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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Dec 2016 16:51:02 +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/22/t1482421885px6njgjz2tg9zi6.htm/, Retrieved Sun, 28 Apr 2024 19:42:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302548, Retrieved Sun, 28 Apr 2024 19:42:38 +0000

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-       [(Partial) Autocorrelation Function] [Autocorrelation (F1)] [2016-12-22 15:51:02] [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=302548&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=302548&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302548&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	-0.008681	-0.0684	0.472861
2	-0.634175	-4.9935	3e-06
3	-0.085684	-0.6747	0.251194
4	0.671096	5.2842	1e-06
5	0.017711	0.1395	0.444771
6	-0.586286	-4.6164	1e-05
7	-0.01815	-0.1429	0.443412
8	0.531153	4.1823	4.6e-05
9	-0.077943	-0.6137	0.270821
10	-0.572198	-4.5055	1.5e-05
11	0.017863	0.1407	0.444299
12	0.592293	4.6637	9e-06
13	-0.088507	-0.6969	0.244235
14	-0.546382	-4.3022	3.1e-05
15	0.056371	0.4439	0.329342
16	0.553809	4.3607	2.5e-05
17	-0.03714	-0.2924	0.385464

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.008681 & -0.0684 & 0.472861 \tabularnewline
2 & -0.634175 & -4.9935 & 3e-06 \tabularnewline
3 & -0.085684 & -0.6747 & 0.251194 \tabularnewline
4 & 0.671096 & 5.2842 & 1e-06 \tabularnewline
5 & 0.017711 & 0.1395 & 0.444771 \tabularnewline
6 & -0.586286 & -4.6164 & 1e-05 \tabularnewline
7 & -0.01815 & -0.1429 & 0.443412 \tabularnewline
8 & 0.531153 & 4.1823 & 4.6e-05 \tabularnewline
9 & -0.077943 & -0.6137 & 0.270821 \tabularnewline
10 & -0.572198 & -4.5055 & 1.5e-05 \tabularnewline
11 & 0.017863 & 0.1407 & 0.444299 \tabularnewline
12 & 0.592293 & 4.6637 & 9e-06 \tabularnewline
13 & -0.088507 & -0.6969 & 0.244235 \tabularnewline
14 & -0.546382 & -4.3022 & 3.1e-05 \tabularnewline
15 & 0.056371 & 0.4439 & 0.329342 \tabularnewline
16 & 0.553809 & 4.3607 & 2.5e-05 \tabularnewline
17 & -0.03714 & -0.2924 & 0.385464 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302548&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]-0.008681[/C][C]-0.0684[/C][C]0.472861[/C][/ROW]
[ROW][C]2[/C][C]-0.634175[/C][C]-4.9935[/C][C]3e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.085684[/C][C]-0.6747[/C][C]0.251194[/C][/ROW]
[ROW][C]4[/C][C]0.671096[/C][C]5.2842[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.017711[/C][C]0.1395[/C][C]0.444771[/C][/ROW]
[ROW][C]6[/C][C]-0.586286[/C][C]-4.6164[/C][C]1e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.01815[/C][C]-0.1429[/C][C]0.443412[/C][/ROW]
[ROW][C]8[/C][C]0.531153[/C][C]4.1823[/C][C]4.6e-05[/C][/ROW]
[ROW][C]9[/C][C]-0.077943[/C][C]-0.6137[/C][C]0.270821[/C][/ROW]
[ROW][C]10[/C][C]-0.572198[/C][C]-4.5055[/C][C]1.5e-05[/C][/ROW]
[ROW][C]11[/C][C]0.017863[/C][C]0.1407[/C][C]0.444299[/C][/ROW]
[ROW][C]12[/C][C]0.592293[/C][C]4.6637[/C][C]9e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.088507[/C][C]-0.6969[/C][C]0.244235[/C][/ROW]
[ROW][C]14[/C][C]-0.546382[/C][C]-4.3022[/C][C]3.1e-05[/C][/ROW]
[ROW][C]15[/C][C]0.056371[/C][C]0.4439[/C][C]0.329342[/C][/ROW]
[ROW][C]16[/C][C]0.553809[/C][C]4.3607[/C][C]2.5e-05[/C][/ROW]
[ROW][C]17[/C][C]-0.03714[/C][C]-0.2924[/C][C]0.385464[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302548&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302548&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	-0.008681	-0.0684	0.472861
2	-0.634175	-4.9935	3e-06
3	-0.085684	-0.6747	0.251194
4	0.671096	5.2842	1e-06
5	0.017711	0.1395	0.444771
6	-0.586286	-4.6164	1e-05
7	-0.01815	-0.1429	0.443412
8	0.531153	4.1823	4.6e-05
9	-0.077943	-0.6137	0.270821
10	-0.572198	-4.5055	1.5e-05
11	0.017863	0.1407	0.444299
12	0.592293	4.6637	9e-06
13	-0.088507	-0.6969	0.244235
14	-0.546382	-4.3022	3.1e-05
15	0.056371	0.4439	0.329342
16	0.553809	4.3607	2.5e-05
17	-0.03714	-0.2924	0.385464

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.008681	-0.0684	0.472861
2	-0.634298	-4.9945	3e-06
3	-0.167646	-1.32	0.095837
4	0.439976	3.4644	0.000485
5	-0.107441	-0.846	0.200405
6	-0.166205	-1.3087	0.097734
7	0.131288	1.0338	0.152631
8	-0.01243	-0.0979	0.461174
9	-0.250096	-1.9693	0.026698
10	-0.172962	-1.3619	0.089078
11	-0.077702	-0.6118	0.271445
12	0.139402	1.0976	0.138301
13	-0.119135	-0.9381	0.175925
14	-0.041375	-0.3258	0.372842
15	0.074352	0.5855	0.280185
16	-0.029585	-0.233	0.408282
17	0.031356	0.2469	0.402901

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.008681 & -0.0684 & 0.472861 \tabularnewline
2 & -0.634298 & -4.9945 & 3e-06 \tabularnewline
3 & -0.167646 & -1.32 & 0.095837 \tabularnewline
4 & 0.439976 & 3.4644 & 0.000485 \tabularnewline
5 & -0.107441 & -0.846 & 0.200405 \tabularnewline
6 & -0.166205 & -1.3087 & 0.097734 \tabularnewline
7 & 0.131288 & 1.0338 & 0.152631 \tabularnewline
8 & -0.01243 & -0.0979 & 0.461174 \tabularnewline
9 & -0.250096 & -1.9693 & 0.026698 \tabularnewline
10 & -0.172962 & -1.3619 & 0.089078 \tabularnewline
11 & -0.077702 & -0.6118 & 0.271445 \tabularnewline
12 & 0.139402 & 1.0976 & 0.138301 \tabularnewline
13 & -0.119135 & -0.9381 & 0.175925 \tabularnewline
14 & -0.041375 & -0.3258 & 0.372842 \tabularnewline
15 & 0.074352 & 0.5855 & 0.280185 \tabularnewline
16 & -0.029585 & -0.233 & 0.408282 \tabularnewline
17 & 0.031356 & 0.2469 & 0.402901 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302548&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]-0.008681[/C][C]-0.0684[/C][C]0.472861[/C][/ROW]
[ROW][C]2[/C][C]-0.634298[/C][C]-4.9945[/C][C]3e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.167646[/C][C]-1.32[/C][C]0.095837[/C][/ROW]
[ROW][C]4[/C][C]0.439976[/C][C]3.4644[/C][C]0.000485[/C][/ROW]
[ROW][C]5[/C][C]-0.107441[/C][C]-0.846[/C][C]0.200405[/C][/ROW]
[ROW][C]6[/C][C]-0.166205[/C][C]-1.3087[/C][C]0.097734[/C][/ROW]
[ROW][C]7[/C][C]0.131288[/C][C]1.0338[/C][C]0.152631[/C][/ROW]
[ROW][C]8[/C][C]-0.01243[/C][C]-0.0979[/C][C]0.461174[/C][/ROW]
[ROW][C]9[/C][C]-0.250096[/C][C]-1.9693[/C][C]0.026698[/C][/ROW]
[ROW][C]10[/C][C]-0.172962[/C][C]-1.3619[/C][C]0.089078[/C][/ROW]
[ROW][C]11[/C][C]-0.077702[/C][C]-0.6118[/C][C]0.271445[/C][/ROW]
[ROW][C]12[/C][C]0.139402[/C][C]1.0976[/C][C]0.138301[/C][/ROW]
[ROW][C]13[/C][C]-0.119135[/C][C]-0.9381[/C][C]0.175925[/C][/ROW]
[ROW][C]14[/C][C]-0.041375[/C][C]-0.3258[/C][C]0.372842[/C][/ROW]
[ROW][C]15[/C][C]0.074352[/C][C]0.5855[/C][C]0.280185[/C][/ROW]
[ROW][C]16[/C][C]-0.029585[/C][C]-0.233[/C][C]0.408282[/C][/ROW]
[ROW][C]17[/C][C]0.031356[/C][C]0.2469[/C][C]0.402901[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302548&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302548&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	-0.008681	-0.0684	0.472861
2	-0.634298	-4.9945	3e-06
3	-0.167646	-1.32	0.095837
4	0.439976	3.4644	0.000485
5	-0.107441	-0.846	0.200405
6	-0.166205	-1.3087	0.097734
7	0.131288	1.0338	0.152631
8	-0.01243	-0.0979	0.461174
9	-0.250096	-1.9693	0.026698
10	-0.172962	-1.3619	0.089078
11	-0.077702	-0.6118	0.271445
12	0.139402	1.0976	0.138301
13	-0.119135	-0.9381	0.175925
14	-0.041375	-0.3258	0.372842
15	0.074352	0.5855	0.280185
16	-0.029585	-0.233	0.408282
17	0.031356	0.2469	0.402901

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 = 12 ; par2 = Double ; par3 = multiplicative ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 4 ; 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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Input Parameters & R Code