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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 20 Dec 2016 14:36:34 +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/20/t1482241024p2vu3idn8g7o9cg.htm/, Retrieved Sat, 27 Apr 2024 23:28:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301663, Retrieved Sat, 27 Apr 2024 23:28:39 +0000

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-       [(Partial) Autocorrelation Function] [PAF 3B] [2016-12-20 13:36:34] [94c1b173d9287822f5e2740a4a602bdd] [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=301663&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=301663&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301663&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	-0.531599	-4.2859	3.1e-05
2	0.129804	1.0465	0.1496
3	-0.144935	-1.1685	0.123436
4	0.138755	1.1187	0.133697
5	0.233801	1.885	0.031953
6	-0.476051	-3.838	0.000142
7	0.232532	1.8747	0.032662
8	0.150688	1.2149	0.114402
9	-0.198247	-1.5983	0.057411
10	0.113131	0.9121	0.182545
11	-0.39367	-3.1739	0.001149
12	0.769259	6.202	0
13	-0.461258	-3.7188	0.00021
14	0.07493	0.6041	0.273938
15	-0.06394	-0.5155	0.303977
16	0.063866	0.5149	0.304183
17	0.138004	1.1126	0.134984
18	-0.35307	-2.8465	0.002954

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.531599 & -4.2859 & 3.1e-05 \tabularnewline
2 & 0.129804 & 1.0465 & 0.1496 \tabularnewline
3 & -0.144935 & -1.1685 & 0.123436 \tabularnewline
4 & 0.138755 & 1.1187 & 0.133697 \tabularnewline
5 & 0.233801 & 1.885 & 0.031953 \tabularnewline
6 & -0.476051 & -3.838 & 0.000142 \tabularnewline
7 & 0.232532 & 1.8747 & 0.032662 \tabularnewline
8 & 0.150688 & 1.2149 & 0.114402 \tabularnewline
9 & -0.198247 & -1.5983 & 0.057411 \tabularnewline
10 & 0.113131 & 0.9121 & 0.182545 \tabularnewline
11 & -0.39367 & -3.1739 & 0.001149 \tabularnewline
12 & 0.769259 & 6.202 & 0 \tabularnewline
13 & -0.461258 & -3.7188 & 0.00021 \tabularnewline
14 & 0.07493 & 0.6041 & 0.273938 \tabularnewline
15 & -0.06394 & -0.5155 & 0.303977 \tabularnewline
16 & 0.063866 & 0.5149 & 0.304183 \tabularnewline
17 & 0.138004 & 1.1126 & 0.134984 \tabularnewline
18 & -0.35307 & -2.8465 & 0.002954 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301663&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]-0.531599[/C][C]-4.2859[/C][C]3.1e-05[/C][/ROW]
[ROW][C]2[/C][C]0.129804[/C][C]1.0465[/C][C]0.1496[/C][/ROW]
[ROW][C]3[/C][C]-0.144935[/C][C]-1.1685[/C][C]0.123436[/C][/ROW]
[ROW][C]4[/C][C]0.138755[/C][C]1.1187[/C][C]0.133697[/C][/ROW]
[ROW][C]5[/C][C]0.233801[/C][C]1.885[/C][C]0.031953[/C][/ROW]
[ROW][C]6[/C][C]-0.476051[/C][C]-3.838[/C][C]0.000142[/C][/ROW]
[ROW][C]7[/C][C]0.232532[/C][C]1.8747[/C][C]0.032662[/C][/ROW]
[ROW][C]8[/C][C]0.150688[/C][C]1.2149[/C][C]0.114402[/C][/ROW]
[ROW][C]9[/C][C]-0.198247[/C][C]-1.5983[/C][C]0.057411[/C][/ROW]
[ROW][C]10[/C][C]0.113131[/C][C]0.9121[/C][C]0.182545[/C][/ROW]
[ROW][C]11[/C][C]-0.39367[/C][C]-3.1739[/C][C]0.001149[/C][/ROW]
[ROW][C]12[/C][C]0.769259[/C][C]6.202[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.461258[/C][C]-3.7188[/C][C]0.00021[/C][/ROW]
[ROW][C]14[/C][C]0.07493[/C][C]0.6041[/C][C]0.273938[/C][/ROW]
[ROW][C]15[/C][C]-0.06394[/C][C]-0.5155[/C][C]0.303977[/C][/ROW]
[ROW][C]16[/C][C]0.063866[/C][C]0.5149[/C][C]0.304183[/C][/ROW]
[ROW][C]17[/C][C]0.138004[/C][C]1.1126[/C][C]0.134984[/C][/ROW]
[ROW][C]18[/C][C]-0.35307[/C][C]-2.8465[/C][C]0.002954[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301663&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301663&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	-0.531599	-4.2859	3.1e-05
2	0.129804	1.0465	0.1496
3	-0.144935	-1.1685	0.123436
4	0.138755	1.1187	0.133697
5	0.233801	1.885	0.031953
6	-0.476051	-3.838	0.000142
7	0.232532	1.8747	0.032662
8	0.150688	1.2149	0.114402
9	-0.198247	-1.5983	0.057411
10	0.113131	0.9121	0.182545
11	-0.39367	-3.1739	0.001149
12	0.769259	6.202	0
13	-0.461258	-3.7188	0.00021
14	0.07493	0.6041	0.273938
15	-0.06394	-0.5155	0.303977
16	0.063866	0.5149	0.304183
17	0.138004	1.1126	0.134984
18	-0.35307	-2.8465	0.002954

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.531599	-4.2859	3.1e-05
2	-0.212981	-1.7171	0.045361
3	-0.254731	-2.0537	0.022015
4	-0.076532	-0.617	0.269688
5	0.43032	3.4694	0.000466
6	-0.190053	-1.5323	0.065156
7	-0.186141	-1.5007	0.069135
8	0.419894	3.3853	0.000605
9	-0.246991	-1.9913	0.025327
10	-0.062182	-0.5013	0.308916
11	-0.173568	-1.3994	0.083231
12	0.492034	3.9669	9.2e-05
13	0.163263	1.3163	0.096354
14	0.05641	0.4548	0.325389
15	0.005575	0.0449	0.482144
16	-0.219136	-1.7667	0.040984
17	-0.358977	-2.8942	0.002585
18	0.029526	0.238	0.406298

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.531599 & -4.2859 & 3.1e-05 \tabularnewline
2 & -0.212981 & -1.7171 & 0.045361 \tabularnewline
3 & -0.254731 & -2.0537 & 0.022015 \tabularnewline
4 & -0.076532 & -0.617 & 0.269688 \tabularnewline
5 & 0.43032 & 3.4694 & 0.000466 \tabularnewline
6 & -0.190053 & -1.5323 & 0.065156 \tabularnewline
7 & -0.186141 & -1.5007 & 0.069135 \tabularnewline
8 & 0.419894 & 3.3853 & 0.000605 \tabularnewline
9 & -0.246991 & -1.9913 & 0.025327 \tabularnewline
10 & -0.062182 & -0.5013 & 0.308916 \tabularnewline
11 & -0.173568 & -1.3994 & 0.083231 \tabularnewline
12 & 0.492034 & 3.9669 & 9.2e-05 \tabularnewline
13 & 0.163263 & 1.3163 & 0.096354 \tabularnewline
14 & 0.05641 & 0.4548 & 0.325389 \tabularnewline
15 & 0.005575 & 0.0449 & 0.482144 \tabularnewline
16 & -0.219136 & -1.7667 & 0.040984 \tabularnewline
17 & -0.358977 & -2.8942 & 0.002585 \tabularnewline
18 & 0.029526 & 0.238 & 0.406298 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301663&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]-0.531599[/C][C]-4.2859[/C][C]3.1e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.212981[/C][C]-1.7171[/C][C]0.045361[/C][/ROW]
[ROW][C]3[/C][C]-0.254731[/C][C]-2.0537[/C][C]0.022015[/C][/ROW]
[ROW][C]4[/C][C]-0.076532[/C][C]-0.617[/C][C]0.269688[/C][/ROW]
[ROW][C]5[/C][C]0.43032[/C][C]3.4694[/C][C]0.000466[/C][/ROW]
[ROW][C]6[/C][C]-0.190053[/C][C]-1.5323[/C][C]0.065156[/C][/ROW]
[ROW][C]7[/C][C]-0.186141[/C][C]-1.5007[/C][C]0.069135[/C][/ROW]
[ROW][C]8[/C][C]0.419894[/C][C]3.3853[/C][C]0.000605[/C][/ROW]
[ROW][C]9[/C][C]-0.246991[/C][C]-1.9913[/C][C]0.025327[/C][/ROW]
[ROW][C]10[/C][C]-0.062182[/C][C]-0.5013[/C][C]0.308916[/C][/ROW]
[ROW][C]11[/C][C]-0.173568[/C][C]-1.3994[/C][C]0.083231[/C][/ROW]
[ROW][C]12[/C][C]0.492034[/C][C]3.9669[/C][C]9.2e-05[/C][/ROW]
[ROW][C]13[/C][C]0.163263[/C][C]1.3163[/C][C]0.096354[/C][/ROW]
[ROW][C]14[/C][C]0.05641[/C][C]0.4548[/C][C]0.325389[/C][/ROW]
[ROW][C]15[/C][C]0.005575[/C][C]0.0449[/C][C]0.482144[/C][/ROW]
[ROW][C]16[/C][C]-0.219136[/C][C]-1.7667[/C][C]0.040984[/C][/ROW]
[ROW][C]17[/C][C]-0.358977[/C][C]-2.8942[/C][C]0.002585[/C][/ROW]
[ROW][C]18[/C][C]0.029526[/C][C]0.238[/C][C]0.406298[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301663&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301663&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	-0.531599	-4.2859	3.1e-05
2	-0.212981	-1.7171	0.045361
3	-0.254731	-2.0537	0.022015
4	-0.076532	-0.617	0.269688
5	0.43032	3.4694	0.000466
6	-0.190053	-1.5323	0.065156
7	-0.186141	-1.5007	0.069135
8	0.419894	3.3853	0.000605
9	-0.246991	-1.9913	0.025327
10	-0.062182	-0.5013	0.308916
11	-0.173568	-1.3994	0.083231
12	0.492034	3.9669	9.2e-05
13	0.163263	1.3163	0.096354
14	0.05641	0.4548	0.325389
15	0.005575	0.0449	0.482144
16	-0.219136	-1.7667	0.040984
17	-0.358977	-2.8942	0.002585
18	0.029526	0.238	0.406298

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):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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Dataset

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Input Parameters & R Code