585564[/C][C]6.2521[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.643339[/C][C]6.869[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.557346[/C][C]5.9508[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.455036[/C][C]4.8585[/C][C]2e-06[/C][/ROW]
[ROW][C]15[/C][C]0.396951[/C][C]4.2383[/C][C]2.3e-05[/C][/ROW]
[ROW][C]16[/C][C]0.414601[/C][C]4.4267[/C][C]1.1e-05[/C][/ROW]
[ROW][C]17[/C][C]0.49232[/C][C]5.2565[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.520877[/C][C]5.5614[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.469091[/C][C]5.0085[/C][C]1e-06[/C][/ROW]
[ROW][C]20[/C][C]0.358158[/C][C]3.8241[/C][C]0.000107[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300126&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300126&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	0.861226	9.1954	0
2	0.737316	7.8724	0
3	0.666394	7.1151	0
4	0.664405	7.0939	0
5	0.744326	7.9472	0
6	0.767111	8.1905	0
7	0.688794	7.3543	0
8	0.560333	5.9827	0
9	0.494565	5.2805	0
10	0.499254	5.3306	0
11	0.585564	6.2521	0
12	0.643339	6.869	0
13	0.557346	5.9508	0
14	0.455036	4.8585	2e-06
15	0.396951	4.2383	2.3e-05
16	0.414601	4.4267	1.1e-05
17	0.49232	5.2565	0
18	0.520877	5.5614	0
19	0.469091	5.0085	1e-06
20	0.358158	3.8241	0.000107

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.861226	9.1954	0
2	-0.017011	-0.1816	0.428098
3	0.136503	1.4575	0.07387
4	0.245911	2.6256	0.004918
5	0.414052	4.4209	1.1e-05
6	0.026693	0.285	0.38808
7	-0.225031	-2.4027	0.008945
8	-0.25287	-2.6999	0.003996
9	0.069364	0.7406	0.230227
10	0.030771	0.3285	0.371551
11	0.246063	2.6272	0.004896
12	0.149797	1.5994	0.056251
13	-0.250151	-2.6709	0.004336
14	-0.059914	-0.6397	0.261823
15	0.088663	0.9467	0.172906
16	0.050508	0.5393	0.295372
17	-0.023428	-0.2501	0.401465
18	-0.062725	-0.6697	0.252194
19	0.045622	0.4871	0.313558
20	-0.093073	-0.9938	0.161224

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.861226 & 9.1954 & 0 \tabularnewline
2 & -0.017011 & -0.1816 & 0.428098 \tabularnewline
3 & 0.136503 & 1.4575 & 0.07387 \tabularnewline
4 & 0.245911 & 2.6256 & 0.004918 \tabularnewline
5 & 0.414052 & 4.4209 & 1.1e-05 \tabularnewline
6 & 0.026693 & 0.285 & 0.38808 \tabularnewline
7 & -0.225031 & -2.4027 & 0.008945 \tabularnewline
8 & -0.25287 & -2.6999 & 0.003996 \tabularnewline
9 & 0.069364 & 0.7406 & 0.230227 \tabularnewline
10 & 0.030771 & 0.3285 & 0.371551 \tabularnewline
11 & 0.246063 & 2.6272 & 0.004896 \tabularnewline
12 & 0.149797 & 1.5994 & 0.056251 \tabularnewline
13 & -0.250151 & -2.6709 & 0.004336 \tabularnewline
14 & -0.059914 & -0.6397 & 0.261823 \tabularnewline
15 & 0.088663 & 0.9467 & 0.172906 \tabularnewline
16 & 0.050508 & 0.5393 & 0.295372 \tabularnewline
17 & -0.023428 & -0.2501 & 0.401465 \tabularnewline
18 & -0.062725 & -0.6697 & 0.252194 \tabularnewline
19 & 0.045622 & 0.4871 & 0.313558 \tabularnewline
20 & -0.093073 & -0.9938 & 0.161224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300126&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]0.861226[/C][C]9.1954[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.017011[/C][C]-0.1816[/C][C]0.428098[/C][/ROW]
[ROW][C]3[/C][C]0.136503[/C][C]1.4575[/C][C]0.07387[/C][/ROW]
[ROW][C]4[/C][C]0.245911[/C][C]2.6256[/C][C]0.004918[/C][/ROW]
[ROW][C]5[/C][C]0.414052[/C][C]4.4209[/C][C]1.1e-05[/C][/ROW]
[ROW][C]6[/C][C]0.026693[/C][C]0.285[/C][C]0.38808[/C][/ROW]
[ROW][C]7[/C][C]-0.225031[/C][C]-2.4027[/C][C]0.008945[/C][/ROW]
[ROW][C]8[/C][C]-0.25287[/C][C]-2.6999[/C][C]0.003996[/C][/ROW]
[ROW][C]9[/C][C]0.069364[/C][C]0.7406[/C][C]0.230227[/C][/ROW]
[ROW][C]10[/C][C]0.030771[/C][C]0.3285[/C][C]0.371551[/C][/ROW]
[ROW][C]11[/C][C]0.246063[/C][C]2.6272[/C][C]0.004896[/C][/ROW]
[ROW][C]12[/C][C]0.149797[/C][C]1.5994[/C][C]0.056251[/C][/ROW]
[ROW][C]13[/C][C]-0.250151[/C][C]-2.6709[/C][C]0.004336[/C][/ROW]
[ROW][C]14[/C][C]-0.059914[/C][C]-0.6397[/C][C]0.261823[/C][/ROW]
[ROW][C]15[/C][C]0.088663[/C][C]0.9467[/C][C]0.172906[/C][/ROW]
[ROW][C]16[/C][C]0.050508[/C][C]0.5393[/C][C]0.295372[/C][/ROW]
[ROW][C]17[/C][C]-0.023428[/C][C]-0.2501[/C][C]0.401465[/C][/ROW]
[ROW][C]18[/C][C]-0.062725[/C][C]-0.6697[/C][C]0.252194[/C][/ROW]
[ROW][C]19[/C][C]0.045622[/C][C]0.4871[/C][C]0.313558[/C][/ROW]
[ROW][C]20[/C][C]-0.093073[/C][C]-0.9938[/C][C]0.161224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300126&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300126&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	0.861226	9.1954	0
2	-0.017011	-0.1816	0.428098
3	0.136503	1.4575	0.07387
4	0.245911	2.6256	0.004918
5	0.414052	4.4209	1.1e-05
6	0.026693	0.285	0.38808
7	-0.225031	-2.4027	0.008945
8	-0.25287	-2.6999	0.003996
9	0.069364	0.7406	0.230227
10	0.030771	0.3285	0.371551
11	0.246063	2.6272	0.004896
12	0.149797	1.5994	0.056251
13	-0.250151	-2.6709	0.004336
14	-0.059914	-0.6397	0.261823
15	0.088663	0.9467	0.172906
16	0.050508	0.5393	0.295372
17	-0.023428	-0.2501	0.401465
18	-0.062725	-0.6697	0.252194
19	0.045622	0.4871	0.313558
20	-0.093073	-0.9938	0.161224

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 0 ; par9 = 0 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 1 ; 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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code