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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 14:29:51 +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/17/t1481981425mch8nuybi5jkxb9.htm/, Retrieved Thu, 02 May 2024 02:36:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300780, Retrieved Thu, 02 May 2024 02:36:59 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-17 13:29:51] [bde5266f17215258f6d7c4cd7e531432] [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=300780&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=300780&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300780&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	0.950072	7.541	0
2	0.901034	7.1517	0
3	0.867187	6.8831	0
4	0.82348	6.5362	0
5	0.764259	6.0661	0
6	0.703928	5.5873	0
7	0.659584	5.2353	1e-06
8	0.615768	4.8875	4e-06
9	0.55898	4.4368	1.9e-05
10	0.502014	3.9846	8.9e-05
11	0.459767	3.6493	0.000268
12	0.415633	3.299	0.000799
13	0.359854	2.8563	0.0029
14	0.307266	2.4388	0.008782
15	0.274145	2.176	0.016658
16	0.237975	1.8889	0.031758
17	0.191573	1.5206	0.066687

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.950072 & 7.541 & 0 \tabularnewline
2 & 0.901034 & 7.1517 & 0 \tabularnewline
3 & 0.867187 & 6.8831 & 0 \tabularnewline
4 & 0.82348 & 6.5362 & 0 \tabularnewline
5 & 0.764259 & 6.0661 & 0 \tabularnewline
6 & 0.703928 & 5.5873 & 0 \tabularnewline
7 & 0.659584 & 5.2353 & 1e-06 \tabularnewline
8 & 0.615768 & 4.8875 & 4e-06 \tabularnewline
9 & 0.55898 & 4.4368 & 1.9e-05 \tabularnewline
10 & 0.502014 & 3.9846 & 8.9e-05 \tabularnewline
11 & 0.459767 & 3.6493 & 0.000268 \tabularnewline
12 & 0.415633 & 3.299 & 0.000799 \tabularnewline
13 & 0.359854 & 2.8563 & 0.0029 \tabularnewline
14 & 0.307266 & 2.4388 & 0.008782 \tabularnewline
15 & 0.274145 & 2.176 & 0.016658 \tabularnewline
16 & 0.237975 & 1.8889 & 0.031758 \tabularnewline
17 & 0.191573 & 1.5206 & 0.066687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300780&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]0.950072[/C][C]7.541[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.901034[/C][C]7.1517[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.867187[/C][C]6.8831[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.82348[/C][C]6.5362[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.764259[/C][C]6.0661[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.703928[/C][C]5.5873[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.659584[/C][C]5.2353[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.615768[/C][C]4.8875[/C][C]4e-06[/C][/ROW]
[ROW][C]9[/C][C]0.55898[/C][C]4.4368[/C][C]1.9e-05[/C][/ROW]
[ROW][C]10[/C][C]0.502014[/C][C]3.9846[/C][C]8.9e-05[/C][/ROW]
[ROW][C]11[/C][C]0.459767[/C][C]3.6493[/C][C]0.000268[/C][/ROW]
[ROW][C]12[/C][C]0.415633[/C][C]3.299[/C][C]0.000799[/C][/ROW]
[ROW][C]13[/C][C]0.359854[/C][C]2.8563[/C][C]0.0029[/C][/ROW]
[ROW][C]14[/C][C]0.307266[/C][C]2.4388[/C][C]0.008782[/C][/ROW]
[ROW][C]15[/C][C]0.274145[/C][C]2.176[/C][C]0.016658[/C][/ROW]
[ROW][C]16[/C][C]0.237975[/C][C]1.8889[/C][C]0.031758[/C][/ROW]
[ROW][C]17[/C][C]0.191573[/C][C]1.5206[/C][C]0.066687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300780&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300780&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	0.950072	7.541	0
2	0.901034	7.1517	0
3	0.867187	6.8831	0
4	0.82348	6.5362	0
5	0.764259	6.0661	0
6	0.703928	5.5873	0
7	0.659584	5.2353	1e-06
8	0.615768	4.8875	4e-06
9	0.55898	4.4368	1.9e-05
10	0.502014	3.9846	8.9e-05
11	0.459767	3.6493	0.000268
12	0.415633	3.299	0.000799
13	0.359854	2.8563	0.0029
14	0.307266	2.4388	0.008782
15	0.274145	2.176	0.016658
16	0.237975	1.8889	0.031758
17	0.191573	1.5206	0.066687

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.950072	7.541	0
2	-0.016459	-0.1306	0.448238
3	0.130353	1.0346	0.152394
4	-0.119358	-0.9474	0.173533
5	-0.164688	-1.3072	0.097953
6	-0.077928	-0.6185	0.269228
7	0.102808	0.816	0.208784
8	0.004351	0.0345	0.486281
9	-0.101537	-0.8059	0.21166
10	-0.060488	-0.4801	0.316405
11	0.054375	0.4316	0.333758
12	-0.04084	-0.3242	0.373445
13	-0.083514	-0.6629	0.254917
14	-0.022815	-0.1811	0.428441
15	0.108245	0.8592	0.196752
16	-0.04458	-0.3538	0.362319
17	-0.056414	-0.4478	0.327927

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.950072 & 7.541 & 0 \tabularnewline
2 & -0.016459 & -0.1306 & 0.448238 \tabularnewline
3 & 0.130353 & 1.0346 & 0.152394 \tabularnewline
4 & -0.119358 & -0.9474 & 0.173533 \tabularnewline
5 & -0.164688 & -1.3072 & 0.097953 \tabularnewline
6 & -0.077928 & -0.6185 & 0.269228 \tabularnewline
7 & 0.102808 & 0.816 & 0.208784 \tabularnewline
8 & 0.004351 & 0.0345 & 0.486281 \tabularnewline
9 & -0.101537 & -0.8059 & 0.21166 \tabularnewline
10 & -0.060488 & -0.4801 & 0.316405 \tabularnewline
11 & 0.054375 & 0.4316 & 0.333758 \tabularnewline
12 & -0.04084 & -0.3242 & 0.373445 \tabularnewline
13 & -0.083514 & -0.6629 & 0.254917 \tabularnewline
14 & -0.022815 & -0.1811 & 0.428441 \tabularnewline
15 & 0.108245 & 0.8592 & 0.196752 \tabularnewline
16 & -0.04458 & -0.3538 & 0.362319 \tabularnewline
17 & -0.056414 & -0.4478 & 0.327927 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300780&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]0.950072[/C][C]7.541[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.016459[/C][C]-0.1306[/C][C]0.448238[/C][/ROW]
[ROW][C]3[/C][C]0.130353[/C][C]1.0346[/C][C]0.152394[/C][/ROW]
[ROW][C]4[/C][C]-0.119358[/C][C]-0.9474[/C][C]0.173533[/C][/ROW]
[ROW][C]5[/C][C]-0.164688[/C][C]-1.3072[/C][C]0.097953[/C][/ROW]
[ROW][C]6[/C][C]-0.077928[/C][C]-0.6185[/C][C]0.269228[/C][/ROW]
[ROW][C]7[/C][C]0.102808[/C][C]0.816[/C][C]0.208784[/C][/ROW]
[ROW][C]8[/C][C]0.004351[/C][C]0.0345[/C][C]0.486281[/C][/ROW]
[ROW][C]9[/C][C]-0.101537[/C][C]-0.8059[/C][C]0.21166[/C][/ROW]
[ROW][C]10[/C][C]-0.060488[/C][C]-0.4801[/C][C]0.316405[/C][/ROW]
[ROW][C]11[/C][C]0.054375[/C][C]0.4316[/C][C]0.333758[/C][/ROW]
[ROW][C]12[/C][C]-0.04084[/C][C]-0.3242[/C][C]0.373445[/C][/ROW]
[ROW][C]13[/C][C]-0.083514[/C][C]-0.6629[/C][C]0.254917[/C][/ROW]
[ROW][C]14[/C][C]-0.022815[/C][C]-0.1811[/C][C]0.428441[/C][/ROW]
[ROW][C]15[/C][C]0.108245[/C][C]0.8592[/C][C]0.196752[/C][/ROW]
[ROW][C]16[/C][C]-0.04458[/C][C]-0.3538[/C][C]0.362319[/C][/ROW]
[ROW][C]17[/C][C]-0.056414[/C][C]-0.4478[/C][C]0.327927[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300780&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300780&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	0.950072	7.541	0
2	-0.016459	-0.1306	0.448238
3	0.130353	1.0346	0.152394
4	-0.119358	-0.9474	0.173533
5	-0.164688	-1.3072	0.097953
6	-0.077928	-0.6185	0.269228
7	0.102808	0.816	0.208784
8	0.004351	0.0345	0.486281
9	-0.101537	-0.8059	0.21166
10	-0.060488	-0.4801	0.316405
11	0.054375	0.4316	0.333758
12	-0.04084	-0.3242	0.373445
13	-0.083514	-0.6629	0.254917
14	-0.022815	-0.1811	0.428441
15	0.108245	0.8592	0.196752
16	-0.04458	-0.3538	0.362319
17	-0.056414	-0.4478	0.327927

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):

par1 = 1 ; par2 = 2 ; par3 = 1 ; par4 = 1 ;

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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