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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 16 Dec 2016 15:29:01 +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/t1481898584a8ws9v9uhlwsdz2.htm/, Retrieved Thu, 02 May 2024 23:13:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300311, Retrieved Thu, 02 May 2024 23:13:56 +0000

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-       [(Partial) Autocorrelation Function] [autocorrelation f...] [2016-12-16 14:29:01] [31f526a885cd288e1bc58dc4a6a7fb1f] [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=300311&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=300311&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300311&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	0.957537	10.313	0
2	0.925819	9.9714	0
3	0.895426	9.644	0
4	0.869485	9.3646	0
5	0.841951	9.0681	0
6	0.815416	8.7823	0
7	0.788189	8.4891	0
8	0.761217	8.1986	0
9	0.728167	7.8426	0
10	0.700131	7.5406	0
11	0.673041	7.2489	0
12	0.649395	6.9942	0
13	0.621913	6.6982	0
14	0.590901	6.3642	0
15	0.566526	6.1017	0
16	0.546099	5.8817	0
17	0.525408	5.6588	0
18	0.504125	5.4296	0
19	0.475449	5.1207	1e-06
20	0.449192	4.8379	2e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.957537 & 10.313 & 0 \tabularnewline
2 & 0.925819 & 9.9714 & 0 \tabularnewline
3 & 0.895426 & 9.644 & 0 \tabularnewline
4 & 0.869485 & 9.3646 & 0 \tabularnewline
5 & 0.841951 & 9.0681 & 0 \tabularnewline
6 & 0.815416 & 8.7823 & 0 \tabularnewline
7 & 0.788189 & 8.4891 & 0 \tabularnewline
8 & 0.761217 & 8.1986 & 0 \tabularnewline
9 & 0.728167 & 7.8426 & 0 \tabularnewline
10 & 0.700131 & 7.5406 & 0 \tabularnewline
11 & 0.673041 & 7.2489 & 0 \tabularnewline
12 & 0.649395 & 6.9942 & 0 \tabularnewline
13 & 0.621913 & 6.6982 & 0 \tabularnewline
14 & 0.590901 & 6.3642 & 0 \tabularnewline
15 & 0.566526 & 6.1017 & 0 \tabularnewline
16 & 0.546099 & 5.8817 & 0 \tabularnewline
17 & 0.525408 & 5.6588 & 0 \tabularnewline
18 & 0.504125 & 5.4296 & 0 \tabularnewline
19 & 0.475449 & 5.1207 & 1e-06 \tabularnewline
20 & 0.449192 & 4.8379 & 2e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300311&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]0.957537[/C][C]10.313[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.925819[/C][C]9.9714[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.895426[/C][C]9.644[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.869485[/C][C]9.3646[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.841951[/C][C]9.0681[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.815416[/C][C]8.7823[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.788189[/C][C]8.4891[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.761217[/C][C]8.1986[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.728167[/C][C]7.8426[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.700131[/C][C]7.5406[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.673041[/C][C]7.2489[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.649395[/C][C]6.9942[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.621913[/C][C]6.6982[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.590901[/C][C]6.3642[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.566526[/C][C]6.1017[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.546099[/C][C]5.8817[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.525408[/C][C]5.6588[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.504125[/C][C]5.4296[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.475449[/C][C]5.1207[/C][C]1e-06[/C][/ROW]
[ROW][C]20[/C][C]0.449192[/C][C]4.8379[/C][C]2e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300311&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300311&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	0.957537	10.313	0
2	0.925819	9.9714	0
3	0.895426	9.644	0
4	0.869485	9.3646	0
5	0.841951	9.0681	0
6	0.815416	8.7823	0
7	0.788189	8.4891	0
8	0.761217	8.1986	0
9	0.728167	7.8426	0
10	0.700131	7.5406	0
11	0.673041	7.2489	0
12	0.649395	6.9942	0
13	0.621913	6.6982	0
14	0.590901	6.3642	0
15	0.566526	6.1017	0
16	0.546099	5.8817	0
17	0.525408	5.6588	0
18	0.504125	5.4296	0
19	0.475449	5.1207	1e-06
20	0.449192	4.8379	2e-06

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.957537	10.313	0
2	0.107584	1.1587	0.124477
3	0.015562	0.1676	0.43359
4	0.044201	0.4761	0.317465
5	-0.018467	-0.1989	0.421346
6	-0.002773	-0.0299	0.488114
7	-0.017723	-0.1909	0.424476
8	-0.01415	-0.1524	0.439568
9	-0.088023	-0.948	0.172541
10	0.023281	0.2507	0.401227
11	0.003929	0.0423	0.483159
12	0.02528	0.2723	0.392947
13	-0.043584	-0.4694	0.319829
14	-0.06787	-0.731	0.233133
15	0.054407	0.586	0.279514
16	0.045163	0.4864	0.313793
17	0.001763	0.019	0.49244
18	-0.016907	-0.1821	0.427913
19	-0.10431	-1.1235	0.131782
20	-0.013407	-0.1444	0.442719

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.957537 & 10.313 & 0 \tabularnewline
2 & 0.107584 & 1.1587 & 0.124477 \tabularnewline
3 & 0.015562 & 0.1676 & 0.43359 \tabularnewline
4 & 0.044201 & 0.4761 & 0.317465 \tabularnewline
5 & -0.018467 & -0.1989 & 0.421346 \tabularnewline
6 & -0.002773 & -0.0299 & 0.488114 \tabularnewline
7 & -0.017723 & -0.1909 & 0.424476 \tabularnewline
8 & -0.01415 & -0.1524 & 0.439568 \tabularnewline
9 & -0.088023 & -0.948 & 0.172541 \tabularnewline
10 & 0.023281 & 0.2507 & 0.401227 \tabularnewline
11 & 0.003929 & 0.0423 & 0.483159 \tabularnewline
12 & 0.02528 & 0.2723 & 0.392947 \tabularnewline
13 & -0.043584 & -0.4694 & 0.319829 \tabularnewline
14 & -0.06787 & -0.731 & 0.233133 \tabularnewline
15 & 0.054407 & 0.586 & 0.279514 \tabularnewline
16 & 0.045163 & 0.4864 & 0.313793 \tabularnewline
17 & 0.001763 & 0.019 & 0.49244 \tabularnewline
18 & -0.016907 & -0.1821 & 0.427913 \tabularnewline
19 & -0.10431 & -1.1235 & 0.131782 \tabularnewline
20 & -0.013407 & -0.1444 & 0.442719 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300311&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]0.957537[/C][C]10.313[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.107584[/C][C]1.1587[/C][C]0.124477[/C][/ROW]
[ROW][C]3[/C][C]0.015562[/C][C]0.1676[/C][C]0.43359[/C][/ROW]
[ROW][C]4[/C][C]0.044201[/C][C]0.4761[/C][C]0.317465[/C][/ROW]
[ROW][C]5[/C][C]-0.018467[/C][C]-0.1989[/C][C]0.421346[/C][/ROW]
[ROW][C]6[/C][C]-0.002773[/C][C]-0.0299[/C][C]0.488114[/C][/ROW]
[ROW][C]7[/C][C]-0.017723[/C][C]-0.1909[/C][C]0.424476[/C][/ROW]
[ROW][C]8[/C][C]-0.01415[/C][C]-0.1524[/C][C]0.439568[/C][/ROW]
[ROW][C]9[/C][C]-0.088023[/C][C]-0.948[/C][C]0.172541[/C][/ROW]
[ROW][C]10[/C][C]0.023281[/C][C]0.2507[/C][C]0.401227[/C][/ROW]
[ROW][C]11[/C][C]0.003929[/C][C]0.0423[/C][C]0.483159[/C][/ROW]
[ROW][C]12[/C][C]0.02528[/C][C]0.2723[/C][C]0.392947[/C][/ROW]
[ROW][C]13[/C][C]-0.043584[/C][C]-0.4694[/C][C]0.319829[/C][/ROW]
[ROW][C]14[/C][C]-0.06787[/C][C]-0.731[/C][C]0.233133[/C][/ROW]
[ROW][C]15[/C][C]0.054407[/C][C]0.586[/C][C]0.279514[/C][/ROW]
[ROW][C]16[/C][C]0.045163[/C][C]0.4864[/C][C]0.313793[/C][/ROW]
[ROW][C]17[/C][C]0.001763[/C][C]0.019[/C][C]0.49244[/C][/ROW]
[ROW][C]18[/C][C]-0.016907[/C][C]-0.1821[/C][C]0.427913[/C][/ROW]
[ROW][C]19[/C][C]-0.10431[/C][C]-1.1235[/C][C]0.131782[/C][/ROW]
[ROW][C]20[/C][C]-0.013407[/C][C]-0.1444[/C][C]0.442719[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300311&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300311&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	0.957537	10.313	0
2	0.107584	1.1587	0.124477
3	0.015562	0.1676	0.43359
4	0.044201	0.4761	0.317465
5	-0.018467	-0.1989	0.421346
6	-0.002773	-0.0299	0.488114
7	-0.017723	-0.1909	0.424476
8	-0.01415	-0.1524	0.439568
9	-0.088023	-0.948	0.172541
10	0.023281	0.2507	0.401227
11	0.003929	0.0423	0.483159
12	0.02528	0.2723	0.392947
13	-0.043584	-0.4694	0.319829
14	-0.06787	-0.731	0.233133
15	0.054407	0.586	0.279514
16	0.045163	0.4864	0.313793
17	0.001763	0.019	0.49244
18	-0.016907	-0.1821	0.427913
19	-0.10431	-1.1235	0.131782
20	-0.013407	-0.1444	0.442719

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

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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')

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code